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A hybrid of the critical three dimensional Gross-Neveu and Thirring models deformed by explicit parity breaking operators is studied in the large N expansion and using the renormalization group. The regime of coupling constants where the theory is stable is identified and criteria for the occurrence of fixed points in that regime are found. For a certain range of Chern-Simons level, we find stable charge-gapped phase with spontaneously broken approximate scale invariance and a parametrically light dilaton. The Chern-Simons level can be tuned to the stability edge resulting in exact scale invariance which is spontaneously broken, accompanied by a massless dilaton. For another, narrow range of Chern-Simons levels we find a conformal window where the theory flows to a Wilson-Fisher-like fixed point and is a novel (and rare) example of a non-supersymmetric non-trivial parity and time reversal violating three dimensional conformal field theory with scalar, spinor and vector fields., Comment: Typos corrected, references added, arguments clarified

Some aspects of the theory of fermions living on three dimensional spacetime with a flat co-dimension one boundary are discussed, particularly a case where the boundary condition preserves scale and translation invariance but violates the residual Lorentz and conformal symmetries. This case is interesting because the Dirac equation has normalizable stationary edge states which must be taken into account in the quantization. We show that a consequence of the edge states for quantization of the Dirac field is that there are no states of the Dirac field theory which are simultaneously scale, C and P invariant even when these are good symmetries of the theory. The scale invariant states of the Dirac field contain either a nonzero scale covariant momentum density or a U(1) charge density concentrated near the edge., Comment: 10 pages, Proceedings of "Gravity, Strings and Fields'', Montreal, July 2023

The multi-critical behaviour of an approximately scale and conformal invariant quantum field theory, which can be regarded as the deformation of the critical Gross-Neveu model in 3+epsilon dimensions by a nearly marginal parity violating operator, is studied using a large $N$ expansion. When epsilon is greater than a number of order 1/N, the deformation is marginally relevant and it is found to exhibit spontaneous breaking of the approximate scale symmetry accompanied by the appearance of a light scalar in its spectrum. The scalar mass is parametrically small, of order epsilon times the fermion mass and it can be identified with a light dilaton. When the dimension is reduced to 3 the deformation of the Gross-Neveu model becomes marginally irrelevant, what was a minimum of the potential becomes a maximum and the theory has a non-perturbative global instability. There is a metastable perturbative phase where the scalar does not condense and the fermions are massless separated by an energy barrier with height of order one (rather than N) from an energetically favoured phase with a runaway condensate.

The flat band of edge states which occur in the simple tight-binding lattice model of graphene with a zig-zag edge have long been conjectured to take up a ferromagnetic configuration. In this work we demonstrate that, for a large class of interaction Hamiltonians which can be added to the tight-binding model, and at the first order in perturbation theory, the degeneracy of the edge states is resolved in such a way that the ground state is in the maximal, spin j = N/2 representation of the spin symmetry where N is the number of edge states.

Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$ symmetries as well as Lorentz and conformal symmetry. We show that there is essentially one special case where a single species of fermion has $CPT$ and the full Poincare and conformal symmetry of the boundary. We show that, with doubled fermions, there is a second special case which respects $CPT$ but still violates Lorentz and conformal symmetry. This second special case is essentially the unique boundary condition where the Dirac operator has fermion zero mode edge states. We discuss how the edge states lead to exotic representations of scale, phase and translation symmetries and how imposing a symmetry requirement leads to edge ferromagnetism of the system. We prove that the exotic ferromagnetic representations are indeed carried by the ground states of the system perturbed by a class of interaction Hamiltonians which includes the non-relativistic Coulomb interaction., Comment: To appear in JHEP, accepted version

It is demonstrated that it is possible to find a field theory containing massless scalar particles which has infrared structure closely resembling that of quantum electrodynamics and perturbative quantum gravity but exhibiting no gauge invariance or internal symmetries at all, and in particular, no apparent asymptotic symmetry. It is shown that, unlike soft photons and gravitons, the soft scalars do not decouple from dressed states and they are generically produced when hard dressed particles interact. However, the entanglement of the hard and resulting soft particles is vanishingly small., Comment: Version to published in :hys. Rev. D

This essay is a tribute to Professor Roman Jackiw on the occasion of his eightieth year. It discusses some ideas about Fermion zero modes and fractional charges and quantum entanglement.

