arXiv subjects

Christopher P. Herzog

Publications and source records attributed to Christopher P. Herzog.

At least 55 records · Page 3Linked to original sources

arXiv2014

Linear Resistivity from Non-Abelian Black Holes

Starting with the holographic p-wave superconductor, we show how to obtain a finite DC conductivity through a non-abelian gauge transformation. The translational symmetry is preserved. We obtain phenomenological similarities with high temperature cuprate superconductors. Our results suggest that a lattice or impurities are not essential to produce a finite DC resistivity with a linear temperature dependence. An analogous field theory calculation for free fermions, presented in the appendix, indicates our results may be a special feature of strong interactions.

hep-th↗

arXiv2014

Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories

We consider single interval Rényi and entanglement entropies for a two dimensional conformal field theory on a circle at nonzero temperature. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass gap, we calculate the leading corrections to the Rényi and entanglement entropy in a low temperature expansion. These corrections have a universal form for any two dimensional conformal field theory that depends only on the size of the mass gap and its degeneracy. We analyze the limits where the size of the interval becomes small and where it becomes close to the size of the spatial circle.

hep-th↗

arXiv2014

Losing Forward Momentum Holographically

We present a numerical scheme for solving Einstein's Equations in the presence of a negative cosmological constant and an event horizon with planar topology. Our scheme allows for the introduction of a particular metric source at the conformal boundary. Such a spacetime has a dual holographic description in terms of a strongly interacting quantum field theory at nonzero temperature. By introducing a sinusoidal static metric source that breaks translation invariance, we study momentum relaxation in the field theory. In the long wavelength limit, our results are consistent with the fluid-gravity correspondence and relativistic hydrodynamics. In the small amplitude limit, our results are consistent with the memory function prediction for the momentum relaxation rate. Our numerical scheme allows us to study momentum relaxation outside these two limits as well.

hep-th↗

arXiv2013

Stress Tensors from Trace Anomalies in Conformal Field Theories

Using trace anomalies, we determine the vacuum stress tensors of arbitrary even dimensional conformal field theories in Weyl flat backgrounds. We demonstrate a simple relation between the Casimir energy on the real line times a sphere and the type A anomaly coefficient. This relation generalizes earlier results in two and four dimensions. These field theory results for the Casimir are shown to be consistent with holographic predictions in two, four, and six dimensions.

hep-th↗

arXiv2013

Tracing Through Scalar Entanglement

As a toy model of a gapped system, we investigate the entanglement entropy of a massive scalar field in 1+1 dimensions at nonzero temperature. In a small mass m and temperature T limit, we put upper and lower bounds on the two largest eigenvalues of the covariance matrix used to compute the entanglement entropy. We argue that the entanglement entropy has exp(-m/T) scaling in the limit m >> T. We comment on the relation between our work and the Ryu-Takayanagi proposal for computing the entanglement entropy holographically.

hep-th↗

arXiv2013

Entanglement Entropy of a Massive Fermion on a Torus

The Renyi entropies of a massless Dirac fermion on a circle with chemical potential are calculated analytically at nonzero temperature by using the bosonization method. The bosonization of a massive Dirac fermion to the sine-Gordon model lets us obtain the small mass corrections to the entropies. We numerically compute the Renyi entropies by putting a massive fermion on the lattice and find agreement between the analytic and numerical results. In the presence of a mass gap, we show that corrections to Renyi and entanglement entropies in the limit m >> T scale as exp(-m/T). We also show that when there is ground state degeneracy in the gapless case, the limits m to zero and T to zero do not commute.

hep-th↗

arXiv2012

Free Energy of D_n Quiver Chern-Simons Theories

We apply the matrix model of Kapustin, Willett and Yaakov to compute the free energy of N=3 Chern-Simons matter theories with D_n quivers in the large N limit. We conjecture a general expression for the free energy that is explicitly invariant under Seiberg duality and show that it can be interpreted as a sum over certain graphs known as signed graphs. Through the AdS/CFT correspondence, this leads to a prediction for the volume of certain tri-Sasaki Einstein manifolds. We also study the unfolding procedure, which relates these D_n quivers to A_{2n-5} quivers. Furthermore, we consider the addition of massive fundamental flavor fields, verifying that integrating these out decreases the free energy in accordance with the F-theorem.

hep-th↗

arXiv2012

The Spin of Holographic Electrons at Nonzero Density and Temperature

We study the Green's function of a gauge invariant fermionic operator in a strongly coupled field theory at nonzero temperature and density using a dual gravity description. The gravity model contains a charged black hole in four dimensional anti-de Sitter space and probe charged fermions. In particular, we consider the effects of the spin of these probe fermions on the properties of the Green's function. There exists a spin-orbit coupling between the spin of an electron and the electric field of a Reissner-Nordstrom black hole. On the field theory side, this coupling leads to a Rashba like dispersion relation. We also study the effects of spin on the damping term in the dispersion relation by considering how the spin affects the placement of the fermionic quasinormal modes in the complex frequency plane in a WKB limit. An appendix contains some exact solutions of the Dirac equation in terms of Heun polynomials.

hep-th↗

arXiv2012

The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a Z_2 outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.

