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Four-point correlation functions are observables of significant interest in holographic field theories. We compute an infinite family of four-point correlation functions of operators in short multiplets of 4D N=4 super Yang-Mills theory in the supergravity regime, by studying the quadratic fluctuations around non-trivial supergravity backgrounds. The supergravity backgrounds are supersymmetric smooth geometries in the family derived by Lin, Lunin and Maldacena. The light probes comprise an infinite sequence of Kaluza-Klein harmonics of the dilaton/axion. For generic parameter values, the supergravity backgrounds are dual to heavy CFT states. However we focus on the limit in which the dual CFT states become light single-particle states. The resulting all-light four-point correlators are related by superconformal Ward identities to previously known four-point correlators of half-BPS chiral primary operators. By verifying that the Ward identities are satisfied, we confirm the validity of the supergravity method., Comment: 26 pages

This report is the outcome of a field study carried out with cattle herders in northern Mursiland, Ethiopia, on behalf of Oxfam GB. Its immediate purpose was to seek the views of local herd-owners on how the pastoral economy could be strengthened, without external intervention, in a remote area prone to cattle disease and drought. A secondary focus, which emerged during the research, is the threat posed to pastoralists by government plans to encourage tourism and to construct dams on the Omo river for electricity generation. The paper considers ways of putting pressure on conservation bodies and civil authorities to protect the vital subsistence resources of the Mursi people., Introduction; Part I: Background; Part II: Herd structure and dynamics: a case study; Part III: Constraints on pastoral production; Part IV: Conclusions and recommendations; Notes; References; Appendix: A meeting to discuss disease and drought

Large classes of multi-center supergravity solutions have been constructed in the study of supersymmetric black holes and their microstates. Many smooth multi-center solutions have the same charges as supersymmetric black holes, with all centers deep inside a long black-hole-like throat. These configurations are constrained by regularity, absence of closed timelike curves, and charge quantization. Due to these constraints, constructing explicit solutions with several centers in generic arrangements, and with all parameters in physically relevant ranges, is a hard task. In this work we present an optimization algorithm, based on evolutionary algorithms and Bayesian optimization, that systematically constructs numerical solutions satisfying all constraints. We exhibit explicit examples of novel five-center and seven-center machine-precision solutions., Comment: 28 pages, 3 figures, v2: increased precision of examples; improved exposition. Python code: https://github.com/SamiRawash/Multicenter-Scaling-Solutions

The BPS sector in AdS_3/CFT_2 duality has been fertile ground for the exploration of gauge/gravity duality, from the match between black hole entropy and the CFT elliptic genus to the construction of large families of geometrical microstates and the identification of the corresponding states in the CFT. Worldsheet methods provide a tool to further explore the relation between string theory in the bulk and corresponding CFT quantities. We show how to match individual BPS strings to their counterparts in the symmetric product orbifold CFT. In the process, we find an exact match between known constructions of microstate geometries and condensates of BPS supergraviton strings, and discuss their role in the broader collection of BPS states. In particular, we explore how microstate geometries develop singularities; and how string theory resolves these singularities through the appearance of ``tensionless'' string dynamics, which is the continuation of structures found in the weak-coupling CFT into the strongly coupled regime described by string theory in the bulk. We argue that such ``tensionless'' strings are responsible for black hole microstructure in the bulk description., Comment: 47 pages, 5 figures

We compute a large collection of string worldsheet correlators describing light probes interacting with heavy black hole microstates. The heavy states consist of NS5 branes carrying momentum and/or fundamental string charge. In the fivebrane decoupling limit, worldsheet string theory on a family of such backgrounds is given by exactly solvable null-gauged WZW models. We construct physical vertex operators in these cosets, including all massless fluctuations. We first compute a large class of novel heavy-light-light-heavy correlators in the AdS$_3$ limit, where the light operators include those dual to chiral primaries of the holographically dual CFT. We compare a subset of these correlators to the holographic CFT at the symmetric product orbifold point, and find precise agreement in all cases, including for light operators in twisted sectors of the orbifold CFT. The agreement is highly non-trivial, and includes amplitudes that describe the analogue of Hawking radiation for these microstates. We further derive a formula for worldsheet correlators consisting of $n$ light insertions on these backgrounds, and discuss which subset of these correlators are likely to be protected. As a test, we compute a heavy-light five-point function, obtaining precisely the same result both from the worldsheet and the symmetric orbifold CFT. This paper is a companion to and extension of [arXiv:2203.13828]., Comment: 67 pages

