arXiv subjects

Suvrat Raju

Publications and source records attributed to Suvrat Raju.

At least 37 records · Page 2Linked to original sources

arXiv2021

Lessons from the Information Paradox

We review recent progress on the information paradox. We explain why exponentially small correlations in the radiation emitted by a black hole are sufficient to resolve the original paradox put forward by Hawking. We then describe a refinement of the paradox that makes essential reference to the black-hole interior. This analysis leads to a broadly-applicable physical principle: in a theory of quantum gravity, a copy of all the information on a Cauchy slice is also available near the boundary of the slice. This principle can be made precise and established -- under weak assumptions, and using only low-energy techniques -- in asymptotically global AdS and in four dimensional asymptotically flat spacetime. When applied to black holes, this principle tells us that the exterior of the black hole always retains a complete copy of the information in the interior. We show that accounting for this redundancy provides a resolution of the information paradox for evaporating black holes and, conversely, that ignoring this redundancy leads to paradoxes even in the absence of black holes. We relate this perspective to recent computations of the Page curve for holographic CFTs coupled to nongravitational baths. But we argue that such models may provide an inaccurate picture of the rate at which information can be extracted from evaporating black holes in asymptotically flat space. We discuss large black holes dual to typical states in AdS/CFT and the new paradoxes that arise in this setting. These paradoxes also extend to the eternal black hole. They can be resolved by assuming that the map between the boundary CFT and the black-hole interior is state dependent. We discuss the consistency of state-dependent bulk reconstructions. We conclude by examining the viability of arguments for firewalls, fuzzballs and other kinds of structure at the horizon.

hep-th↗

arXiv2020

The Holographic Nature of Null Infinity

We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment $(-\infty,u)$ of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space.

hep-th↗

arXiv2020

Did the Indian lockdown avert deaths?

Within the context of SEIR models, we consider a lockdown that is both imposed and lifted at an early stage of an epidemic. We show that, in these models, although such a lockdown may delay deaths, it eventually does not avert a significant number of fatalities. Therefore, in these models, the efficacy of a lockdown cannot be gauged by simply comparing figures for the deaths at the end of the lockdown with the projected figure for deaths by the same date without the lockdown. We provide a simple but robust heuristic argument to explain why this conclusion should generalize to more elaborate compartmental models. We qualitatively discuss some important effects of a lockdown, which go beyond the scope of simple models, but could cause it to increase or decrease an epidemic's final toll. Given the significance of these effects in India, and the limitations of currently available data, we conclude that simple epidemiological models cannot be used to reliably quantify the impact of the Indian lockdown on fatalities caused by the COVID-19 pandemic.

q-bio.PE↗

arXiv2019

Is Holography Implicit in Canonical Gravity?

We conjecture that, in asymptotically anti-de Sitter space, two solutions of the Wheeler-DeWitt equation that coincide asymptotically must also coincide in the bulk. This suggests that the essential elements of holography are already present in canonical gravity. Our argument sheds light on why holography works only in gravitational theories, and also on the significance of anti-de Sitter boundary conditions.

gr-qc↗

arXiv2019

A simple quantum test for smooth horizons

We develop a new test that provides a necessary condition for a quantum state to be smooth in the vicinity of a null surface: near-horizon modes that can be defined locally near any patch of the null surface must be correctly entangled with each other and with their counterparts across the surface. This test is considerably simpler to implement than a full computation of the renormalized stress-energy tensor. We apply this test to Reissner-Nordstrom black holes in asymptotically anti-de Sitter space and provide numerical evidence that the inner horizon of such black holes is singular in the Hartle-Hawking state. We then consider BTZ black holes, where we show that our criterion for smoothness is satisfied as one approaches the inner horizon from outside. This results from a remarkable conspiracy between the properties of mode-functions outside the outer horizon and between the inner and outer horizon. Moreover, we consider the extension of spacetime across the inner horizon of BTZ black holes and show that it is possible to define modes behind the inner horizon that are correctly entangled with modes in front of the inner horizon. Although this provides additional suggestions for the failure of strong cosmic censorship, we lay out several puzzles that must be resolved before concluding that the inner horizon will be traversable.

hep-th↗

arXiv2019

A Toy Model of the Information Paradox in Empty Space

A sharp version of the information paradox involves a seeming violation of the monogamy of entanglement during black hole evaporation. We construct an analogous paradox in empty anti-de Sitter space. In a local quantum field theory, Bell correlations between operators localized in mutually spacelike regions are monogamous. We show, through a controlled calculation, that this property can be violated by an order-1 factor in a theory of gravity. This example demonstrates that what appears to be a violation of the monogamy of entanglement may just be a subtle violation of locality in quantum gravity.

