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.
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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)