Light probes interacting with heavy bound states such as black holes give rise to interesting observables containing valuable dynamical information. Recently, a family of black hole microstates was shown to admit an exact string worldsheet description. We construct the physical vertex operators of these models, and derive their form in the low-energy AdS$_3$ limit. We then compute an extensive set of novel heavy-light correlators in these backgrounds. A subset of these provide the first match between worldsheet correlators in black hole microstates and the holographically dual conformal field theory, in a highly non-trivial way. We further conjecture a closed formula for heavy-light correlators with an arbitrary number of light insertions. As an application, we compute the analogue of the Hawking radiation rate for these microstates., Comment: 5 pages + references. v2: minor improvements to exposition

Gravitational solutions involving shockwaves have attracted significant recent interest in the context of black holes and quantum chaos. Certain classes of supersymmetric two-charge black hole microstates are described by supergravity solutions containing shockwaves, that are horizonless and smooth away from the shockwave. These configurations have been used to describe how black hole microstates absorb and scramble perturbations. In this paper we construct the first family of asymptotically flat supersymmetric three-charge microstate solutions that contain shockwaves. We identify a family of holographically dual states of the D1-D5 CFT and show that these pass a set of tests, including a precision holographic test. We find precise agreement between gravity and CFT. Our results may prove useful for constructing more general families of black hole microstate solutions., Comment: 40 pages, v2: typos fixed

Given an asymptotically Anti-de Sitter supergravity solution, one can obtain a microscopic interpretation by identifying the corresponding state in the holographically dual conformal field theory. This is of particular importance for heavy pure states that are candidate black hole microstates. Expectation values of light operators in such heavy CFT states are encoded in the asymptotic expansion of the dual bulk configuration. In the D1-D5 system, large families of heavy pure CFT states have been proposed to be holographically dual to smooth horizonless supergravity solutions. We derive the precision holographic dictionary in a new sector of light operators that are superdescendants of scalar chiral primaries of dimension (1,1). These operators involve the action of the supercharges of the chiral algebra, and they play a central role in the proposed holographic description of recently-constructed supergravity solutions known as "supercharged superstrata". We resolve the mixing of single-trace and multi-trace operators in the CFT to identify the combinations that are dual to single-particle states in the bulk. We identify the corresponding gauge-invariant combinations of supergravity fields. We use this expanded dictionary to probe the proposed holographic description of supercharged superstrata, finding precise agreement between gravity and CFT., Comment: 50 pages, v3: typos fixed

Recently an exact worldsheet description of strings propagating in certain black hole microstate geometries was constructed in terms of null-gauged WZW models. In this paper we consider a family of such coset models, in which the currents being gauged are specified by a set of parameters that a priori take arbitrary values. We show that consistency of the spectrum of the worldsheet CFT implies a set of quantisation conditions and parity restrictions on the gauging parameters. We also derive these constraints from an independent geometrical analysis of smoothness, absence of horizons and absence of closed timelike curves. This allows us to prove that the complete set of consistent backgrounds in this class of models is precisely the general family of (NS5-decoupled) non-BPS solutions known as the JMaRT solutions, together with their various (BPS and non-BPS) limits. We clarify several aspects of these backgrounds by expressing their six-dimensional solutions explicitly in terms of five non-negative integers and a single length-scale. Finally we study non-trivial two-charge limits, and exhibit a novel set of non-BPS supergravity solutions describing bound states of NS5 branes carrying momentum charge., Comment: 43 pages, v3: typos corrected

We explore the stringy structure of 1/2-BPS bound states of NS fivebranes carrying momentum or fundamental string charge, in the decoupling limits leading to little string theory and to AdS3/CFT2 duality. We develop an exact worldsheet description of these states using null-gauged sigma models, and illustrate the construction by deriving the closed-form solution sourced by an elliptical NS5-F1 supertube. The Calabi-Yau/Landau-Ginsburg correspondence maps this geometrical worldsheet description to a non-compact LG model whose superpotential is determined by the fivebrane source configuration. Singular limits of the 1/2-BPS configuration space result when the fivebrane worldvolume self-intersects, as can be seen from both sides of the CY/LG duality - on the Landau-Ginsburg side from the degeneration of the superpotential(s), and on the geometrical side from an analysis of D-brane probes. These singular limits are a portal to black hole formation via the condensation of the branes that are becoming massless, and thus exhibit in the gravitational bulk description the central actors in the non-gravitational dual theory underlying black hole thermodynamics., Comment: 65 pages, 12 figures. v2: minor corrections