hep-th↗

arXiv2019

A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta

We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of these correlators is bounded by $e^{-βR}$, where $R$ is the radius of the smallest sphere that contains the polygon formed by the momenta. We show that perturbative quantum field theories can saturate this bound through suitably high-order loop diagrams. We also consider holographic theories in $d$-spacetime dimensions, where we show that the leading two-point function of generalized free-fields saturates the bound in $d = 2$ and is below the bound for $d > 2$. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.

hep-th↗

arXiv2018

A Critique of the Fuzzball Program

We explore the viability of fuzzballs as candidate microstate geometries for the black hole, and their possible role in resolutions of the information paradox. We argue that if fuzzballs provide a description of black-hole microstates, then the typical fuzzball geometry can only differ significantly from the conventional black-hole geometry at a Planck-scale-distance from the horizon. However, precisely in this region, quantum fluctuations in the fuzzball geometry become large and the fuzzball geometry becomes unreliable. We verify these expectations through a detailed calculation of quantum expectation values and quantum fluctuations in the two-charge fuzzball geometries. We then examine some of the solutions discovered in arXiv:1607.03908. We show, based on a calculation of a probe two-point function in this background, that these solutions, and others in their class, violate robust expectations about the gap in energies between successive energy eigenstates, and differ too much from the conventional black hole to represent viable microstates. We conclude that while fuzzballs are interesting star-like solutions in string theory, they do not appear to be relevant for resolving the information paradox, and cannot be used to make valid inferences about black-hole interiors.

hep-th↗

arXiv2018

Quantum information measures for restricted sets of observables

We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure the expectation values of two operators, $\langle O_1 \rangle$ and $\langle O_2 \rangle$, but may not have access to $\langle O_1 O_2 \rangle$. This problem is relevant for the study of localized quantum information in gravity since the set of approximately-local operators in a region may not be closed under arbitrary products. While we cannot naturally associate a density matrix with a state in this setting, it is still possible to define a modular operator for a state, and distinguish between two states using a relative modular operator. These operators are defined on a little Hilbert space, which parameterizes small deformations of the system away from its original state, and they do not depend on the structure of the full Hilbert space of the theory. We extract a class of relative-entropy-like quantities from the spectrum of these operators that measure the distance between states, are monotonic under contractions of the set of available observables, and vanish only when the states are equal. Consequently, these distance-measures can be used to define measures of bipartite and multipartite entanglement. We describe applications of our measures to coarse-grained and fine-grained subregion dualities in AdS/CFT and provide a few sample calculations to illustrate our formalism.

hep-th↗

arXiv2017

Loss of locality in gravitational correlators with a large number of insertions

We review lessons from the AdS/CFT correspondence that indicate that the emergence of locality in quantum gravity is contingent on considering observables with a small number of insertions. Correlation functions where the number of insertions scales with a power of the central charge of the CFT are sensitive to nonlocal effects in the bulk theory, which arise from a combination of the effects of the bulk Gauss law and a breakdown of perturbation theory. To examine whether a similar effect occurs in flat space, we consider the scattering of massless particles in the bosonic string and the superstring in the limit where the number of external particles, n, becomes very large. We use estimates of the volume of the Weil-Petersson moduli space of punctured Riemann surfaces to argue that string amplitudes grow factorially in this limit. We verify this factorial behaviour through an extensive numerical analysis of string amplitudes at large n. Our numerical calculations rely on the observation that, in the large n limit, the string scattering amplitude localizes on the Gross-Mende saddle points, even though individual particle energies are small. This factorial growth implies the breakdown of string perturbation theory for $n \sim (M_{pl}/E)^{d-2}$ in d dimensions where E is the typical individual particle energy. We explore the implications of this breakdown for the black hole information paradox. We show that the loss of locality suggested by this breakdown is precisely sufficient to resolve the cloning and strong subadditivity paradoxes.

hep-th↗

arXiv2017

Smooth Causal Patches for AdS Black Holes

We review the paradox of low energy excitations about an AdS black hole. An appropriately chosen unitary operator in the boundary theory can create a locally strong excitation near the black hole horizon, whose global energy is small as a result of the gravitational redshift. The paradox is that this seems to violate a general rule of statistical mechanics, which states that an operator with energy parametrically smaller than $k T$ cannot create a significant excitation in a thermal system. When we carefully examine the position dependence of the boundary unitary operator that produces the excitation and the bulk observable necessary to detect the anomalously large effect, we find that they do not both fit in a single causal patch. This follows from a remarkable property of position space AdS correlators that we establish explicitly, and resolves the paradox in a generic state of the system, since no combination of observers can both create the excitation and observe its effect. As a special case of our analysis, we show how this resolves the "Born rule" paradox of arXiv:1506.01337 and we verify our solution using an independent calculation. We then consider boundary states that are finely tuned to display a spontaneous excitation outside the causal patch of the infalling observer, and we propose a version of causal patch complementarity in AdS/CFT that resolves the paradox for such states as well.

