arXiv subjects

Raghu Mahajan

Publications and source records attributed to Raghu Mahajan.

33 records · Page 2Linked to original sources

arXiv2020

Entanglement islands in higher dimensions

It has been suggested in recent work that the Page curve of Hawking radiation can be recovered using computations in semi-classical gravity provided one allows for "islands" in the gravity region of quantum systems coupled to gravity. The explicit computations so far have been restricted to black holes in two-dimensional Jackiw-Teitelboim gravity. In this note, we numerically construct a five-dimensional asymptotically AdS geometry whose boundary realizes a four-dimensional Hartle-Hawking state on an eternal AdS black hole in equilibrium with a bath. We also numerically find two types of extremal surfaces: ones that correspond to having or not having an island. The version of the information paradox involving the eternal black hole exists in this setup, and it is avoided by the presence of islands. Thus, recent computations exhibiting islands in two-dimensional gravity generalize to higher dimensions as well.

hep-th↗

arXiv2019

Matrix ensembles with global symmetries and 't Hooft anomalies from 2d gauge theory

The Hilbert space of a quantum system with internal global symmetry $G$ decomposes into sectors labelled by irreducible representations of $G$. If the system is chaotic, the energies in each sector should separately resemble ordinary random matrix theory. We show that such "sector-wise" random matrix ensembles arise as the boundary dual of two-dimensional gravity with a $G$ gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the consequences of 't Hooft anomalies in the matrix ensembles, which are incorporated by adding specific topological terms to the gauge theory action. The effect is to introduce projective representations into the decomposition of the Hilbert space. Finally, we consider ensembles with $G$ symmetry and time reversal symmetry, and analyze a simple case of a mixed anomaly between time reversal and an internal $\mathbb{Z}_2$ symmetry.

hep-th↗

arXiv2019

The Page curve of Hawking radiation from semiclassical geometry

We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for "islands" in determining the entanglement wedge.

hep-th↗

arXiv2019

An Index for Quantum Integrability

The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive quantization. We define an integrability index $\mathcal{I}(J)$ for each spin $J$, with the property that $\mathcal{I}(J)$ is a lower bound on the number of quantum conserved currents of spin $J$. In particular, a positive value for the index establishes the existence of quantum conserved currents. For a general coset model, with or without extra discrete symmetries, we derive an explicit formula for a generating function that encodes the indices for all spins. We apply our techniques to the $\mathbb{CP}^{N-1}$ model, the $O(N)$ model, and the flag sigma model $\frac{U(N)}{U(1)^{N}}$. For the $O(N)$ model, we establish the existence of a spin-6 quantum conserved current, in addition to the well-known spin-4 current. The indices for the $\mathbb{CP}^{N-1}$ model for $N>2$ are all non-positive, consistent with the fact that these models are not integrable. The indices for the flag sigma model $\frac{U(N)}{U(1)^{N}}$ for $N>2$ are all negative. Thus, it is unlikely that the flag sigma models are integrable.

hep-th↗

arXiv2018

The Conformal Bootstrap at Finite Temperature

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a "thermal inversion formula" whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical $O(N)$ model at leading order in $1/N$. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.

hep-th↗

arXiv2018

Parity and the modular bootstrap

We consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation $P$. Combining $P$ with modular inversion $S$ leads to a continuous family of fixed points of the $SP$ transformation. A particular subset of this locus of fixed points exists along the line of positive left- and right-moving temperatures satisfying $β_L β_R = 4π^2$. We use this fixed locus to prove a conjecture of Hartman, Keller, and Stoica that the free energy of a large-$c$ CFT$_2$ with a suitably sparse low-lying spectrum matches that of AdS$_3$ gravity at all temperatures and all angular potentials. We also use the fixed locus to generalize the modular bootstrap equations, obtaining novel constraints on the operator spectrum and providing a new proof of the statement that the twist gap is smaller than $(c-1)/12$ when $c>1$. At large $c$ we show that the operator dimension of the first excited primary lies in a region in the $(h,\overline{h})$-plane that is significantly smaller than $h+\overline{h}<c/6$. Our results for the free energy and constraints on the operator spectrum extend to theories without parity symmetry through the construction of an auxiliary parity-invariant partition function.

hep-th↗

arXiv2018

Does the SYK model have a spin glass phase?