The N=4 superconformal Yang-Mills theory on flat four-dimensional Minkowski space is a de-confined gauge theory in the sense that the string tension for fundamental representation coloured quarks vanishes. In fact, static fundamental representation quarks which lie in certain half-BPS super-multiplets do not interact at all. An interesting question asks whether such quarks would carry a well-defined global colour charge which, when the gauge is fixed, should have the status of an internal symmetry. We shall present a simple paradigmatic model which suggests that the answer to this question lies in the way in which infrared divergences are dealt with., Comment: 28 pages, 2 figures, typos fixed and some clarification added

We shall outline some results regarding the infrared catastrophes of quantum electrodynamics and perturbative quantum gravity and their implications for information loss in quantum processes involving electrically or gravitationally charged particles. We will argue that two common approaches to the solution of the infrared problem, using transition probabilities which are inclusive of copious soft photon and graviton production and using dressed states describe fundamentally different quantizations of electrodynamics and low energy gravity which are, in principle, distinguishable by experiments., Comment: Summary of a plenary talk given at "Lie Theory and Its Applications in Physics", Varna, Bulgaria, June 2019

We study a class of defect quantum field theories where the quantum field theory in the 3+1-dimensional bulk is a free photon and charged matter and the interactions of the photons with the charges occur entirely on a 2+1-dimensional defect. We observe that at the fully quantum level, the effective action of such a theory is still a defect field theory with free photons propagating in the bulk and the nonlinearities in the quantum corrections to the Maxwell equations confined to the defect. We use this observation to show that the defect field theory has interesting electromagnetic properties. The electromagnetic fields sourced by static test charges are attenuated as if the bulk surrounding them were filled with a dielectric material. This is particularly interesting when the observer and test charge are on opposite sides of the defect. Then the effect is isotropic and it is operative even in the region near the defect. If the defect is in a time reversal violating state, image charges have the appearance of electrically and magnetically charged dyons. We present the example of a single layer in a quantum Hall state. We observe that the charge screening effect in charge neutral graphene should be significant, and even more dramatic when the layer is in a metallic state with mobile electrons., Comment: 25 pages, 1 figure, clarified eq (8.8)

Lectures presented at the Les Houches 2016 Summer School "Integrability: from Statistical Systems to Gauge Theory"., Comment: To appear in proceedings of the Les Houches 2016 Summer School l "Integrability: from Statistical Systems to Gauge Theory"

These are the notes for a lecture which I presented at the International Conference on New Frontiers in Physics in Kolymbari, Crete in July, 2018. They review an idea which posits a phase of a two-dimensional system of cold N-component Fermions which exhibits spontaneously broken approximate scale symmetry when studied in the large N expansion. Near criticality, the phase exhibits anomalously small pressure and large compressibility. Some of the consequences of the approximate scale symmetry, such as the existence of a dilaton and its properties are discussed., Comment: To be published in proceedings of "International Conference on New Frontiers in Physics", Kolymbari, Crete, July, 2018

We find a simple model of an insulating state of a quantum wire which has a single isolated edge mode. We argue that, when brought to proximity, the edge modes on independent wires naturally form Bell entangled states which could be used for elementary quantum processes such as teleportation. We give an example of an algorithm which teleports the spin state of an electron from one quantum wire to another., Comment: 5 pages, 3 figures

