The 23th DAE-BRNS High Energy Physics Symposium was held at IIT Madras from Dec 10 – Dec 14. It was an interesting event. I met lots of very smart people. My abstract based on my paper [1] had been selected for a talk in the “Formal Theory” parallel session on Dec 11. Interestingly the talk preceding mine was delivered by Suresh Govindarajan (INSPIRE) who is a faculty at IITM and a hardcore string theorist. Also in attendance was Prof G. Rajasekaran, who is an emeritus faculty at the Institute of Mathematical Sciences, Chennai and himself a distinguished high energy physicist. Naturally, following Govindarajan’s highly mathematical talk on the existence of BKM superalgebras – of which, I understood perhaps the first three slides – I felt a little trepidatious, especially since the number of mathematical formulae in his talk was several orders of magnitude greater than in mine!
Naveen, a PhD student also from NITK, was kind enough to record my talk on his phone 1 . The result is viewable on YouTube.
Table of Contents
Connecting String Theory and LQG
Couple of days later I had a nice conversation with Prof Govindarajan 2 where he conveyed to me that the general feeling among many in the strings community was that loops and strings would ultimately have to come together. He mentioned the following questions as his main concerns:
Matter Degrees of Freedom
Where is the matter in LQG? In String Theory matter arises “naturally” from compactification of $n>4$ dimensions. The compactified dimensions behave like scalar and gauge fields in the non-compactified geometry. I mentioned to him that LQG does have candidates for matter in the form of topological degrees of freedom known as “preons” [2, 3]. Of course, much work is still to be done to understand how the entire spectrum of the standard model can arise from these topological defects. I made some early efforts trying to connect quantum computation gates and elementary particles in LQG in [4] and to show how non-abelian gauge fields – such as those in the Standard Model – can arise naturally from defects in spin-networks in [5].
Degenerate geometry in LQG
Suresh’s next concern was about the existence of geometries in LQG where the tetrad $e_\mu^I$ (which determines the metric geometry via the relation $ g_{\mu\nu} = e_\mu^I e_\nu^J \eta_{IJ}$) is allowed to be degenerate – $\ie~\text{det}(e_\mu^I) = 0$. In such cases the resulting metric exists, however its inverse $g^{\mu\nu}$ does not (because matrices with zero determinant do not have well-defined inverses). His concern might have been motivated by Kaul and Sengupta’s recent work on degenerate spacetimes in the connection formulation of gravity. I explained that there is nothing non-physical about having degenerate spacetimes. One can do all the usual physics with scalars, vectors and spinors in such geometries. However, one also has new physics in such regimes which cannot be captured by the metric formulation. In particular with degenerate tetrads one can have geometries with non-zero torsion even without any spinning matter present [6, 7].
Background dependence of string theory
String theory as it is usually defined, is a manifestly background dependent theory. Now, presumably a theory of quantum gravity should be background independent. One should be able to extract physical information such as correlation functions, scattering amplitudes and such without having to worry about the background geometry the given processes take place in. Moreover, since in the strong quantum gravity regime, even the gravitational field will be involved in scattering processes, our quantum gravity theory should be able to handle cases which involve transitions between geometries which cannot be treated as perturbations of a given background. Suresh recognizes this shortcoming of String Theory and mentioned it as such to me.
It is in this respect that LQG trumps String Theory. Background independence is manifest and non-negotiable in LQG. We need to be able to incorporate background independence in a meaningful way in the String framework whether it is via String Field Theory or some other approach. LQG can provide pointers on how this might be accomplished.
Extra dimensions or Lack Thereof
Extra dimensions are a given in String Theory. The requirement of conformal invariance of the string worldsheet enforces that the spacetime dimensions much be $D = 26$ for the bosonic string and $D = 10$ for the fermionic (or supersymmetric) string. In order to obtain our familiar four dimensional spacetime, these extra dimensions have to be gotten “rid off” in some way. The most method is compactification [8, 9] , wherein six (in the case of $D = 10$ superstring theory) dimensions are “rolled up” and only four “large” space+time dimensions remain. The compactified dimensions still manifest physically as effective scalar or gauge fields propagating in the background of the four large dimensions. These extra dimensions are also the source of much criticism of String Theory. It turns out that there is a huge ($\sim 10^{500}$ ways in which the extra dimensions can be compactified and which one of these, if any, compactifications can give rise to our Universe with the Standard Model and all its interactions is a notoriously intractable problem.
