We show that the near-brane back-reaction of M2 branes ending on M5 branes has a rich “spike structure” that is determined by partitioning the numbers of M2 branes that are terminating on groups of M5 branes. The near-brane limit of the metric describing these branes has an AdS factor, implying the existence of a dual CFT. Each partition of the M2 and M5 charges among spikes gives rise to a different “mohawk” revealing a new layer of brane fractionation. We conjecture that all these mohawks are dual to ground states of near-brane-intersection CFT’s. We show that the supergravity solutions describing these mohawks are part of the large families of AdS × $\textit{S}$ × $\textit{S}$ solutions described in [1]. We identify precisely which of these families are relevant to brane intersections and show that the AdS invariance emerges from the self-similarity of the spikes.

France

Iosif Bena

Soumangsu Chakraborty

Dimitrios Toulikas

United States

Nicholas Warner

The M2-M5 Mohawk

We provide a new roadmap for constructing microstates of non-extremal black holes in supergravity. First, we review the non-linear sigma model of five-dimensional supergravity governing stationary solutions with a U(1) isometry and present the first generalized Ernst formulation of this model. We then revisit solution-generating techniques associated to the coset model symmetry, Ernst formalism and inverse scattering method. While some of these techniques have been extensively used to generate non-extremal black holes and black rings in supergravity, we demonstrate how they can be adapted to construct systematically non-BPS smooth horizonless geometries that have the same mass and charges as non-extremal black holes. To illustrate these methods, we construct novel static solutions of this type, including a non-BPS generalization of the $$ \frac{1}{2} $$ -BPS Gibbons-Hawking center, which has served as the fundamental building block of multicenter microstates of BPS black holes.

Pierre Heidmann

Microstates of non-extremal black holes: a new hope

In [1], it was pointed out that superstring theory on with ( , ) -field background and / = $$ \sqrt{k} $$ < 1 is dual to a symmetric product CFT deformed by an operator in the twisted sector. We generalize the analysis of [1] to > 1, and show that the resulting picture matches that discussed in the bosonic case in [2]. We argue that in the critical case, = 1 [3], the twisted deformation remains non-trivial. This resolves some confusions in the literature.

Israel

Amit Giveon

David Kutasov

Effective

We revisit the problem of computing the determinant of Klein-Gordon operator ∆ = −∇2 + M 2 on Euclideanized AdS 3 with the Euclideanized time coordinate compactified with period β, H 3/Z, by explicitly computing its eigenvalues and computing their product. Upon assuming that eigenfunctions are normalizable on H 3/Z, we found that there are no such eigenfunctions. Upon closer examination, we discover that the intuition that H 3/Z is like a box with normalizable eigenfunctions was false, and that there is, instead, a set of eigenfunctions which forms a continuum. Somewhat to our surprise, we find that there is a different operator   <math> <mover> <mtext>∆</mtext> <mo>~</mo> </mover> </math>  $$ \overset{\sim }{\Delta } $$  = r 2∆, which has the property that (1) the determinant of ∆ and the determinant of r 2∆ have the same dependence on β, and that (2) the Green’s function of ∆ can be spectrally decomposed into eigenfunctions of   <math> <mover> <mtext>∆</mtext> <mo>~</mo> </mover> </math>  $$ \overset{\sim }{\Delta } $$ . We identify the   <math> <mover> <mtext>∆</mtext> <mo>~</mo> </mover> </math>  $$ \overset{\sim }{\Delta } $$  operator as the “weighted Laplacian” in the context of warped compactifications, and comment on possible applications.

