arXiv subjects

Gordon W. Semenoff

Publications and source records attributed to Gordon W. Semenoff.

At least 37 records · Page 2Linked to original sources

arXiv2017

World-line instantons and the Schwinger effect as a WKB exact path integral

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.

hep-th↗

arXiv2016

Scattering and momentum space entanglement

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.

hep-th↗

arXiv2016

Topology of Fermi Surfaces and anomaly inflows

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.

cond-mat.mes-hall↗

arXiv2016

The D3-probe-D7 brane holographic fractional topological insulator

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.

hep-th↗

arXiv2016

On the Light dilaton in the Large N Tri-critical O(N) Model

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.

hep-th↗

arXiv2016

Phase structure of a holographic double monolayer Dirac semimetal

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.

hep-th↗

arXiv2015

String worldsheet for accelerating quark

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.

hep-th↗

arXiv2014

Holographic D3-probe-D5 Model of a Double Layer Dirac Semimetal

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.

hep-th↗

arXiv2014

Exciton Condensation in a Holographic Double Monolayer Semimetal

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.

hep-th↗

arXiv2014

Holographic Accelerated Heavy Quark-Anti-Quark Pair

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 $s=\sqrtλ$ for the entanglement entropy of the quark and anti-quark.

hep-th↗

arXiv2014

Universal Bose Gases Near Resonance: A Rigorous Solution

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 $ε$ expansion near four spatial dimension. In dimension $d = 4 - ε$, the chemical potential of Bose gases near resonances is shown to approach the universal value $ε^{(2/(4-ε))} ε_F \sqrt{2/3} (1 + 0.474 ε- i 1.217 ε+ ...)$, where $ε_F$ is the Fermi energy defined for a Fermi gas of density $n$, and the condensation fraction is equal to $2/3 (1 + 0.0877 ε+ ...)$. We also discuss the implications on ultra-cold gases in physical dimensions.

cond-mat.quant-gas↗

arXiv2013

D3-D7 Holographic dual of a perturbed 3D CFT

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 $N_7<<N_3$ limit, a number of solutions which are dual to conformal field theories with Fermion content have been found. We use holographic techniques to study perturbations of a particular one of the conformal field theories by relevant operators. Generally, the response of a conformal field theory to such a perturbation grows and becomes nonperturbative at low energy scales. We shall find that a perturbation which switches on a background magnetic field $B$ and Fermion mass $m$ induces a renormalization group flow that can be studied perturbatively in the limit of small $m^2/B$. We solve the leading order explicitly. We find that, for one particular value of internal flux, the system exhibits magnetic catalysis, the spontaneous breaking of chiral symmetry enhanced by the presence of the magnetic field. In the process, we derive formulae predicting the Debye screening length of the Fermion-antiFermion plasma at finite density and the diamagnetic moment of the ground state of the Fermion system in the presence of a magnetic field.

hep-th↗

arXiv2013

Giant D5 Brane Holographic Hall State

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.

hep-th↗

arXiv2012

Chiral primary one-point functions in the D3-D7 defect conformal field theory

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.

hep-th↗

arXiv2012

D7-anti-D7 bilayer: holographic dynamical symmetry breaking

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.

hep-th↗

arXiv2012

D3-D5 Holography with Flux

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.

hep-th↗

arXiv2011

Holographic Schwinger Effect

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.

hep-th↗

arXiv2011

Chiral Symmetry Breaking in Graphene

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.

hep-th↗