Extra dimensions are not present, and in fact are not needed, in Loop Quantum Gravity. This is considered a net plus for LQG. However the optimism might be short-lived. All those extra dimensions in String Theory, which seem like so much clutter, can actually be used to produce experimentally verifiable predictions about QCD scattering processes! Sakai and Sugimoto [10] first initiated this approach by constructing a holographic dual of large-N QCD. Following this work many authors, including Aalok Misra and his brilliant student Vikas Yadav, whom I had the pleasure of meeting at this conference, have managed to use the Sakai-Sugimoto framework to predict decay widths of glueballs [11] (bound states of gluons) which appear to match very nicely with lattice QCD calculations. LQG is yet to deliver on any such quantitive particle physics related predictions, though it does have several predictions on the astrophysical front [12, 13, 14], which if confirmed would be a stunning success.
Noncommutative Geometry and Preons
Another very interesting talk was delivered by Prof. Rajiv Gavai from TIFR on work [15] done with Pulkit Ghoderao and P. Ramadevi, on the possible detection of non-commutative effects by measuring the Lamb shift of the hydrogen atom or in accelerator experiments. Two mathematical quantities $A, B$ are said to be “non-commutative” (or “non-commuting” or “do not commute”), when they dont’ satisfy the following relation:
$$ [A,B] = 0 $$
where $ [A,B] = AB – BA $ is referred to as the “commutator”. Experts may skip the following subsection.
Non-commutativity for Non-Experts
A trivial example is any pair of complex numbers $ z_1, z_2 $. Using the rules of complex multiplication one can easily see that $ [z_1, z_2] = 0$ for all $z_1, z_2 \in \mathbb{C}$. This is also obviously also true for all real numbers which are a subset of the complex numbers. However, this is not true for quaternions and octonions, which along with the real and complex numbers, constitute the only four normed division algebras (see for e.g. [16]) possible mathematically. It is also not true, in general, for matrices. One can see this by taking any two $ 2 \times 2$ matrices with random elements and calculating the commutator.
Another example is given by operators in quantum theory. Position $x$ and momentum $p$ are represented by operators $ \hat x$ and $\hat p$, respectively. While the classical variables commute: $ { x, p } = 0$ 3, their operator versions don’t: $[ \hat x, \hat p] = i\hbar \ne 0 $. In this sense, the phase space of a quantum mechanical system is an example of a non-commutative geometry.
The non-commutativity Ghoderao et al.’s work is concerned with is between different spatial co-ordinates:
$$ [x_i, x_j] = i \theta_{ij} $$
where $\theta_{ij}$ measures the amount of non-commutativity. Now this is very interesting. For instance, if you consider a particle in a plane, the operation $ x y$ correspond to walking one unit in the $y$ direction, followed by one unit in the $x$ direction. $ y x$ is defined in the same way. Now, normally we expect that both operations should get us to the same point, $\ie$ $ xy = yx$. However, if we were living on a non-commutative plane then this would no longer be true. In a sense, non-commutativity measures the presence of “non-abelian defects” in geometry. Both String Theory and LQG generically predict non-commutative effects arising from quantum geometry. Thus the existence of such an effect would provide very strong support for both theories and also allow us to differentiate between various models.
Composite Particles and Non-commutativity
Ghoderao et al’s result can be summarized in one sentence
in a non-commutative geometry, quarks can form composite particles such as protons and neutrons, if and only if, they (quarks) have substructure.
Now this is a stunning result which also applies to leptons such as electrons, muons and neutrinos. The reason I found this work particularly exciting is because it provides very strong circumstantial evidence for the preon model of elementary particles developed by my good friend and collaborator Sundance Bilson-Thompson [2] 4. This model predicts precisely such a substructure for the leptons and quarks. It would be very interesting to try to understand the relationship between the Bilson-Thompson model and non-commutative geometry.