We argue that the Sachdev-Ye-Kitaev model has no spin glass phase, based on calculations involving both the nearly-conformal limit and the strongly-coupled Schwarzian limit of the model. This conclusion is supported by numerical computations of eigenvalue statistics with up to 46 Majorana fermions. In addition, we find numerically that the distribution of the ground state energy is Gaussian.

hep-th↗

arXiv2017

An upper bound on transport

The linear growth of operators in local quantum systems leads to an effective lightcone even if the system is non-relativistic. We show that consistency of diffusive transport with this lightcone places an upper bound on the diffusivity: $D \lesssim v^2 τ_\text{eq}$. The operator growth velocity $v$ defines the lightcone and $τ_\text{eq}$ is the local equilibration timescale, beyond which the dynamics of conserved densities is diffusive. We verify that the bound is obeyed in various weakly and strongly interacting theories. In holographic models this bound establishes a relation between the hydrodynamic and leading non-hydrodynamic quasinormal modes of planar black holes. Our bound relates transport data --- including the electrical resistivity and the shear viscosity --- to the local equilibration time, even in the absence of a quasiparticle description. In this way, the bound sheds light on the observed $T$-linear resistivity of many unconventional metals, the shear viscosity of the quark-gluon plasma and the spin transport of unitary fermions.

hep-th↗

arXiv2016

Late-time Structure of the Bunch-Davies FRW Wavefunction

In this short note we organize a perturbation theory for the Bunch-Davies wavefunction in flat, accelerating cosmologies. The calculational technique avoids the in-in formalism and instead uses an analytic continuation from Euclidean signature. We will consider both massless and conformally coupled self-interacting scalars. These calculations explicitly illustrate two facts. The first is that IR divergences get sharper as the acceleration slows. The second is that UV-divergent contact terms in the Euclidean computation can contribute to the absolute value of the wavefunction in Lorentzian signature. Here UV divergent refers to terms involving inverse powers of the radial cutoff in the Euclidean computation. In Lorentzian signature such terms encode physical time dependence of the wavefunction.

hep-th↗

arXiv2016

Entanglement structure of non-equilibrium steady states

We study the problem of calculating transport properties of interacting quantum systems, specifically electrical and thermal conductivities, by computing the non-equilibrium steady state (NESS) of the system biased by contacts. Our approach is based on the structure of entanglement in the NESS. With reasonable physical assumptions, we show that a NESS close to local equilibrium is lightly entangled and can be represented via a computationally efficient tensor network. We further argue that the NESS may be found by dynamically evolving the system within a manifold of appropriate low entanglement states. A physically realistic law of dynamical evolution is Markovian open system dynamics, or the Lindblad equation. We explore this approach in a well-studied free fermion model where comparisons with the literature are possible. We study both electrical and thermal currents with and without disorder, and compute entropic quantities such as mutual information and conditional mutual information. We conclude with a discussion of the prospects of this approach for the challenging problem of transport in strongly interacting systems, especially those with disorder.

cond-mat.str-el↗

arXiv2016

Transport in Chern-Simons-Matter Theories

The frequency-dependent longitudinal and Hall conductivities --- $σ_{xx}$ and $σ_{xy}$ --- are dimensionless functions of $ω/T$ in 2+1 dimensional CFTs at nonzero temperature. These functions characterize the spectrum of charged excitations of the theory and are basic experimental observables. We compute these conductivities for large $N$ Chern-Simons theory with fermion matter. The computation is exact in the 't Hooft coupling $λ$ at $N = \infty$. We describe various physical features of the conductivity, including an explicit relation between the weight of the delta function at $ω= 0$ in $σ_{xx}$ and the existence of infinitely many higher spin conserved currents in the theory. We also compute the conductivities perturbatively in Chern-Simons theory with scalar matter and show that the resulting functions of $ω/T$ agree with the strong coupling fermionic result. This provides a new test of the conjectured 3d bosonization duality. In matching the Hall conductivities we resolve an outstanding puzzle by carefully treating an extra anomaly that arises in the regularization scheme used.

hep-th↗

arXiv2014

Holographic mutual information and distinguishability of Wilson loop and defect operators