We use the large N approximation to find an exotic phase of a cold, two-dimensional, N-component Fermi gas which exhibits dynamically broken approximate scale symmetry. We identify a particular weakly damped collective excitation as the dilaton, the pseudo-Goldstone boson associated with the broken approximate scale symmetry. We argue that the symmetry breaking phase is stable for a range of parameters of the theory and there is a fluctuation induced first order quantum phase transition between the normal and the scale symmetry breaking phases which can be driven by tuning the chemical potential. We find that the compressibility of the gas at its lower critical density is anomalously large, 2N times that of a perfect gas at the same density., Comment: 5 pages

We revisit the problem of charged string pair creation in a constant external electric field. The string states are massive and creation of pairs from the vacuum is a tunnelling process, analogous to the Schwinger process where charged particle-anti-particle pairs are created by an electric field. We find the instantons in the worldsheet sigma model which are responsible for the tunnelling events. We evaluate the sigma model partition function in the multi-instanton sector in the WKB approximation which keeps the classical action and integrates the quadratic fluctuations about the solution. We find that the summation of the result over all multi-instanton sectors reproduces the known amplitude. This suggests that corrections to the WKB limit must cancel. To show that they indeed cancel, we identify a fermionic symmetry of the sigma model which occurs in the instanton sectors and which is associated with collective coordinates. We demonstrate that the action is symmetric and that the interaction action is an exact form. These conditions are sufficient for localization of the worldsheet functional integral onto its WKB limit., Comment: 40 pages; Expanded discussion section, added references

We derive a formula for the entanglement entropy of two regions in momentum space that is generated by the scattering of weakly interacting scalar particles. We discuss an example where weak interactions entangle momentum scales above and below an infrared cutoff.

We present a simple proof that the imaginary part of the world-line path integral which computes the rate of Schwinger pair production of charged particles in a constant electric field, is given exactly by the semiclassical WKB limit., Comment: 5 pages; corrected typos, added reference

The leading order of the large N limit of the O(N) symmetric phi-six theory in three dimensions has a phase which exhibits spontaneous breaking of scale symmetry accompanied by a massless dilaton which is a Goldstone boson. At the next-to-leading order in large N, the phi-six coupling has a beta function of order 1/N and it is expected that the dilaton acquires a small mass, proportional to the beta function and the condensate. In this note, we show that this "light dilaton" is actually a tachyon. This indicates an instability of the phase of the theory with spontaneously broken approximate scale invariance., Comment: Eight pages, 2 figures

The D3-probe-D7 brane system, oriented so as to have 2+1-dimensional Poincare symmetry, is argued to be the holographic representation of a strongly correlated fractional topological insulator which exhibits a zero-field quantized Hall effect with half-units of Hall conductivity. The phase diagram of the system with charge density and external magnetic field is found and, as well as charge gapped quantum Hall states, it exhibits metallic and semi-metallic phases with interesting behaviours. The relationship of this to other models of fractional topological insulators is discussed., Comment: 22 pages, 2 figures, text restructured, five additional plots included, published version

We study a holographic D3/probe-D5-brane model of a double monolayer Dirac semimetal in a magnetic field and in the presence of a nonzero temperature. Intra- and inter-layer exciton condensates can form by varying the balanced charge density on the layers, the spatial separation and the temperature. Constant temperature phase diagrams for a wide range of layer separations and charge densities are found. The presence of a finite temperature makes the phase diagrams extremely rich and in particular leads to the appearance of a symmetric phase which was missing at zero temperature., Comment: 25 pages, 21 figures, references added

We derive a rigorous classification of topologically stable Fermi surfaces of non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations. For systems on an infinite crystal it is shown that there can only be topologically unstable Fermi surfaces. For systems on a half- space and with a gapped bulk, our derivation naturally yields a $\mathit{K}$-theory classification. Given the $d-1$-dimensional surface Brillouin zone $\mathrm{X}_{s}$ of a $d$-dimensional half-space, our result implies that different classes of globally stable Fermi surfaces belong in $\mathit{K^{-1}}\mathrm{(X_{s})}$ for systems with only discrete translation-invariance. This result has a chiral anomaly inflow interpretation, as it reduces to the spectral flow for $d = 2$. Through equivariant homotopy methods we extend these results for symmetry classes $AI,\,AII,\, C$ and $D$ and discuss their corresponding anomaly inflow interpretation., Comment: Removed Born-von Karman boundary conditions for $\mathbb{R}^{d}$ and $\mathbb{R}^{d-1}\times [0,\infty)$ and includes the 'weak' topological phase found by Kitaev for $\Xi^2 = I, d= 2$