Fermi Arcs and AdS/CFT
Finally, there was very interesting work presented by Wadbor Wahlang who is a graduate student working under Sayan Chakrabarti at IIT Guwahati. This work was about understanding the origin of Fermi arcs in Weyl semi-metals 5 from a holographic perspective.
As is well understood by now [17, 18, 19] the AdS/CFT correspondence can be used to explore the phase diagram of condensed matter systems. Essentially what Wahlang and Chakrabarti do is to couple free fermion fields to the usual scalar field living in the bulk AdS spacetime and use that to calculate the spectral function of the boundary field theory. In the event that the fermionic fields they use are Weyl fermions, the spectral function exhibits Fermi arcs. I am looking forward to seeing this work on the arXiv.
- It might seem a bit narcissistic to some to record one’s own conference talks. However, for scientists, talks are the best way to communicate our ideas to our own community and to the general public. They also serve to help us improve our presentation skills. There’s really no downside to recording your own talks, except perhaps the realization that you’re not quite as slim as you’d like to imagine. ↩
- This version is only my recollection of my conversation with Prof Govindarajan and has not been endorsed or approved by him. Any errors or omissions are solely mine. ↩
- We are using curly braces ${,}$ because in classical mechanics the commutator is given by the Poisson bracket which is written in this way, whereas square braces $[,]$ are typically used to represent commutators of quantum mechanical quantities. ↩
- Just to clarify, I met Sundance long after he had discovered the “Bilson-Thompson” mode and I had no role in its discovery. I did try to explain how it could be embedded into LQG in [3] ↩
- See, for $\eg$ [20] for an introduction to the concept of Weyl fermions, Weyl semi-metals and Fermi arcs. ↩
[Bibtex]
@article{Vaid2017Connecting,
abstract = {We argue that String Theory and Loop Quantum Gravity can be thought of as describing different regimes of a single unified theory of quantum gravity. LQG can be thought of as providing the pre-geometric exoskeleton out of which macroscopic geometry emerges and String Theory then becomes the {\textbackslash}emph\{effective\} theory which describes the dynamics of that exoskeleton. The core of the argument rests on the claim that the Nambu-Goto action of String Theory can be viewed as the expectation value of the LQG area operator evaluated on the string worldsheet.},
archiveprefix = {arXiv},
author = {Vaid, Deepak},
date-modified = {2024-08-25 13:14:15 +0530},
eprint = {1711.05693},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Vaid_Connecting Loop Quantum Gravity and String Theory via Quantum Geometry_2017.pdf},
keywords = {area operator,conformal invariance,emergent gravity,loop quantum gravity,nambu-goto action,quantum gravity,string theory,unification,vaid_deepak},
month = nov,
title = {Connecting {{Loop Quantum Gravity}} and {{String Theory}} via {{Quantum Geometry}}},
urldate = {2017-11-16},
year = {2017}}[Bibtex]
@article{Vaid2010Embedding,
abstract = {We argue that the Quadratic Spinor Lagrangian approach allows us to approach the problem of forming a geometrical condensate of spinorial tetrads in a natural manner. This, along with considerations involving the discrete symmetries of lattice triangulations, lead us to discover that the quasiparticles of such a condensate are tetrahedra with braids attached to its faces and that these braid attachments correspond to the preons in Bilson-Thompson's model of elementary particles. These "spatoms" can then be put together in a tiling to form more complex structures which encode both geometry and matter in a natural manner. We conclude with some speculations on the relation between this picture and the computational universe hypothesis.},
archiveprefix = {arXiv},
author = {Vaid, Deepak},
eprint = {1002.1462v1},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Vaid_Embedding the Bilson-Thompson Model in a LQG-like framework_2010.pdf},