Akikazu Hashimoto

Brazil

Horatiu Nastase

Path integral of free fields and the determinant of Laplacian in warped space-time

We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized   <math> <msub> <mi>J</mi> <mn>3</mn> </msub> <msub> <mover> <mi>J</mi> <mo>¯</mo> </mover> <mn>3</mn> </msub> </math>  $$ {J}_3{\overline{J}}_3 $$  deformed AdS 3 with periodic Euclidean time as an integral transform of the partition function of the undeformed Euclideanized AdS 3. Such a deformation is interpretable as an irrelevant “single-trace   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformation” of the boundary. We will do this by first establishing a formal procedure to compute a worldsheet torus zero point function for an exactly marginal   <math> <mi>J</mi> <mover> <mi>J</mi> <mo>¯</mo> </mover> </math>  $$ J\overline{J} $$  deformation of a sigma model with U(1) L  × U(1) R  global symmetry. We then describe how this procedure is implemented on SL(2, R) sigma model and its Euclidean continuation. Finally, we describe the embedding of the deformed SL(2, R) torus amplitude into critical string theory and interpret the result as the leading perturbative contribution to the thermal partition function of the deformed theory.

Thermal partition function of   <math> <msub> <mi>J</mi> <mn>3</mn> </msub> <msub> <mover> <mi>J</mi> <mo>¯</mo> </mover> <mn>3</mn> </msub> </math>  $$ {J}_3{\overline{J}}_3 $$  deformed AdS 3

Aspects of superstring theory on deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  holography, are presented. The excitation energy of a singly wound long string plus its contribution to the energy of the black hole, 1/p fraction of the black-hole energy, is the same as that in   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformed CFT2 with c = 6k. This supports the claim that the black hole can be thought of as a state in a symmetric product of p CFT2’s of central charge 6k, where the black-hole energy is split equally among all p factors. A comment on superstring theory on deformed global AdS3 is also presented.

On string theory on deformed BTZ and   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \textrm{T}\overline{\textrm{T}} $$

We continue our exploration of the holographic duality between string theory in backgrounds that interpolate between asymptotically linear dilaton spacetime in the UV and <math altimg='si2.svg'><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math> in the IR, and the corresponding boundary theories. In previous papers, <cross-refs refid='br0010 br0020' id='crs0010'>[1,2]</cross-refs>, we showed that states in the bulk theory that are described by non-trivial asymptotically linear dilaton geometries, such as black holes and deformed global <math altimg='si2.svg'><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math>, can be described in the boundary theory by a single-trace <math altimg='si1.svg'><mi>T</mi><mover accent='true'><mrow><mi>T</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> deformation of a symmetric product theory. In those papers, we restricted to states with vanishing (angular) momentum; in this paper, we extend the analysis to states with arbitrary momentum, and show that the picture presented in the earlier papers generalizes to this case.

Netherlands

Momentum in single-trace <math altimg='si1.svg'><mi>T</mi><mover accent='true'><mrow><mi>T</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> holography

We construct a two-parameter four-dimensional non-BPS NS-NS smooth microstate solution that asymptotes to flat spacetime with a linear dilaton in type II superstring theory. From the microscopic point of view, the background is made out of a certain number of decoupled (i.e. g  s  → 0) NS5 branes wrapping T 3 × S 1 × S 1 with fundamental strings wrapping non-contractable cycles of S 1 × S 1 with integer momentum modes along them. We show that perturbative worldsheet theory in this background is given by a null-gauged WZW model. We also show that the consistency of the worldsheet theory imposes non-trivial constraints on the supergravity background.

Shaun Hampton

A 4d non-BPS NS-NS microstate

We explore the holographic duality between string theory in backgrounds that interpolate between asymptotically linear dilaton spacetime in the UV and AdS 3 in the IR, and single-trace   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformed CFT. In particular, we explain how the deformation of states in the boundary theory is reflected in the bulk geometry, and show that the coupling above which the deformed energy of the SL(2, ℝ) invariant ground state of the IR CFT becomes complex is a maximal coupling.

Comments on single-trace   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  holography

We compute the leading correction to entanglement entropy in   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformed massive QFTs. We show that both for massive scalar and Dirac fermion, the leading order correction to the entanglement entropy of half space comes from the boundary of the entangling surface. For the case of massive scalar, the boundary term is finite while for massive fermion, it diverges logarithmically giving rise to an additional log-square divergence in the entanglement entropy.