At high energy densities, fivebranes are populated by a Hagedorn phase of so-called "little strings", whose statistical mechanics underlies black fivebrane thermodynamics. A particular limit of this phase yields BTZ black holes in $AdS_3$, leading us to the idea that in this context fuzzballs and highly excited little strings are one and the same. We explore these ideas through an analysis of D-brane probes of fivebrane supertube backgrounds. String theory dynamics on these backgrounds is described by an exactly solvable null-gauged WZW model. We develop the formalism of null gauging on worldsheets with boundaries, and find that D-branes wrapping topology at the bottom of the supertube throat are avatars of the "long string" structure that dominates the thermodynamics of the black hole regime, appearing here as excitations of supertubes lying near but slightly outside the black hole regime., Comment: 78 pages, 15 figures. v2: references added

Holography can provide a microscopic interpretation of a gravitational solution as corresponding to a particular CFT state: the asymptotic expansion in gravity encodes the expectation values of operators in the dual CFT state. Such a correspondence is particularly valuable in black hole physics. We study supersymmetric D1-D5-P black holes, for which recently constructed microstate solutions known as "superstrata" provide strong motivation to derive the explicit D1-D5 holographic dictionary for CFT operators of total dimension two. In this work we derive the explicit map between one-point functions of scalar chiral primaries of dimension (1,1) and the asymptotic expansions of families of asymptotically AdS$_3\times$S$^3 \times$M supergravity solutions, with M either T$^4$ or K3. We include all possible mixings between single-trace and multi-trace operators. We perform several tests of the holographic map, including new precision holographic tests of superstrata, that provide strong supporting evidence for the proposed dual CFT states., Comment: 44 pages, v2: minor edits and typo fixes

It has been suggested by A. Sen that the entropy of two-charge supersymmetric bound states in string theory should be accounted for by adding the entropy of source-free horizonless supergravity solutions to the entropy associated with the horizons of small black holes. This would imply that the entropy arises differently depending on the duality frame: in the D1-D5 frame one would count source-free horizonless solutions, while in the NS1-P frame one would compute the area of a horizon. This might lead to the belief that the microstates are described by fuzzball solutions in the D1-D5 duality frame but by a black hole with a horizon in the latter. We argue that this is not the case, and that the microstates are fuzzballs in all duality frames. We observe that the scaling argument used by Sen fails to account for the entropy in the D1-P and other duality frames. We also note that the traditional extremal black hole solution is not a complete string background, since finite-action paths connect the exterior near-horizon extremal throat to the region inside the horizon, including the singularity. The singularity of the traditional black hole solution does not give a valid boundary condition for a fundamental string; correcting this condition by resolving the singularity modifies the black hole to a fuzzball with no horizon. We argue that for questions of counting states, the traditional black hole solution should be understood through its Euclidean continuation as a saddle point, and that the Lorentzian states being counted are fuzzballs in all duality frames., Comment: 26 pages, 1 figure

AdS$_2$ plays an extremely important role in black-hole physics. We construct several infinite families of supergravity solutions that are asymptotically AdS$_2$ in the UV, and terminate in the IR with a cap that is singular in two dimensions but smooth in ten dimensions. These solutions break conformal invariance, and should correspond to supersymmetric ground states of a holographically dual CFT$_1$. We solve the free massless scalar wave equation on a family of these solutions, finding towers of finite-energy normalizable bound-state excitations. We discuss the intriguing possibility that these excitations correspond to time-dependent excitations of the dual CFT$_1$, which would imply that this CFT$_1$ is dynamical rather than topological, and hence cannot have a conformally invariant ground state., Comment: 50 pages, 5 figures, v2: typos corrected, reference added