keywords = {bilson-thompson,bilson-thompson model,braids,computational_universe,condensate,defects,discrete-symmetries,elementary_particles,many body,preons,quadratic-spinor-lagrangian,quantum gravity,quantum_gravity,standard_model,topology,vaid_deepak},
month = feb,
pages = {1--10},
title = {Embedding the {{Bilson-Thompson Model}} in a {{LQG-like}} Framework},
year = {2010}}[Bibtex]
@article{Vaid2013Elementary,
abstract = {It is shown that there exists a mapping between the fermions of the Standard Model (SM) represented as braids in the Bilson-Thompson model, and a set of gates which can perform Universal Quantum Computation (UQC). This leads us to conjecture that the "Computational Universe Hypothesis" (CUH) can be given a concrete implementation in a new physical framework where elementary particles and the gauge bosons (which intermediate interactions between fermions) are interpreted as the components of a quantum computational network, with the particles serving as quantum computational gates and the gauge fields as the information carrying entities.},
archiveprefix = {arXiv},
author = {Vaid, Deepak},
eprint = {1307.0096},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Vaid_Elementary Particles as Gates for Universal Quantum Computation_2013.pdf},
keywords = {bilson-thompson,braids,computational_universe,fqxi,large_gauge_transformation,lqg,preons,quantum_computation,quantum_gates,quantum_gravity,universal,vaid_d},
month = jun,
pages = {8},
title = {Elementary {{Particles}} as {{Gates}} for {{Universal Quantum Computation}}},
year = {2013}}@article{Kaul2016Degenerate,
author = {Kaul, Romesh K. and Sengupta, Sandipan},
doi = {10.1103/PhysRevD.93.084026},
file = {/Volumes/Data/owncloud/root/research/zotero/storage/NB6ZLK87/Kaul\;Sengupta_Degenerate spacetimes in first order gravity_2016.pdf;/Volumes/Data/owncloud/root/research/zotero/storage/TV5ZPXD7/1602.html},
keywords = {_tablet},
langid = {english},
month = feb,
title = {Degenerate Spacetimes in First Order Gravity},
urldate = {2018-12-19},
year = {2016},
bdsk-url-1 = {https://doi.org/10.1103/PhysRevD.93.084026}}![[doi]](https://i0.wp.com/www.quantumofgravity.com/blog/wp-content/plugins/papercite/img/external.png?resize=10%2C10&ssl=1){kind=small}
H. Kawai, D. C. Lewellen, and H. S. H. Tye, “Construction of Four-Dimensional Fermionic String Models,” Physical review letters, vol. 57, p. 1832–1835, 1986. [Bibtex]
@article{Kawai1986Construction,
abstract = {We present a simple set of rules for constructing ultraviolet-finite closed-fermionic-string models. In particular, the method easily gives four-dimensional models which possess N=1 super-symmetry, chiral fermions, and phenomenologically interesting gauge groups.},
author = {Kawai, Hikaru and Lewellen, David C and Tye, S Henry H},
doi = {10.1103/PhysRevLett.57.1832},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {4d,classic,closed_strings,compactification,fermions,kawai_h,lewellen_d,nosource,phenomenology,prl,string_theory,supersymmetry,tye_s},
month = oct,
pages = {1832--1835},
publisher = {American Physical Society},
title = {Construction of {{Four-Dimensional Fermionic String Models}}},
volume = {57},
year = {1986},
bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.57.1832}}[Bibtex]
@article{Kawai1987Construction,
abstract = {The construction of four-dimensional closed fermionic string models is discussed. The approach is based on a fermionic formulation of all internal (i.e. toroidally compactified) coordinates. Modular invariance, world sheet supersymmetry, (super)conformal invariance and proper space-time spin-statistics impose stringent constraints on the model building. Using these constraints on the boundary conditions (spin structure) of the world sheet fermions, we obtain a simple set of rules for constructing ultraviolet-finite closed fermionic string models. For a large subclass of these models, this "spin structure" construction can be related to bosonic constructions via the fermionic charge lattice. These charge lattices are odd lorentzian self-dual lattices shifted by a fixed vector and form a nontrivial generalization of the lorentzian self-dual even-integer lattices considered by Narian. In particular, four-dimensional models with N = 4, N = 2, and N = 1 supersymmetry as well as non-supersymmetric tachyon-free chiral models can easily be construted. Some models may be interpreted as charge lattices moded by discrete symmetries - in particular Z2 type orbifolds. String interactions and other related issues are also discussed. ?? 1987.},
