arXiv subjects

Gordon W. Semenoff

Publications and source records attributed to Gordon W. Semenoff.

At least 55 records · Page 3Linked to original sources

arXiv2011

Large Representation Recurrences in Large N Random Unitary Matrix Models

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.

hep-th↗

arXiv2011

Holographic Fermionic Fixed Points in d=3

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.

hep-th↗

arXiv2011

Magnetic Catalysis and Quantum Hall Ferromagnetism in Weakly Coupled Graphene

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.

hep-th↗

arXiv2011

On the Spectrum of the AdS_5xS^5 String at large lambda

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 \sqrtλ=R^2/α' 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-λlimit. 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 λ^{-1/4}.

hep-th↗

arXiv2011

Comments on k-Strings at Large N

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.

hep-lat↗

arXiv2010

Electronic zero modes of vortices in Hall states of gapped graphene

Recent observation of a metal-insulator phase transition in the $ν=0$ 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.

hep-th↗

arXiv2009

Coulomb interaction at the metal-insulator critical point in graphene

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 $ε=d-1$, with $d$ as the spatial dimension. The $O(ε)$ 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.

cond-mat.str-el↗

arXiv2009

Hot Giant Loop Holography

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.

hep-th↗

arXiv2008

Finite size Giant Magnons in the string dual of N=6 superconformal Chern-Simons theory

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.

hep-th↗

arXiv2008

Finite Size Giant Magnon

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.

hep-th↗

arXiv2007

Quantum fluctuation-induced uniaxial and biaxial spin nematics

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.

cond-mat.other↗

arXiv2007

Gauge invariant finite size spectrum of the giant magnon

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.

hep-th↗

arXiv2007

Discrete symmetries and 1/3-quantum vortices in condensates of F=2 cold atoms

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 $2π/3$ (or $4π/3$) and therefore 1/3- (or 2/3-) quantum vortices in condensates. We also briefly discuss 1/3-quantum vortices in condensates of trimers.

cond-mat.other↗

arXiv2006

Teleportation by a Majorana Medium

It is argued that Majorana zero modes in a system of quantum fermions can mediate a teleportation-like process with the actual transfer of electronic material between well separated points. The problem is formulated in the context of a quasi-realistic and exactly solvable model of a quantum wire embedded in a bulk p-wave superconductor. An explicit computation of the tunneling amplitude is given.

cond-mat.other↗

arXiv2006

Exact 1/4 BPS Loop - Chiral Primary Correlator

Correlation functions of 1/4 BPS Wilson loops with the infinite family of 1/2 BPS chiral primary operators are computed in $\mathcal{N}=4$ super Yang-Mills theory by summing planar ladder diagrams. Leading loop corrections to the sum are shown to vanish. The correlation functions are also computed in the strong-coupling limit by examining the supergravity dual of the loop-loop correlator. The strong coupling result is found to agree with the extrapolation of the planar ladders. The result is related to known correlators of 1/2 BPS Wilson loops and 1/2 BPS chiral primaries by a simple re-scaling of the coupling constant, similar to an observation of Drukker, hep-th/0605151, for the case of the 1/4 BPS loop vacuum expectation value.

hep-th↗

arXiv2006

Quantum insulating states of F=2 cold atoms in optical lattices

In this Letter we study various spin correlated insulating states of F=2 cold atoms in optical lattices. We find that the effective spin exchange interaction due to virtual hopping contains an {\em octopole} coupling between two neighboring lattice sites. Depending on scattering lengths and numbers of particles per site the ground states are either rotationally invariant dimer or trimer Mott insulators or insulating states with various spin orders. Three spin ordered insulating phases are ferromagnetic, cyclic and nematic Mott insulators. We estimate the phase boundaries for states with different numbers of atoms per lattice site.

cond-mat.other↗

arXiv2006

Finite size corrections and integrability of $\mathcal{N}=2$ SYM and DLCQ strings on a pp-wave

We compute the planar finite size corrections to the spectrum of the dilatation operator acting on two-impurity states of a certain limit of conformal $\mathcal{N}=2$ quiver gauge field theory which is a $Z_M$-orbifold of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We match the result to the string dual, IIB superstrings propagating on a pp-wave background with a periodically identified null coordinate. Up to two loops, we show that the computation of operator dimensions, using an effective Hamiltonian technique derived from renormalized perturbation theory and a twisted Bethe ansatz which is a simple generalization of the Beisert-Dippel-Staudacher~\cite{Beisert:2004hm} long range spin chain, agree with each other and also agree with a computation of the analogous quantity in the string theory. We compute the spectrum at three loop order using the twisted Bethe ansatz and find a disagreement with the string spectrum very similar to the known one in the near BMN limit of $\mathcal{N}=4$ super-Yang-Mills theory. We show that, like in $\mathcal{N}=4$, this disagreement can be resolved by adding a conjectured ``dressing factor'' to the twisted Bethe ansatz. Our results are consistent with integrability of the $\mathcal{N}=2$ theory within the same framework as that of $\mathcal{N}=4$.

hep-th↗

arXiv2006

AdS/CFT v.s. String Loops

The one string-loop correction to the energies of two impurity BMN states are computed using IIB light-cone string field theory with an improved 3-string vertex that has been proposed by Dobashi and Yoneya. As in previous published computations, the string vertices are truncated to the 2-impurity channel. The result is compared with the prediction from non-planar corrections in the BMN limit of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. It is found to agree at leading order -- one-loop in Yang-Mills theory -- and is close but not quite in agreement at order two Yang-Mills loops. Furthermore, in addition to the leading 1/2 power in the t'Hooft coupling, which is generic in string field theory, and which we have previously argued cancels, we find that the 3/2 and 5/2 powers are also miraculously absent.

hep-th↗