String theory dynamics on certain fivebrane supertube backgrounds is described by an exactly solvable null-gauged WZW model. We use this description to compute the spectrum of closed string excitations on the three-charge non-supersymmetric solution found by Jejjala, Madden, Ross and Titchener, as well as its supersymmetric limit. The low-lying spectrum matches that of supergravity modes in the effective geometry and exhibits an underlying group-theoretic structure. Winding sectors describe strings carrying the same charges as the background; processes whereby strings turn into flux or vice-versa are mediated by large gauge transformations on the worldsheet. The S-matrix of such wound strings probes microstructure of the fivebrane source that is hidden in the supergravity approximation., Comment: 54 pages; version published in JHEP

We construct an infinite family of smooth asymptotically-flat supergravity solutions that have the same charges and angular momenta as general supersymmetric D1-D5-P black holes, but have no horizon. These solutions resemble the corresponding black hole to arbitrary accuracy outside of the horizon: they have asymptotically flat regions, AdS_3 x S^3 throats and very-near-horizon AdS_2 throats, which however end in a smooth cap rather than an event horizon. The angular momenta of the solutions are general, and in particular can take arbitrarily small values. Upon taking the AdS_3 x S^3 decoupling limit, we identify the holographically-dual CFT states., Comment: 49 pages, 3 figures

The study of non-supersymmetric black hole microstates offers the potential to resolve the black hole information paradox. A system of equations was recently obtained that enables the systematic construction of non-supersymmetric smooth horizonless supergravity solutions, that are candidates to describe microstates of non-extremal black holes. Within this system we construct a family of six-dimensional supergravity solutions that feature two topologically-nontrivial three-cycles known as bolts. The two bolts touch at a single point and are supported by fluxes. We find that the fluxes on the two three-cycles can be either aligned or anti-aligned, and exhibit examples of both. We present several examples of smooth solutions, including near-extremal solutions that have an approximate AdS$_3$ region, and far-from extremal solutions that have arbitrarily small charge compared to their mass., Comment: 41 pages, v2: typos corrected, published version

We examine some recently-constructed families of asymptotically-AdS$_3 \times$S$^3$ supergravity solutions that have the same charges and mass as supersymmetric D1-D5-P black holes, but that cap off smoothly with no horizon. These solutions, known as superstrata, are quite complicated, however we show that, for an infinite family of solutions, the null geodesic problem is completely integrable, due to the existence of a non-trivial conformal Killing tensor that provides a quadratic conservation law for null geodesics. This implies that the massless scalar wave equation is separable. For another infinite family of solutions, we find that there is a non-trivial conformal Killing tensor only when the left-moving angular momentum of the massless scalar is zero. We also show that, for both these families, the metric degrees of freedom have the form they would take if they arose from a consistent truncation on S$^3$ down to a (2+1)-dimensional space-time. We discuss some of the broader consequences of these special properties for the physics of these black-hole microstate geometries., Comment: 24 pages, 1 figure

The low-energy description of wrapped M5 branes in compactifications of M-theory on a Calabi-Yau threefold times a circle is given by a conformal field theory studied by Maldacena, Strominger and Witten and known as the MSW CFT. Taking the threefold to be T$^6$ or K3xT$^2$, we construct a map between a sub-sector of this CFT and a sub-sector of the D1-D5 CFT. We demonstrate this map by considering a set of D1-D5 CFT states that have smooth horizonless bulk duals, and explicitly constructing the supergravity solutions dual to the corresponding states of the MSW CFT. We thus obtain the largest known class of solutions dual to MSW CFT microstates, and demonstrate that five-dimensional ungauged supergravity admits much larger families of smooth horizonless solutions than previously known., Comment: 48 pages, v2: typos corrected, references added

We introduce a solvable system of equations that describes non-extremal multicenter solutions to six-dimensional ungauged supergravity coupled to tensor multiplets. The system involves a set of functions on a three-dimensional base metric. We obtain a family of non-extremal axisymmetric solutions that generalize the known multicenter extremal solutions, using a particular base metric that introduces a bolt. We analyze the conditions for regularity, and in doing so we show that this family does not include solutions that contain an extremal black hole and a smooth bolt. We determine the constraints that are necessary to obtain smooth horizonless solutions involving a bolt and an arbitrary number of Gibbons-Hawking centers., Comment: 32 pages

We construct the first family of horizonless supergravity solutions that have the same mass, charges and angular momenta as general supersymmetric rotating D1-D5-P black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well-approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the holographically-dual states in the N=(4,4) D1-D5 orbifold CFT. Our solutions are among the states counted by the CFT elliptic genus, and provide examples of smooth microstate geometries within the ensemble of supersymmetric black-hole microstates., Comment: 5 pages, 1 figure