The possibility of inter-layer exciton condensation in a holographic D3-probe-D5 brane model of a strongly coupled double monolayer Dirac semi-metal in a magnetic field is studied in detail. It is found that, when the charge densities on the layers are exactly balanced so that, at weak coupling, the Fermi surfaces of electrons in one monolayer and holes in the other monolayer would be perfectly nested, inter-layer condensates can form for any separation of the layers. The case where both monolayers are charge neutral is special. There, the inter-layer condensate occurs only for small separations and is replaced by an intra-layer exciton condensate at larger separations. The phase diagram for charge balanced monolayers for a range layer separations and chemical potentials is found. We also show that, in semi-metals with multiple species of massless fermions, the balance of charges required for Fermi surface nesting can occur spontaneously by breaking some of the internal symmetry of the monolayers. This could have important consequences for experimental attempts to find inter-layer condensates., Comment: minor correction to references

The formation of intra-layer and inter-layer exciton condensates in a model of a double monolayer Weyl semi-metal is studied in the strong coupling limit using AdS/CFT duality. We find a rich phase diagram which includes phase transitions between inter-layer and intra-layer condensates as the charge densities and the separation of the layers are varied. The tendency to inter-layer condensation is strongest when the charge densities are balanced so that the weak coupling electron and hole Fermi surfaces would be nested. For systems with multiple species of massless Fermions, we find a novel phase transition where the charge balance for nesting occurs spontaneously., Comment: 4 pages, 2 figures

We consider the AdS bulk dual to an external massive quark in SYM following an arbitrary trajectory on Minkowski background. While a purely outgoing boundary condition on the gluonic field allows one to express the corresponding string worldsheet in a closed form, the setup has curious consequences. In particular, we argue that any quark whose trajectory on flat spacetime approaches that of a light ray in the remote past (as happens e.g. in the case of uniform acceleration) must necessarily be accompanied by an anti-quark. This is puzzling from the field theory standpoint, since one would expect that a sole quark following any timelike trajectory should be allowed. We explain the resolution in terms of boundary and initial conditions. We analyze the configuration in global AdS, which naturally suggests a modification to the boundary conditions allowing for a single accelerated quark without accompanying anti-quark. We contrast this resolution with earlier proposals., Comment: 28 pages, 8 figures; v2: minor clarifications added

The problem of a heavy quark-anti-quark pair which have constant eternal acceleration in opposite directions in the vacuum of deconfined maximally supersymmetric Yang-Mills theory is studied both in perturbation theory and at strong coupling using AdS/CFT. Perturbation theory is summed to obtain what is conjectured to be an exact result. It is shown to agree with a particular prescription for computing the disc amplitude in the string theory dual and it yields a value $s=\sqrt{\lambda}$ for the entanglement entropy of the quark and anti-quark., Comment: 4 pages, 4 figures

A detailed study of the semiclassical expansion of the world line path integral for a charged relativistic particle in a constant external electric field is presented. We show that the Schwinger formula for charged particle pair production is reproduced exactly by the semiclassical expansion around classical instanton solutions when the leading order of fluctuations is taken into account. We prove that all corrections to this leading approximation vanish and that the WKB approximation to the world line path integral is exact., Comment: 16 pages; corrected and expanded localization argument in section III. Added references and expanded appendices. Corrected typos

