The information paradox: conflicts and resolutions

Many relativists have been long convinced that black hole evaporation leads to information loss or remnants. String theorists have however not been too worried about the issue, largely due to a belief that the Hawking argument for information loss is flawed in its details. A recently derived inequality shows that the Hawking argument for black holes with horizon can in fact be made rigorous. What happens instead is that in string theory black hole microstates have no horizons. Thus the evolution of radiation quanta with E ~ kT is modified by order unity at the horizon, and we resolve the information paradox. We discuss how it is still possible for E >> kT objects to see an approximate black hole like geometry. We also note some possible implications of this physics for the early Universe.Comment: 26 pages, 8 figures, Latex; (Expanded version of) proceedings for Lepton-Photon 201

Comments on black holes I: The possibility of complementarity

We comment on a recent paper of Almheiri, Marolf, Polchinski and Sully who argue against black hole complementarity based on the claim that an infalling observer 'burns' as he approaches the horizon. We show that in fact measurements made by an infalling observer outside the horizon are statistically identical for the cases of vacuum at the horizon and radiation emerging from a stretched horizon. This forces us to follow the dynamics all the way to the horizon, where we need to know the details of Planck scale physics. We note that in string theory the fuzzball structure of microstates does not give any place to 'continue through' this Planck regime. AMPS argue that interactions near the horizon preclude traditional complementarity. But the conjecture of 'fuzzball complementarity' works in the opposite way: the infalling quantum is absorbed by the fuzzball surface, and it is the resulting dynamics that is conjectured to admit a complementary description.Comment: 34 pages, 6 figures, v3: clarifications & references adde

Excitations in the deformed D1D5 CFT

We perform some simple computations for the first order deformation of the D1D5 CFT off its orbifold point. It had been shown earlier that under this deformation the vacuum state changes to a squeezed state (with the further action of a supercharge). We now start with states containing one or two initial quanta and write down the corresponding states obtained under the action of deformation operator. The result is relevant to the evolution of an initial excitation in the CFT dual to the near extremal D1D5 black hole: when a left and a right moving excitation collide in the CFT, the deformation operator spreads their energy over a larger number of quanta, thus evolving the state towards the infrared.Comment: 26 pages, Latex, 4 figure

Deforming the D1D5 CFT away from the orbifold point

The D1D5 brane bound state is believed to have an `orbifold point' in its moduli space which is the analogue of the free Yang Mills theory for the D3 brane bound state. The supergravity geometry generated by D1 and D5 branes is described by a different point in moduli space, and in moving towards this point we have to deform the CFT by a marginal operator: the `twist' which links together two copies of the CFT. In this paper we find the effect of this deformation operator on the simplest physical state of the CFT -- the Ramond vacuum. The twist deformation leads to a final state that is populated by pairs of excitations like those in a squeezed state. We find the coefficients characterizing the distribution of these particle pairs (for both bosons and fermions) and thus write this final state in closed form.Comment: 30 pages, 4 figures, Late

Black-hole entropy from supergravity superstrata states

This work of JdB was supported in part by the Foundation of Fundamental Research on Matter (FOM) and by an NWO Spinoza grant. The work of MS was supported in part by Grant-in-Aid for Young Scientists (B) 24740159 from the Japan Society for the Promotion of Science (JSPS)

Modular differential equations for characters of RCFT

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.Comment: 13 page

Emission from the D1D5 CFT: Higher Twists

We study a certain class of nonextremal D1D5 geometries and their ergoregion emission. Using a detailed CFT computation and the formalism developed in arXiv:0906.2015 [hep-th], we compute the full spectrum and rate of emission from the geometries and find exact agreement with the gravity answer. Previously, only part of the spectrum had been reproduced using a CFT description. We close with a discussion of the context and significance of the calculation.Comment: 39 pages, 6 figures, late

An Exact Fluctuating 1/2-BPS Configuration

This work explores the role of thermodynamic fluctuations in the two parameter giant and superstar configurations characterized by an ensemble of arbitrary liquid droplets or irregular shaped fuzzballs. Our analysis illustrates that the chemical and state-space geometric descriptions exhibit an intriguing set of exact pair correction functions and the global correlation lengths. The first principle of statistical mechanics shows that the possible canonical fluctuations may precisely be ascertained without any approximation. Interestingly, our intrinsic geometric study exemplifies that there exist exact fluctuating 1/2-BPS statistical configurations which involve an ensemble of microstates describing the liquid droplets or fuzzballs. The Gaussian fluctuations over an equilibrium chemical and state-space configurations accomplish a well-defined, non-degenerate, curved and regular intrinsic Riemannian manifolds for all physically admissible domains of black hole parameters. An explicit computation demonstrates that the underlying chemical correlations involve ordinary summations, whilst the state-space correlations may simply be depicted by standard polygamma functions. Our construction ascribes definite stability character to the canonical energy fluctuations and to the counting entropy associated with an arbitrary choice of excited boxes from an ensemble of ample boxes constituting a variety of Young tableaux.Comment: Minor changes, added references, 30 pages, 4 figures, PACS numbers: 04.70.-s: Physics of black holes; 04.70.-Bw: Classical black holes; 04.50.Gh Higher-dimensional black holes, black strings, and related objects; 04.60.Cf Gravitational aspects of string theory, accepted for publication in JHE

Intertwining Relations for the Deformed D1D5 CFT

The Higgs branch of the D1D5 system flows in the infrared to a two-dimensional N=(4,4) SCFT. This system is believed to have an "orbifold point" in its moduli space where the SCFT is a free sigma model with target space the symmetric product of copies of four-tori; however, at the orbifold point gravity is strongly coupled and to reach the supergravity point one needs to turn on the four exactly marginal deformations corresponding to the blow-up modes of the orbifold SCFT. Recently, technology has been developed for studying these deformations and perturbing the D1D5 CFT off its orbifold point. We present a new method for computing the general effect of a single application of the deformation operators. The method takes the form of intertwining relations that map operators in the untwisted sector before application of the deformation operator to operators in the 2-twisted sector after the application of the deformation operator. This method is computationally more direct, and may be of theoretical interest. This line of inquiry should ultimately have relevance for black hole physics.Comment: latex, 23 pages, 3 figure

Black Hole Deconstruction

A D4-D0 black hole can be deconstructed into a bound state of D0 branes with a D6-anti-D6 pair containing worldvolume fluxes. The exact spacetime solution is known and resembles a D0 accretion disk surrounding a D6-anti-D6 core. We find a scaling limit in which the disk and core drop inside an AdS_2 throat. Crossing this AdS_2 throat and the D0 accretion disk into the core, we find a second scaling region describing the D6-anti-D6 pair. It is shown that the M-theory lift of this region is AdS_3 x S^2. Surprisingly, time translations in the far asymptotic region reduce to global, rather than Poincare, time translations in this core AdS_3. We further find that the quantum mechanical ground state degeneracy reproduces the Bekenstein-Hawking entropy-area law.Comment: 11 page