Antibranes provide some of the most generic ways to uplift Anti-de Sitter flux compactifications to de Sitter, and there is a growing body of evidence that antibranes placed in long warped throats such as the Klebanov-Strassler warped deformed conifold solution have a brane-brane-repelling tachyon. This tachyon was first found in the regime of parameters in which the backreaction of the antibranes is large, and its existence was inferred from a highly nontrivial cancellation of certain terms in the inter-brane potential. We use a brane effective action approach, similar to that proposed by Michel, Mintun, Polchinski, Puhm and Saad in arXiv:1412.5702, to analyze antibranes in Klebanov-Strassler when their backreaction is small, and find a regime of parameters where all perturbative contributions to the action can be computed explicitly. We find that the cancellation found at strong coupling is also present in the weak-coupling regime, and we establish its existence to all loops. Our calculation indicates that the spectrum of the antibrane worldvolume theory is not gapped, and may generically have a tachyon. Hence uplifting mechanisms involving antibranes remain questionable even when backreaction is small., Comment: 27 pages, 5 figures, v2: Added clarification of statements, version accepted for publication in JHEP

Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions., Comment: 68 pages, v3: minor clarifications, typos corrected

We construct the first smooth horizonless supergravity solutions that have two topologically-nontrivial three-cycles supported by flux, and that have the same mass and charges as a non-extremal D1-D5-P black hole. Our configurations are solutions to six-dimensional ungauged supergravity coupled to a tensor multiplet, and uplift to solutions of Type IIB supergravity. The solutions represent multi-center generalizations of the non-BPS solutions of Jejjala, Madden, Ross, and Titchener, which have over-rotating angular momenta. By adding an additional Gibbons-Hawking center, we succeed in lowering one of the two angular momenta below the cosmic censorship bound, and bringing the other very close to this bound. Our results demonstrate that it is possible to construct multi-center horizonless solutions corresponding to non-extremal black holes, and offer the prospect of ultimately establishing that finite-temperature black holes have nontrivial structure at the horizon., Comment: 40 pages

Non-supersymmetric black hole microstates are of great interest in the context of the black hole information paradox. We identify the holographic description of the general class of non-supersymmetric orbifolded D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. This class includes both completely smooth solutions and solutions with conical defects, and in the near-decoupling limit these solutions describe degrees of freedom in the cap region. The CFT description involves a general class of states obtained by fractional spectral flow in both left-moving and right-moving sectors, generalizing previous work which studied special cases in this class. We compute the massless scalar emission spectrum and emission rates in both gravity and CFT and find perfect agreement, thereby providing strong evidence for our proposed identification. We also investigate the physics of ergoregion emission as pair creation for these orbifolded solutions. Our results represent the largest class of non-supersymmetric black hole microstate geometries with identified CFT duals presently known., Comment: 35 pages, v2: comments added, typos corrected, reference added

The D1D5 CFT gives a holographic dual description of a near-extremal black hole in string theory. The interaction in this theory is given by a marginal deformation operator, which is composed of supercharges acting on a twist operator. The twist operator links together different copies of a free CFT. We study the effect of this deformation operator when it links together CFT copies with winding numbers M and N to produce a copy with winding M+N, populated with excitations of a particular form. We compute the effect of the deformation operator in the full supersymmetric theory, firstly on a Ramond-Ramond ground state and secondly on states with an initial bosonic or fermionic excitation. Our results generalize recent work which studied only the bosonic sector of the CFT. Our findings are a step towards understanding thermalization in the D1D5 CFT, which is related to black hole formation and evaporation in the bulk., Comment: 54 pages, 3 figures, v3: typos corrected

The D1D5 CFT is a holographic dual of a near-extremal black hole in string theory. The interaction in this theory involves a twist operator which joins together different copies of a free CFT. Given a large number of D1 and D5 branes, the effective length of the circle on which the CFT lives is very large. We develop a technique to study the effect of the twist operator in the limit where the wavelengths of excitations are short compared to this effective length, which we call the 'continuum limit'. The method uses Bogoliubov coefficients to compute the effect of the twist operator in this limit. For bosonic fields, we use the method to reproduce recent results describing the effect of the twist operator when it links together CFT copies with windings M and N, producing a copy of winding M+N. We also comment on possible generalizations of our results. The methods developed here may help in understanding the twist interaction at higher orders. This in turn should provide insight into the thermalization process in the D1D5 CFT, which gives a holographic description of black hole formation., Comment: 51 pages, 2 figures