We obtain a rigorous solution of universal Bose gases near resonance and offer an answer to one of the long-standing challenges of quantum gases at large scattering lengths, where the standard dilute theory breaks down. The solution was obtained by using an $\epsilon$ expansion near four spatial dimension. In dimension $d = 4 - \epsilon$, the chemical potential of Bose gases near resonances is shown to approach the universal value $\epsilon^{(2/(4-\epsilon))} \epsilon_F \sqrt{2/3} (1 + 0.474 \epsilon - i 1.217 \epsilon + ...)$, where $\epsilon_F$ is the Fermi energy defined for a Fermi gas of density $n$, and the condensation fraction is equal to $2/3 (1 + 0.0877 \epsilon + ...)$. We also discuss the implications on ultra-cold gases in physical dimensions., Comment: 5 pages, 1 figure

We find a new holographic description of strongly coupled defect field theories using probe D5 branes. We consider a system where a large number of probe branes, which are asymptotically D5 branes, blow up into a D7 brane suspended in the bulk of anti-de Sitter space. For a particular ratio of charge density to external magnetic field, so that the Landau level filling fraction per color is equal to one, the D7 brane exhibits an incompressible charge-gapped state with one unit of integer quantized Hall conductivity. The detailed configuration as well as ungapped, compressible configurations for a range of parameters near the gapped one are found by solving the D5 and D7 brane embedding equations numerically and the D7 is shown to be preferred over the D5 by comparing their energies. We then find integer quantum Hall states with higher filling fractions as a stack of D5 branes which blow up to multiple D7 branes where each D7 brane has filling fraction one. We find indications that the n D7 branes describing the filling fraction n state are coincident with a residual SU(n) symmetry when n is a divisor of the total number of D5 branes. We examine the issue of stability of the larger filling fraction Hall states. We argue that, in the D7 brane phase, chiral symmetry restoration could be a first order phase transition., Comment: 30 pages, 15 figures, typos fixed, some clarifying comments added

We compute the one-point functions of chiral primary operators in the non-supersymmetric defect conformal field theory that is dual to the IIB string theory on $AdS_5\times S^5$ background with a probe D7 brane with internal gauge field flux, both in perturbative Yang-Mills theory and in the string theory dual. The former is expected to be accurate at weak coupling whereas the latter should be accurate in the planar strong coupling limit of the gauge theory. We consider the distinct cases where the D7 brane has geometry $AdS_4\times S^4$ with an instanton bundle of the worldvolume gauge fields on $S^4$ and $AdS_4\times S^2\times S^2$ with Dirac monopole bundles on each $S^2$. The gauge theory computation and the string theory computation can be compared directly in the planar limit and then a subsequent limit where the worldvolume flux is large. We find that there is exact agreement between the two in the leading order., Comment: v2 minor edits and additional references added

An appropriately oriented D3-D7-brane system is the holographic dual of relativistic Fermions occupying a 2+1-dimensional defect embedded in 3+1-dimensional spacetime. The Fermions interact via fields of ${\mathcal N}=4$ Yang-Mills theory in the 3+1-dimensional bulk. Recently, using internal flux to stabilize the system in the probe $N_7<

We consider a holographic model of dynamical symmetry breaking in 2+1-dimenisons, where a parallel D7-anti-D7 brane pair fuse into a single object, corresponding to the U(1)XU(1)->U(1) symmetry breaking pattern. We show that the current-current correlation functions can be computed analytically and exhibit the low momentum structure that is expected when global symmetries are spontaneously broken. We also find that these correlation functions have poles attributable to infinite towers of vector mesons with equally spaced masses., Comment: 4 pages, 3 figures

It is shown that the Berezinski-Kosterlitz-Thouless phase transition that has been found in D3-D5 brane systems with nonzero magnetic field and charge density can also be found by tuning an extra-dimensional magnetic flux. We find numerical solutions for the probe D5-brane embedding and discuss properties of the solutions. We also demonstrate that the nontrivial embeddings include those which can be regarded as spontaneously breaking chiral symmetry.