author = {Kawai, Hikaru and Lewellen, David C. and Henry Tye, S. H.},
doi = {10.1016/0550-3213(87)90208-2},
issn = {05503213},
journal = {Nuclear Physics, Section B},
keywords = {4d,classic,closed_strings,compactification,fermions,kawai_h,lattice_models,lewellen_d,phenomenology,string_theory,supersymmetry,tye_s},
month = jan,
number = {C},
pages = {1--76},
title = {Construction of Fermionic String Models in Four Dimensions},
volume = {288},
year = {1987},
bdsk-url-1 = {https://doi.org/10.1016/0550-3213(87)90208-2}}[Bibtex]
@article{Sakai2005Low-Energy,
abstract = {We present a holographic dual of four-dimensional, large N\_c QCD with massless flavors. This model is constructed by placing N\_f probe D8-branes into a D4 background, where supersymmetry is completely broken. The chiral symmetry breaking in QCD is manifested as a smooth interpolation of D8 - anti-D8 pairs in the supergravity background. The meson spectrum is examined by analyzing a five-dimensional Yang-Mills theory that originates from the non-Abelian DBI action of the probe D8-brane. It is found that our model yields massless pions, which are identified with Nambu-Goldstone bosons associated with the chiral symmetry breaking. We obtain the low-energy effective action of the pion field and show that it contains the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon is identified with the Skyrmion. We also derive the effective action including the lightest vector meson. Our model is closely related to that in the hidden local symmetry approach, and we obtain a Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation among the couplings. Furthermore, we investigate the Chern-Simons term on the probe brane and show that it leads to the Wess-Zumino-Witten term. The mass of the {\textbackslash}eta' meson is also considered, and we formulate a simple derivation of the {\textbackslash}eta' mass term satisfying the Witten-Veneziano formula from supergravity.},
archiveprefix = {arXiv},
author = {Sakai, Tadakatsu and Sugimoto, Shigeki},
date-modified = {2024-08-25 13:14:14 +0530},
doi = {10.1143/PTP.113.843},
eprint = {hep-th/0412141},
file = {/Volumes/Data/owncloud/root/research/zotero_pdfs/Sakai_Sugimoto_2005_Low Energy Hadron Physics in Holographic QCD.pdf},
isbn = {0033-068X},
issn = {0033-068X},
journal = {Progress of Theoretical Physics},
keywords = {_tablet},
month = apr,
number = {4},
pages = {843--882},
title = {Low {{Energy Hadron Physics}} in {{Holographic QCD}}},
urldate = {2018-12-14},
volume = {113},
year = {2005},
bdsk-url-1 = {https://doi.org/10.1143/PTP.113.843}}@article{Rovelli2014Planck,
abstract = {A star that collapses gravitationally can reach a further stage of its life, where quantum-gravitational pressure counteracts weight. The duration of this stage is very short in the star proper time, yielding a bounce, but extremely long seen from the outside, because of the huge gravitational time dilation. Since the onset of quantum-gravitational effects is governed by energy density ---not by size--- the star can be much larger than planckian in this phase. The object emerging at the end of the Hawking evaporation of a black hole can then be larger than planckian by a factor \$(m/m\_\{{\textbackslash}scriptscriptstyle P\}){\textasciicircum}n\$, where \$m\$ is the mass fallen into the hole, \$m\_\{{\textbackslash}scriptscriptstyle P\}\$ is the Planck mass, and \$n\$ is positive. We consider arguments for \$n=1/3\$ and for \$n=1\$. There is no causality violation or faster-than-light propagation. The existence of these objects alleviates the black-hole information paradox. More interestingly, these objects could have astrophysical and cosmological interest: they produce a detectable signal, of quantum gravitational origin, around the \$10{\textasciicircum}\{-14\} cm\$ wavelength.},