The D1D5 CFT has been very useful in the study of black holes. The interaction in this theory involves a twist operator, which links together different copies of a free CFT. For the bosonic fields, we examine the action of this twist when it links together CFT copies with winding numbers M and N to produce a copy with winding M+N. Starting with the vacuum state generates a squeezed state, which we compute. Starting with an initial excitation on one of the copies gives a linear combination of excitations on the final state, which we also compute. These results generalize earlier computations where these quantities were computed for the special case M=N=1. Our results should help in understanding the thermalization process in the D1D5 CFT, which gives the dual of black hole formation in the bulk., Comment: 25 pages, 2 figures, v3: minor clarifications

The construction of neutral black hole microstates is an important problem, with implications for the information paradox. In this paper we conjecture a construction of non-supersymmetric supergravity solutions describing D-brane configurations which carry mass and angular momentum, but no other conserved charges. We first study a classical string solution which locally carries dipole winding and momentum charges in two compact directions, but globally carries no net winding or momentum charge. We investigate its backreaction in the D1-D5 duality frame, where this object becomes a supertube which locally carries oscillating dipole D1-D5 and NS1-NS5 charges, and again carries no net charge. In the limit of an infinite straight supertube, we find an exact supergravity solution describing this object. We conjecture that a similar construction may be carried out based on a class of two-charge non-supersymmetric D1-D5 solutions. These results are a step towards demonstrating how neutral black hole microstates may be constructed in string theory., Comment: 24 pages, 2 figures, v3: estimate of radiation rate added, references added

A lot of confusion surrounds the issue of black hole complementarity, because the question has been considered without discussing the mechanism which guarantees unitarity. Considering such a mechanism leads to the following: (1) The Hawking quanta with energy E of order the black hole temperature T carry information, and so only appropriate processes involving E>>T quanta can have any possible complementary description with an information-free horizon; (2) The stretched horizon describes all possible black hole states with a given mass M, and it must expand out to a distance s_{bubble} before it can accept additional infalling bits; (3) The Hawking radiation has a specific low temperature T, and infalling quanta interact significantly with it only within a distance s_{alpha} of the horizon. One finds s_{alpha} << s_{bubble} for E>>T, and this removes the argument against complementarity recently made by Almheiri et al. In particular, the condition E>>T leads to the notion of 'fuzzball complementarity', where the modes around the horizon are indeed correctly entangled in the complementary picture to give the vacuum., Comment: 52 pages, 13 figures, v3: comments on Rindler space added, references added

The geometries describing D1-D5-P bound states in string theory have three regions: flat asymptotics, an anti-de Sitter throat, and a 'cap' region at the bottom of the throat. We identify the CFT description of a known class of supersymmetric D1-D5-P microstate geometries which describe degrees of freedom in the cap region. The class includes both regular solutions and solutions with conical defects, and generalizes configurations with known CFT descriptions: a parameter related to spectral flow in the CFT is generalized from integer to fractional values. We provide strong evidence for this identification by comparing the massless scalar excitation spectrum between gravity and CFT and finding exact agreement., Comment: 37 pages, 1 figure, v2: comment added, typos corrected, references added

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 added

We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a travelling-wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T^4. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state., Comment: 37 pages

In this talk we review recent calculations of the asymptotic supergravity fields sourced by bound states of D1 and D5-branes carrying travelling waves. We compute disk one-point functions for the massless closed string fields. At large distances from the branes, the effective open string coupling is small, even in the regime of parameters where the classical D1-D5-P black hole may be considered. The fields sourced by the branes differ from the black hole solution by various multipole moments, and have led to the construction of a new 1/8-BPS ansatz in type IIB supergravity., Comment: 14 pages, 3 figures, Contribution to the proceedings of the Black Objects in Supergravity School, Frascati, 2011

