Microstate solutions from black hole deconstruction

Journal of High Energy Physics, Dec 2015

We present a new family of asymptotic AdS 3 × S 2 solutions to eleven dimensional supergravity compactified on a Calabi-Yau threefold. They originate from the backreaction of S 2-wrapped M2-branes, which play a central role in the deconstruction proposal for the microscopic interpretation of the D4-D0 black hole entropy. We show that they are free of possible pathologies such as closed timelike curves and discuss their holographic interpretation.

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Microstate solutions from black hole deconstruction

HJE Microstate solutions from black hole deconstruction Joris Raeymaekers 1 2 4 Dieter Van den Bleeken 1 2 3 0 solutions to eleven di- 1 34342 Bebek , Istanbul , Turkey 2 Na Slovance 2 , 182 21 Prague 8 , Czech Republic 3 Physics Department, Bogazici University 4 Institute of Physics of the ASCR We present a new family of asymptotic AdS3 mensional supergravity compacti ed on a Calabi-Yau threefold. They originate from the backreaction of S2-wrapped M2-branes, which play a central role in the deconstruction proposal for the microscopic interpretation of the D4-D0 black hole entropy. that they are free of possible pathologies such as closed timelike curves and discuss their holographic interpretation. - M-Theory 1 Introduction: the black hole deconstruction proposal 2 E ective three-dimensional description 3 Probe approximation 4 Backreacted M2-particle in the center of AdS3 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Setting up the equations Perturbative solution Asymptotics Properties of the 3D geometry Holographic interpretation: dual eld theory Holographic one-point functions More general solutions 5 Backreacted M2-particle at nite radius 6 Lift to 5 dimensions 7 Outlook A Near-brane expansion B Holographic renormalization for 3D axion-dilaton gravity C Review of 5D axion-dilaton solutions D Killing spinors 1 5 Introduction: the black hole deconstruction proposal Starting with the seminal work of Strominger and Vafa [1], string theory has proven highly successful in giving microscopic accountings of the Bekenstein-Hawking entropy of certain supersymmetric black holes. Such accountings typically make optimal use of the protected nature of the entropy or index to do the computation in a regime where gravitational backreaction is absent and the relevant degrees of freedom are weakly coupled D-brane excitations. This approach leaves unanswered the question what the microstates evolve to in the regime where gravitational backreaction is signi cant. Furthermore, with the advent of AdS/CFT it became clear that the black hole microstates correspond to states in the Hilbert space of a CFT which captures the degrees of freedom in a near-horizon { 1 { AdS throat region. According to the standard AdS/CFT prescription, states in the CFT correspond semiclassically to turning on normalizeable uctuations of the bulk elds near the boundary, and these are expected to lead to solutions of the full string/M theory on the AdS background. E orts to construct such solutions within the supergravity approximation to string/M theory can be grouped loosely under the fuzzball or microstate geometry program (see [2] and [3] for reviews and further references), although to which extent and under which circumstances the 2-derivative low energy supergravity approximation is su cient for this purpose is still a matter of debate. In this work we will make progress towards constructing supergravity solutions carrying the same charges as a large black hole in the context of the black hole deconstruction proposal [4]. In this proposal, it is argued that the leading contribution to the entropy of a 4D black hole arises from the large degeneracy of states carried by certain wrapped M2-branes, which so far were approximated as probes in the background of other rigid constituent branes. Our goal in this work is to construct the fully backreacted solutions.1 Our solutions contain brane sources near which the supergravity approximation breaks down, as might have been expected. Following the terminology of [3] we will refer to such solutions as microstate solutions as opposed to smooth microstate geometries. Let us brie y review the main ingredients of the black hole deconstruction proposal. We start from the setup rst introduced and studied by Maldacena, Strominger and Witten (MSW) [5]: consider M-theory on the background R1;3 S1 X, with X a Calabi-Yau threefold. When the radius of the circle is small in 11D Planck units, the type IIA string theory picture is appropriate. One can consider BPS states which are point-like in R1;3, arising from wrapped (D6, D4, D2, D0) branes2 and labelled by a charge vector = (p0; pA; qA; q0). In the M-theory frame, these lift to (KK monopole, M5, M2, momentum) charges respectively, but we choose to use the IIA language throughout this paper. It is possible to construct a regular black hole carrying D4-D0 charges (0; pA; 0; q0) which breaks half of the supersymmetry of the background3 and whose Bekenstein-Hawking entropy can be computed to be: by the D4-brane. S = 2 pq0p3 where p3 DABC pApBpC where is triple self-intersection of the four-cycle in X wrapped We then proceed to take an M-theory decoupling limit R l11 ! 1 ; V 1 VX of this decoupling limit see [7]. Note that one can de ne a 't Hooft like coupling that is 1A rst attempt in this direction appeared in [6], and we will comment in detail on the relation with present work below. 2The D2/M2 brane charges discussed here, denoted as qA, should not be co (...truncated)


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Joris Raeymaekers, Dieter Van den Bleeken. Microstate solutions from black hole deconstruction, Journal of High Energy Physics, 2015, pp. 1-38, Volume 2015, Issue 12, DOI: 10.1007/JHEP12(2015)095