We study tunneling pair creation of W-Bosons by an external electric field on the Coulomb branch of N=4 supersymmetric Yang-Mills theory. We use AdS/CFT holography to find a generalization of Schwinger's formula for the pair production rate to the strong coupling, planar limit which includes the exchange of virtual massless particles to all orders. We find that the pair creation formula has an upper critical electric field beyond which the process is no longer exponentially suppressed. The value of the critical field is identical to that which occurs in the Born-Infeld action of probe D3-branes in the AdS5XS5 background., Comment: 4 pages, 2 figures, To appear in Physical Review Letters

The question of whether the Coulomb interaction is strong enough to break the sublattice symmetry of un-doped graphene is discussed. We formulate a strong coupling expansion where the ground state of the Coulomb Hamiltonian is found exactly and the kinetic hopping Hamiltonian is treated as a perturbation. We argue that many of the properties of the resulting system would be shared by graphene with a Hubbard model interaction. In particular, the best candidate sublattice symmetry breaking ground state is an antiferromagnetic Mott insulator. We discuss the results of some numerical simulations which indicate that the Coulomb interaction is indeed subcritical. We also point out the curious fact that, if the electron did not have spin degeneracy, the tendency to break chiral symmetry would be much greater and even relatively weak Coulomb interactions would likely gap the spectrum., Comment: 18 pages, 6 figures, to appear in Proceedings of the Nobel Symposium on Graphene and Quantum Matter

In a random unitary matrix model at large N, we study the properties of the expectation value of the character of the unitary matrix in the rank k symmetric tensor representation. We address the problem of whether the standard semiclassical technique for solving the model in the large N limit can be applied when the representation is very large, with k of order N. We find that the eigenvalues do indeed localize on an extremum of the effective potential; however, for finite but sufficiently large k/N, it is not possible to replace the discrete eigenvalue density with a continuous one. Nonetheless, the expectation value of the character has a well-defined large N limit, and when the discreteness of the eigenvalues is properly accounted for, it shows an intriguing approximate periodicity as a function of k/N., Comment: 24 pages, 11 figures

We present a top-down string theory holographic model of strongly interacting relativistic 2+1-dimensional fermions, paying careful attention to the discrete symmetries of parity and time reversal invariance. Our construction is based on probe $D7$-branes in $AdS_5 \times S^5$, stabilized by internal fluxes. We find three solutions, a parity and time reversal invariant conformal field theory which can be viewed as a particular deformation of Coulomb interacting graphene, a parity and time reversal violating but gapless field theory and a system with a parity and time reversal violating charge gap. We show that the Chern-Simons-like electric response function, which is generated perturbatively at one-loop order by parity violating fermions and which is protected by a no-renormalization theorem at orders beyond one loop, indeed appears with the correctly quantized coefficient in the charge gapped theory. In the gapless parity violating solution, the Chern-Simons response function obtains quantum corrections which we compute in the holographic theory., Comment: 25 pages, six figures

We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2)XU(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry., Comment: 35 pages

We present a computation of the k-string tension in the large N limit of the two dimensional lattice Yang-Mills theory. It is well known that the problems of computing the partition function and the Wilson loop can be both reduced to a unitary matrix integral which has a third order phase transition separating weak and strong coupling. We give an explicit computation of the interaction energy for k-strings in the large N limit when k/N is held constant and non-zero. In this limit, the interaction energy is finite and attractive. We show that, in the strong coupling phase, the k -> N - k duality is realized as a first order phase transition. We also show that the lattice k-string tension reduces to the expected Casimir scaling in the continuum limit., Comment: 13 pages, three figures, added references and a clarification