archiveprefix = {arXiv},
author = {Rovelli, Carlo and Vidotto, Francesca},
doi = {10.1142/S0218271814420267},
eprint = {1401.6562},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Rovelli;Vidotto_Planck stars_2014.pdf},
issn = {0218-2718},
keywords = {cosmology,gravitational_collapse,observational,prediction,quantum_bounce,quantum_gravity,rovelli,singularity,star,vidotto_francesca},
month = jan,
title = {Planck Stars},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1142/S0218271814420267}}[Bibtex]
@article{Barrau2014Fast,
abstract = {We estimate the size of a primordial black hole exploding today via a white hole transition, and the power in the resulting explosion, using a simple model. We point out that Fast Radio Bursts, strong signals with millisecond duration, probably extragalactic and having unknown source, have wavelength not far from the expected size of the exploding hole. We also discuss the possible higher energy components of the signal.},
archiveprefix = {arXiv},
author = {Barrau, Aur{\'e}lien and Rovelli, Carlo and Vidotto, Francesca},
date-modified = {2024-08-25 13:14:04 +0530},
doi = {10.1103/PhysRevD.90.127503},
eprint = {1409.4031},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Barrau;Rovelli;Vidotto_Fast radio bursts and white hole signals_2014.pdf},
issn = {15502368},
journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
number = {12},
title = {Fast Radio Bursts and White Hole Signals},
volume = {90},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1103/PhysRevD.90.127503}}[Bibtex]
@article{Barrau2017Bouncing,
abstract = {Non-perturbative quantum-gravity effects can change the fate of black holes and make them bounce in a time scale shorter than the Hawking evaporation time. In this article, we show that this hypothesis can account for the GeV excess observed from the galactic center by the Fermi satellite. By carefully taking into account the secondary component due to the decay of unstable hadrons, we show that the model is fully self-consistent. This phenomenon presents a specific redshift-dependence that could allow to distinguish it from other astrophysical phenomena possibly contributing to the GeV excess.},
archiveprefix = {arXiv},
author = {Barrau, Aur{\'e}lien and Bolliet, Boris and Schutten, Marrit and Vidotto, Francesca},
date-modified = {2024-08-25 13:14:04 +0530},
doi = {10.1016/j.physletb.2017.05.040},
eprint = {1606.08031},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Barrau et al_Bouncing black holes in quantum gravity and the Fermi gamma-ray excess_2017.pdf},
isbn = {8392233778},
issn = {03702693},
journal = {Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics},
month = jun,
pages = {58--62},
title = {Bouncing Black Holes in Quantum Gravity and the {{Fermi}} Gamma-Ray Excess},
urldate = {2018-10-28},
volume = {772},
year = {2017},
bdsk-url-1 = {https://doi.org/10.1016/j.physletb.2017.05.040}}[Bibtex]
@article{Ghoderao2018Probing,
abstract = {Examining quantum electrodynamics in non-commutative (NC) spaces along with composite operators in these spaces, we show that i) any charge g for a fermion matter field is allowed provided the basic NC photon-photon coupling is g, however no other multiples of g are permitted and ii) composite operators do not have a simple transformation which can be attributed to the effective total charge of the composite particle. Taken together these results place a limit on the scale of non-commutativity to be at most smaller that current LHC limits for compositeness. Furthermore, they also suggest that a substructure at still smaller scales is needed if such spaces are to be a physical reality.},
archiveprefix = {arXiv},
author = {Ghoderao, Pulkit S. and Gavai, Rajiv V. and Ramadevi, P.},
date-modified = {2024-08-25 13:14:08 +0530},
eprint = {1806.06015},
file = {/Users/deepak/ownCloud/root/research/mendeley/Ghoderao;Gavai;Ramadevi_Probing the scale of non-commutativity of space_2018.pdf},
keywords = {_tablet},
month = jun,
title = {Probing the Scale of Non-Commutativity of Space},
urldate = {2018-12-11},
year = {2018}}[Bibtex]