hep-th↗

arXiv2017

The Sensitivity of Black Holes to Low Energy Excitations

A general principle of statistical mechanics is that low energy excitations of a thermal state change expectation values of observables by a very small amount. However some observables in the vicinity of the horizon of a large black hole in anti-de Sitter space naively seem to violate this bound. This potential violation is related to the question of whether the black hole interior can be described in AdS/CFT. Here we point out that if the possible excitations are limited to those produced by a simple local source on the boundary, and the possible observables are limited to products of field operators in a single causal patch in the bulk, then these violations disappear.

hep-th↗

arXiv2017

The Breakdown of String Perturbation Theory for Many External Particles

We consider massless string scattering amplitudes in a limit where the number of external particles becomes very large, while the energy of each particle remains small. Using the growth of the volume of the relevant moduli space, and by means of independent numerical evidence, we argue that string perturbation theory breaks down in this limit. We discuss some remarkable implications for the information paradox.

hep-th↗

arXiv2016

A toy model of black hole complementarity

We consider the algebra of simple operators defined in a time band in a CFT with a holographic dual. When the band is smaller than the light crossing time of AdS, an entire causal diamond in the center of AdS is separated from the band by a horizon. We show that this algebra obeys a version of the Reeh-Schlieder theorem: the action of the algebra on the CFT vacuum can approximate any low energy state in the CFT arbitrarily well, but no operator within the algebra can exactly annihilate the vacuum. We show how to relate local excitations in the complement of the central diamond to simple operators in the band. Local excitations within the diamond are invisible to the algebra of simple operators in the band by causality, but can be related to complicated operators called "precursors". We use the Reeh-Schlieder theorem to write down a simple and explicit formula for these precursors on the boundary. We comment on the implications of our results for black hole complementarity and the emergence of bulk locality from the boundary.

hep-th↗

arXiv2016

Estimating the frequency of nuclear accidents

We used Bayesian methods to compare the predictions of probabilistic risk assessment -- the theoretical tool used by the nuclear industry to predict the frequency of nuclear accidents -- with empirical data. The existing record of accidents with some simplifying assumptions regarding their probability distribution is sufficient to rule out the validity of the industry's analyses at a very high confidence level. We show that this conclusion is robust against any reasonable assumed variation of safety standards over time, and across regions. The debate on nuclear liability indicates that the industry has independently arrived at this conclusion. We pay special attention to the Indian situation, where we show that the existing operating experience provides insufficient data to make any reliable claims about the safety of future reactors. We briefly discuss some policy implications.

physics.soc-ph↗

arXiv2015

Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior

We revisit the "state-dependence" of the map that we proposed recently between bulk operators in the interior of a large AdS black hole and operators in the boundary CFT. By refining recent versions of the information paradox, we show that this feature is necessary for the CFT to successfully describe local physics behind the horizon --- not only for single-sided black holes but even in the eternal black hole. We show that state-dependence is invisible to an infalling observer who cannot differentiate these operators from those of ordinary quantum effective field theory. Therefore the infalling observer does not observe any violations of quantum mechanics. We successfully resolve a large class of potential ambiguities in our construction. We analyze states where the CFT is entangled with another system and show that the ER=EPR conjecture emerges from our construction in a natural and precise form. We comment on the possible semi-classical origins of state-dependence.

hep-th↗

arXiv2015

Local Operators in the Eternal Black Hole

We show that, in the AdS/CFT correspondence, states obtained by Hamiltonian evolution of the thermofield doubled state are also dual to an eternal black hole geometry, which is glued to the boundary with a time shift generated by a large diffeomorphism. We describe gauge invariant relational observables that probe the black hole interior in these states and constrain their properties using effective field theory. By adapting recent versions of the information paradox we show that these observables are necessarily described by state-dependent bulk-boundary maps, which we construct explicitly.

hep-th↗

arXiv2014

Multipoint correlators of conformal field theories: implications for quantum critical transport

We compute three-point correlators between the stress-energy tensor and conserved currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then do the computation using holography. In the holographic approach, the correlators are computed from an effective action on 3+1 dimensional anti-de Sitter space (AdS_4) proposed by Myers et al., and depend upon the co-efficient, γ, of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus fixing the values of γ. The CFTs of free fermions and bosons take the values γ=1/12,-1/12 respectively, and so saturate the bound |γ| <= 1/12 obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of γ. The value of γalso controls the frequency dependence of the conductivity, and other properties of quantum-critical transport at non-zero temperatures. Our results for the values of γlead to an appealing physical interpretation of particle-like or vortex-like transport near quantum phase transitions of interest in condensed matter physics.This paper includes appendices reviewing key features of the AdS/CFT correspondence for condensed matter physicists.

cond-mat.str-el↗