The mutual information of disconnected regions in large $N$ gauge theories with holographic gravity duals can undergo phase transitions. These occur when connected and disconnected bulk Ryu-Takayanagi surfaces exchange dominance. That is, the bulk `soap bubble' snaps as the boundary regions are drawn apart. We give a gauge-theoretic characterization of this transition: States with and without a certain defect operator insertion -- the defect separates the entangled spatial regions -- are shown to be perfectly distinguishable if and only if the Ryu-Takayanagi surface is connected. Meanwhile, states with and without a certain Wilson loop insertion -- the Wilson loop nontrivially threads the spatial regions -- are perfectly distinguishable if and only if the Ryu-Takayanagi surface is disconnected. The quantum relative entropy of two perfectly distinguishable states is infinite. The results are obtained by relating the soap bubble transition to Hawking-Page (deconfinement) transitions in the Renyi entropies, where defect operators and Wilson loops are known to act as order parameters.

hep-th↗

arXiv2014

Chern-Simons-Ghost Theories and de Sitter Space

We explore Chern-Simons theories coupled to fundamental ghost-like matter in the large $N$ limit at 't Hooft coupling $λ$. These theories have been conjectured to be holographically dual to parity-violating, asymptotically dS$_4$ universes with a tower of light higher-spin fields. On $\mathbb{R}^3$, to all orders in large-$N$ perturbation theory, we show that Chern-Simons-ghost theories are related to ordinary Chern-Simons-matter theories by mapping $N \rightarrow - N$ and keeping $λ$ fixed. Consequently, the bosonization duality of ordinary Chern-Simons-matter theories extends to a bosonization duality of Chern-Simons-ghost theories on $\mathbb R^3$. On $S^1 \times S^2$, in the small-$S^1$ limit, neither $N \rightarrow -N$ nor bosonization hold, as we show by extensively studying large-$N$ saddles of the theories with both ghost and ordinary matter. The partition functions we compute along the way can be viewed as pieces of the late-time Hartle-Hawking wavefunction for the bulk dS$_4$ gravity theories.

hep-th↗

arXiv2014

Transport near the Ising-nematic quantum critical point of metals in two dimensions

We consider two-dimensional metals near a Pomeranchuk instability which breaks 90$^\circ$ lattice rotation symmetry. Such metals realize strongly-coupled non-Fermi liquids with critical fluctuations of an Ising-nematic order. At low temperatures, impurity scattering provides the dominant source of momentum relaxation, and hence a non-zero electrical resistivity. We use the memory matrix method to compute the resistivity of this non-Fermi liquid to second order in the impurity potential, without assuming the existence of quasiparticles. Impurity scattering in the $d$-wave channel acts as a random "field" on the Ising-nematic order. We find contributions to the resistivity with a nearly linear temperature dependence, along with more singular terms; the most singular is the random-field contribution which diverges in the limit of zero temperature.

cond-mat.str-el↗

arXiv2013

Non-Fermi liquids and the Wiedemann-Franz law

A general discussion of the ratio of thermal and electrical conductivities in non-Fermi liquid metals is given. In metals with sharp Drude peaks, the relevant physics is correctly organized around the slow relaxation of almost-conserved momenta. While in Fermi liquids both currents and momenta relax slowly, due to the weakness of interactions among low energy excitations, in strongly interacting non-Fermi liquids typically only momenta relax slowly. It follows that the conductivities of such non-Fermi liquids are obtained within a fundamentally different kinematics to Fermi liquids. Among these strongly interacting non-Fermi liquids we distinguish cases with only one almost-conserved momentum, which we term hydrodynamic metals, and with many patchwise almost-conserved momenta. For all these cases, we obtain universal expressions for the ratio of conductivities that violate the Wiedemann-Franz law. We further discuss the case in which long-lived `cold' quasiparticles, in general with unconventional scattering rates, coexist with strongly interacting hot spots, lines or bands. For these cases, we characterize circumstances under which non-Fermi liquid transport, in particular a linear in temperature resistivity, is and is not compatible with the Wiedemann-Franz law. We suggest the likely outcome of future transport experiments on CeCoIn5, YbRh2Si2 and Sr3Ru2O7 at their critical magnetic fields.

cond-mat.str-el↗