@article{Hartnoll2008Holographic,
abstract = {It has been shown that a gravitational dual to a superconductor can be obtained by coupling anti-de Sitter gravity to a Maxwell field and charged scalar. We review our earlier analysis of this theory and extend it in two directions. First, we consider all values for the charge of the scalar field. Away from the large charge limit, backreaction on the spacetime metric is important. While the qualitative behaviour of the dual superconductor is found to be similar for all charges, in the limit of arbitrarily small charge a new type of black hole instability is found. We go on to add a perpendicular magnetic field B and obtain the London equation and magnetic penetration depth. We show that these holographic superconductors are Type II, i.e., starting in a normal phase at large B and low temperatures, they develop superconducting droplets as B is reduced.},
archiveprefix = {arXiv},
author = {Hartnoll, Sean A and Herzog, Christopher P and Horowitz, Gary T and Pope, Giacomo},
date-modified = {2024-08-25 13:14:09 +0530},
doi = {10.1088/1126-6708/2008/12/015},
eprint = {0810.1563},
isbn = {1029-8479},
issn = {1029-8479},
journal = {Journal of High Energy Physics},
keywords = {High Energy Physics - Theory},
month = oct,
number = {12},
pages = {15},
publisher = {IOP Publishing},
title = {Holographic {{Superconductors}}},
volume = {2008},
year = {2008},
bdsk-url-1 = {https://doi.org/10.1088/1126-6708/2008/12/015}}[Bibtex]
@article{Hartman2010Cooper,
abstract = {We show that a quartic contact interaction between charged fermions can lead to Cooper pairing and a superconducting instability in the background of a charged asymptotically Anti-de Sitter black hole. For a massless fermion we obtain the zero mode analytically and compute the dependence of the critical temperature T\_c on the charge of the fermion. The instability we find occurs at charges above a critical value, where the fermion dispersion relation near the Fermi surface is linear. The critical temperature goes to zero as the marginal Fermi liquid is approached, together with the density of states at the Fermi surface. Besides the charge, the critical temperature is controlled by a four point function of a fermionic operator in the dual strongly coupled field theory.},
archiveprefix = {arXiv},
author = {Hartman, Thomas and Hartnoll, Sean A.},
doi = {10.1007/JHEP06(2010)005},
eprint = {1003.1918},
file = {/Volumes/Data/owncloud/root/research/zotero_pdfs/Hartman;Hartnoll_Cooper pairing near charged black holes_2010.pdf},
issn = {11266708},
journal = {Journal of High Energy Physics},
keywords = {AdS-CFT correspondence,Black holes,Spontaneous symmetry breaking},
number = {6},
title = {Cooper Pairing near Charged Black Holes},
volume = {2010},
year = {2010},
bdsk-url-1 = {https://doi.org/10.1007/JHEP06(2010)005}}@article{Rao2016Weyl,
abstract = {We begin this review with an introduction and a discussion of Weyl fermions as emergent particles in condensed matter systems, and explain how high energy phenomena like the chiral anomaly can be seen in low energy experiments. We then explain the current interest in the field due to the recent discovery of real materials which behave like Weyl semi-metals. We then describe a simple lattice model of a topological insulator, which can be turned into a Weyl semi-metal on breaking either time-reversal or inversion symmetry, and show how flat bands or Fermi arcs develop. Finally, we describe some new phenomena which occur due to the chiral nature of the Weyl nodes and end with possible future prospects in the field, both in theory and experiment.},
archiveprefix = {arXiv},
author = {Rao, Sumathi},
eprint = {1603.02821},
file = {/Volumes/Data/owncloud/root/research/zotero/storage/JNQBVKX6/Rao_Weyl semi-metals _2016.pdf;/Volumes/Data/owncloud/root/research/zotero/storage/DEH36A5V/1603.html},
journal = {arXiv:1603.02821 [cond-mat]},
keywords = {_tablet,Condensed Matter - Mesoscale and Nanoscale Physics},
month = mar,
primaryclass = {cond-mat},
shorttitle = {Weyl Semi-Metals},
title = {Weyl Semi-Metals : A Short Review},
urldate = {2018-12-17},
year = {2016}}