hep-th↗

arXiv2012

Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification

We consider N=3 supersymmetric Chern-Simons (CS) theories that contain product U(N) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these theories on an S^3 in the large N limit. We show that the only such CS theories for which the long range forces between the eigenvalues cancel have quivers which are in one-to-one correspondence with the simply laced affine Dynkin diagrams. As the A_n series was studied in detail before, in this paper we compute the partition function for the D_4 quiver. The D_4 example gives further evidence for a conjecture that the saddle point eigenvalue distribution is determined by the distribution of gauge invariant chiral operators. We also see that the partition function is invariant under a generalized Seiberg duality for CS theories.

hep-th↗

arXiv2011

From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))

The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace quiver gauge theories with {\cal N}=3 supersymmetry and U(N)^d gauge groups in the limit of large N. In its simplest application, the matrix model computes the free energy of the gauge theory on S^3. The conjectured F-theorem states that this quantity should decrease under renormalization group flow. We show that for a simple class of such flows, the F-theorem holds for our necklace theories. We also provide a relationship between matrix model eigenvalue distributions and numbers of chiral operators that we conjecture holds more generally. Through the AdS/CFT correspondence, there is therefore a natural dual geometric interpretation of the matrix model saddle point in terms of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d submanifolds. As a final bonus, our analysis gives us the partition function of the T(U(N)) theory on S^3.

hep-th↗

arXiv2011

Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories

We give further support for our conjecture relating eigenvalue distributions of the Kapustin-Willett-Yaakov matrix model in the large N limit to numbers of operators in the chiral ring of the corresponding supersymmetric three-dimensional gauge theory. We show that the relation holds for non-critical R-charges and for examples with {\mathcal N}=2 instead of {\mathcal N}=3 supersymmetry where the bifundamental matter fields are nonchiral. We prove that, for non-critical R-charges, the conjecture is equivalent to a relation between the free energy of the gauge theory on a three sphere and the volume of a Sasaki manifold that is part of the moduli space of the gauge theory. We also investigate the consequences of our conjecture for chiral theories where the matrix model is not well understood.

hep-th↗

arXiv2011

Multi-Matrix Models and Tri-Sasaki Einstein Spaces

Localization methods reduce the path integrals in {\cal N} >= 2 supersymmetric Chern-Simons gauge theories on S^3 to multi-matrix integrals. A recent evaluation of such a two-matrix integral for the {\cal N}=6 superconformal U(N) x U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, explaining, in particular the N^{3/2} scaling of the free energy. We study a class of p-matrix integrals describing {\cal N}=3 superconformal U(N)^p Chern-Simons gauge theories. We present a simple method that allows us to evaluate the eigenvalue densities and the free energies in the large N limit keeping the Chern-Simons levels k_i fixed. The dual M-theory backgrounds are AdS_4 x Y, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the k_i. The gravitational free energy scales inversely with the square root of the volume of Y. We find a general formula for the p-matrix free energies that agrees with the available results for volumes of the tri-Sasaki Einstein spaces Y, thus providing a thorough test of the corresponding AdS_4/CFT_3 dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.

hep-th↗

arXiv2011

Sum Rules from an Extra Dimension

Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green's functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning their large and small frequency behavior and their pole structure. From these results, it is straightforward to prove the validity of various sum rules on the field theory side of the duality. We introduce a novel contraction mapping we use to study the large frequency behavior of the Green's functions.

hep-th↗

arXiv2011

Transport in holographic superfluids

We construct a slowly varying space-time dependent holographic superfluid and compute its transport coefficients. Our solution is presented as a series expansion in inverse powers of the charge of the order parameter. We find that the shear viscosity associated with the motion of the condensate vanishes. The diffusion coefficient of the superfluid is continuous across the phase transition while its third bulk viscosity is found to diverge at the critical temperature. As was previously shown, the ratio of the shear viscosity of the normal component to the entropy density is 1/(4 pi). As a consequence of our analysis we obtain an analytic expression for the backreacted metric near the phase transition for a particular type of holographic superfluid.

hep-th↗

arXiv2011

An Analytic Holographic Superconductor

We investigate a holographic superconductor that admits an analytic treatment near the phase transition. In the dual 3+1 dimensional field theory, the phase transition occurs when a scalar operator of scaling dimension two gets a vacuum expectation value. We calculate current-current correlation functions along with the speed of second sound near the critical temperature. We also make some remarks about critical exponents. An analytic treatment is possible because an underlying Heun equation describing the zero mode of the phase transition has a polynomial solution. Amusingly, the treatment here may generalize for an order parameter with any integer spin, and we propose a Lagrangian for a spin two holographic superconductor.

hep-th↗

arXiv2010

Gauge gravity duality for d-wave superconductors: prospects and challenges

We write down an action for a charged, massive spin two field in a fixed Einstein background. Despite some technical problems, we argue that in an effective field theory framework and in the context of the AdS/CFT correspondence, this action can be used to study the properties of a superfluid phase transition with a d-wave order parameter in a dual strongly interacting field theory. We investigate the phase diagram and the charge conductivity of the superfluid phase. We also explain how possible couplings between the spin two field and bulk fermions affect the fermion spectral function.

hep-th↗

arXiv2010

The Perfect Atom: Bound States of Supersymmetric Quantum Electrodynamics

We study hydrogen-like atoms in N=1 supersymmetric quantum electrodynamics with an electronic and a muonic family. These atoms are bound states of an anti-muon and an electron or their superpartners. The exchange of a photino converts different bound states into each other. We determine the energy eigenstates and calculate the spectrum to fourth order in the fine structure constant. A difference between these perfect atoms and non-supersymmetric ones is the absence of hyperfine structure. We organize the eigenstates into super multiplets of the underlying symmetry algebra.

hep-th↗