We put forth a program for perturbatively quantizing the bosonic sector of the IIB superstring on AdS_5xS^5 in the large radius of curvature R (i.e. flat-space) limit, and in light-cone gauge. Using the quantization of the massive particle on AdS_5xS^5 as a guiding exercise, we read off the correct scaling of the particle coordinates in the large radius limit. In the corresponding large \sqrt{\lambda}=R^2/\alpha' limit of the string the oscillator modes must be scaled differently from the zero modes. We compute the bosonic string Hamiltonian in this limit which gives the flat-space mass-squared operator at leading order, followed by a harmonic oscillator potential in the zero modes at subleading order. Using these ingredients we calculate the leading and sub-leading terms in the conformal dimension of the length-four Konishi state in the large-\lambda limit. Furthermore we work out the relevant terms of the energy expansion to next-to-next-to leading order, which are plagued by severe ordering ambiguities. This prevents us from determining the corrections to the spectrum at order {\lambda}^{-1/4}., Comment: 24 pages. v2: typos fixed

Recent observation of a metal-insulator phase transition in the $\nu=0$ Hall state of graphene has inspired the idea that charge carriers in the metallic state could be fractionally charged vortices. We examine the question of whether vortices in particular gapped states of graphene and subject to external magnetic and pseudo-magnetic fields could have the mid-gap zero mode electron states which would allow them to be charged., Comment: 8pgs

We compute the renormalization group flow of the long-ranged electron-electron interaction at the Gross-Neveu quantum critical point between the semimetal and the excitonic insulator in graphene, perturbatively in the small parameter $\epsilon=d-1$, with $d$ as the spatial dimension. The $O(\epsilon)$ correction to the usual beta-function makes the long-range interaction only more irrelevant at the critical than at the Gaussian fixed point. A weak long-range tail of the Coulomb interaction is found to be marginally irrelevant also in arbitrary dimension when the number of Dirac fermions is large. Its ultimate irrelevancy notwithstanding, it is shown that the metal-insulator transition may still be induced by increasing only the long-range tail of the Coulomb interaction., Comment: 4 pages, 4 figures; published version

We argue that there is a phase transition in the expectation value of the Polyakov loop operator in the large N limit of the high temperature deconfined phase of N=4 Yang-Mills theory on a spatial S^3. It occurs for large completely symmetric representation of the SU(N) symmetry group. We speculate that this transition is reflected in the string theory dual as a critical behavior of the D3-brane duals of large representation loops., Comment: 4 pages, 1 figure, final section updated

We find the exact solution for a finite size Giant Magnon in the $SU(2)\times SU(2)$ sector of the string dual of the $\mathcal{N}=6$ superconformal Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. The finite size Giant Magnon solution consists of two magnons, one in each $SU(2)$. In the infinite size limit this solution corresponds to the Giant Magnon solution of arXiv:0806.4959. The magnon dispersion relation exhibits finite-size exponential corrections with respect to the infinite size limit solution., Comment: 11 pages, the orbifold case is discussed

The quantization of the giant magnon away from the infinite size limit is discussed. We argue that this quantization inevitably leads to string theory on a Z_M-orbifold of S^5. This is shown explicitly and examined in detail in the near plane-wave limit.

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the $R$-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model., Comment: 12 pages, some clarifications, references added

It is shown that zero point quantum fluctuations (ZPQFs) completely lift the accidental continuous degeneracy that is found in mean field analysis of quantum spin nematic phases of hyperfine spin 2 cold atoms. The result is two distinct ground states which have higher symmetries: a uniaxial spin nematic and a biaxial spin nematic with dihedral symmetry ${Dih}_4$. There is a novel first order quantum phase transition between the two phases as atomic scattering lengths are varied. We find that the ground state of $^{87}Rb$ atoms should be a uniaxial spin nematic. We note that the energy barrier between the phases could be observable in dynamical experiments., Comment: 4 pages, 2 figures included; published version

In this Letter we study discrete symmetries of mean field manifolds of condensates of F=2 cold atoms, and various unconventional quantum vortices. Discrete quaternion symmetries result in two species of spin defects that can only appear in integer vortices while {\em cyclic} symmetries are found to result in a phase shift of $2\pi/3$ (or $4\pi/3$) and therefore 1/3- (or 2/3-) quantum vortices in condensates. We also briefly discuss 1/3-quantum vortices in condensates of trimers., Comment: 4 pages, 2 figures included; published version