If one attempts to add momentum-carrying waves to a black string then the solution develops a singularity at the horizon; this is a manifestation of the 'no hair theorem' for black objects. However individual microstates of a black string do not have a horizon, and so the above theorem does not apply. We construct a perturbation that adds momentum to a family of microstates of the extremal D1-D5 string. This perturbation is analogous to the 'singleton' mode localized at the boundary of AdS; to leading order it is pure gauge in the AdS interior of the geometry., Comment: 24 pages, 4 figures

The bound states of the D1D5 brane system have a known gravitational description: flat asymptotics, an anti-de Sitter region, and a 'cap' ending the AdS region. We construct perturbations that correspond to the action of chiral algebra generators on Ramond ground states of D1D5 branes. Abstract arguments in the literature suggest that the perturbation should be pure gauge in the AdS region; our perturbation indeed has this structure, with the nontrivial deformation of the geometry occurring at the 'neck' between the AdS region and asymptotic infinity. This 'non-gauge' deformation is needed to provide the nonzero energy and momentum carried by the perturbation. We also suggest implications this structure may have for the majority of microstates which live at the cap., Comment: 41 pages, 6 figures, v2: cross-check of results added, to appear in JHEP

We derive the long range supergravity fields sourced by a D1-D5-P bound state from disk amplitudes for massless closed string emission. We suggest that since the parameter controlling the string perturbation expansion for this calculation decreases with distance from the bound state, the resulting asymptotic fields are valid even in the regime of parameters in which there is a classical black hole solution with the same charges. The supergravity fields differ from the black hole solution by multipole moments and are more general than those contained within known classes of solutions in the literature, whilst still preserving four supersymmetries. Our results support the conjecture that the black hole solution should be interpreted as a coarse-grained description rather than an exact description of the gravitational field sourced by D1-D5-P bound states in this regime of parameters., Comment: 48 pages, 2 figures, v2: typos corrected

We calculate the supergravity fields sourced by a D-brane with a null travelling wave from disk amplitudes in type IIB string theory compactified on T^4 x S^1. The amplitudes reproduce all the non-trivial features of the previously known two-charge supergravity solutions in the D-brane/momentum frame, providing a direct link between the microscopic bound states and their macroscopic descriptions., Comment: 13 pages, v2: minor typos corrected, published version

The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition. The Brauer algebra basis for complex matrix models developed earlier is useful in projecting to a sector which matches the state counting of N free fermions on a circle. The Brauer algebra projection is characterized by the vanishing of a scale invariant laplacian constructed from the complex matrix. The special case of N=2 is studied in detail: the ring of gauge invariant functions as well as a ring of scale and gauge invariant differential operators are characterized completely. The orthonormal basis of wavefunctions in this special case is completely characterized by a set of five commuting Hamiltonians, which display free particle structures. Applications to the reduced matrix quantum mechanics coming from radial quantization in N=4 SYM are described. We propose that the string dual of the complex matrix harmonic oscillator quantum mechanics has an interpretation in terms of strings and branes in 2+1 dimensions., Comment: 64 pages, v2: Exposition improved, minor corrections; v3: Typos corrected, published version

Structural relaxation in the peptide model N-methylacetamide (NMA) is studied experimentally by ultrafast optical Kerr-effect spectroscopy over the normal-liquid temperature range and compared to the relaxation measured in water at room temperature. It is seen that in both hydrogen-bonding liquids, beta relaxation is present and in each case it is found that this can be described by the Cole-Cole function. For NMA in this temperature range, the alpha and beta relaxations are each found to have an Arrhenius temperature dependence with indistinguishable activation energies. It is known that the variations on the Debye function, including the Cole-Cole function, are unphysical, and we introduce two general modifications: one allows for the initial rise of the function, determined by the librational frequencies, and the second allows the function to be terminated in the alpha relaxation.

When salts are added to water, the viscosity generally increases suggesting the ions increase the strength of the water's hydrogen-bond network. However, infrared pump-probe measurements on electrolyte solutions have found that ions have no influence on the rotational dynamics of water molecules implying no enhance-ment or breakdown of the hydrogen-bond network. Here we report optical Kerr-effect and dielectric relaxa-tion spectroscopic measurements, which have enabled us to separate the effects of rotational and transitional motions of the water molecules. These data show that electrolyte solutions behave like a supercooled liquid approaching a glass transition in which rotational and translational molecular motions are decoupled. It is now possible to understand previously conflicting viscosity data, nuclear magnetic resonance relaxation, and ultrafast infrared spectroscopy in a single unified picture.