The infrared dynamics of the SYK model, as well as its associated tensor models, exhibit some of the non trivial features expected of a holographic dual of near extremal black holes. These include developing certain symmetries of the near horizon geometry and exhibiting maximal chaos. In this paper we present a generalization of these tensor models to include fields with fewer tensor indices and which can be thought of as describing probes in a black hole background. In large N limit, dynamics of the original model remain unaffected by the probe fields and some of the four point functions involving probe fields exhibit maximal chaos, a non trivial feature expected of a black hole probe.

France

Nick Halmagyi

Swapnamay Mondal

Tensor models for black hole probes

We compute the on-shell action of static, BPS black holes in AdS4 from   <math> <mi>N</mi> <mo>=</mo> <mn>2</mn> </math>  $$ \mathcal{N}=2 $$  gauged supergravity coupled to vector multiplets and show that for a certain class it is equal to minus the entropy of the black hole. Holographic renormalization is used to demonstrate that with Neumann boundary conditions on the scalar fields, the divergent and finite contributions from the asymptotic boundary vanish. The entropy arises from the extrinsic curvature on Σ g  × S 1 evaluated at the horizon, where Σ g  may have any genus g ≥ 0. This provides a clarification of the equivalence between the partition function of the twisted ABJM theory on Σ g  × S 1 and the entropy of the dual black hole solutions. It also demonstrates that the complete entropy resides on the AdS2 × Σ g  horizon geometry, implying the absence of hair for these gravity solutions.

Shailesh Lal

On the on-shell: the action of AdS4 black holes

We study Heterotic supergravity on Hyper-Kähler manifolds in the presence of non-trivial warping and three form flux with Abelian bundles in the large charge limit. We find exact, regular solutions for multi-centered Gibbons-Hawking spaces and Atiyah-Hitchin manifolds. In the case of Atiyah-Hitchin, regularity requires that the circle at infinity is of the same order as the instanton number, which is taken to be large. Alternatively there may be a non-trivial density of smeared five branes at the bolt.

Dan Israël

Matthieu Sarkis

Eirik Svanes

Heterotic Hyper-Kähler flux backgrounds

We study heterotic supergravity on the conifold and its ℤ 2 orbifold with Abelian gauge fields and three-form flux. By taking a limit of large five brane charge, we are able suppress non-linear curvature corrections and construct exact supersymmetric solutions. At large distances, these solutions are generically locally Ricci-flat, have a magnetic flux through the two-sphere at infinity as well as non-zero five-brane charge. For a given flux, our family of solutions has three real parameters, the size of the pair of two spheres in the IR and the dilaton zero mode. We present an explicit analytic solution for a decoupled near horizon region which is not asymptotically locally Ricci-flat and where for a given flux, the size of the cycles is frozen and the only parameter is the dilaton zero mode. We also present an exactly solvable worldsheet CFT for this near horizon region. When one of the two cycles has vanishing size, the near horizon region no longer exists but nonetheless we obtain a solution on the (unorbifolded) resolved conifold.

The Abelian heterotic conifold

We study N = 2 $$ \mathcal{N}=2 $$ gauged supergravity with U(1) gauge group coupled to n v vector multiplets and find quite general analytic solutions for quarter-BPS black holes with mass, NUT and dyonic Maxwell charges. The solutions we find have running scalar fields and flow in the IR region to a horizon geometry of the form AdS 2 × Σ g .

Harold Erbin

Quarter-BPS black holes in AdS 4 -NUT from N = 2 $$ \mathcal{N}=2 $$ gauged supergravity

We analyze the gauging of Abelian isometries on the hypermultiplet scalar manifolds of N $$ \mathcal{N} $$ = 2 supergravity in four dimensions. This involves a study of symmetric special quaternionic-Kähler manifolds, building on the work of de Wit and Van Proeyen. In particular we compute the general set of Killing prepotentials and associated compensators for these manifolds. This allows us to glean new insights about AdS 4 vacua which preserve the full N $$ \mathcal{N} $$ = 2 supersymmetry as well as BPS static black hole horizons.

Abelian hypermultiplet gaugings and BPS vacua in N $$ \mathcal{N} $$ =2 supergravity

We complete the study of static BPS, asymptotically AdS 4 black holes within N $$ \mathcal{N} $$ =2 FI-gauged supergravity and where the scalar manifold is a symmetric very special Kähler manifold. We find the analytic form for the general solution to the BPS equations, the horizon appears as a double root of a particular quartic polynomial whereas in previous work this quartic polynomial further factored into a pair of double roots. A new and distinguishing feature of our solutions is that the phase of the supersymmetry parameter varies throughout the black hole. The general solution has 2 n v independent parameters; there are two algebraic constraints on 2 n v + 2 charges, matching our previous analysis on BPS solutions of the form AdS 2 × Σ g . As a consequence we have proved that every BPS geometry of this form can arise as the horizon geometry of a BPS AdS 4 black hole. When specialized to the STU-model our solutions uplift to M-theory and describe a stack of M2-branes wrapped on a Riemman surface in a Calabi-Yau fivefold with internal angular momentum.

Static BPS black holes in AdS 4 with general dyonic charges

We compute four-derivative corrections to the AdS supergravity actions arising from the near-horizon geometry of N M5-branes wrapped on either one or two Riemann surfaces. This setup features the novel presence of both gauged isometries as well as nontrivial hypermultiplets. We argue that the 5d Chern-Simons terms receive not only higher-derivative corrections but also contributions from Killing vector parameters, which we find must also be corrected. We check the central charges found by our supergravity methods against the dual field theory results and find perfect agreement at leading and subleading order in N . Along the way, we find higher derivative corrections to general AdS 5 and AdS 3 × Σ g geometries.

Switzerland

Marco Baggio

Netherlands

Daniel Mayerson

Daniel Robbins

United Kingdom

Brian Wecht

Higher derivative corrections and central charges from wrapped M5-branes

We study supersymmetric probe M5-branes in the AdS 4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M 3 . This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS 4 requires it to wrap a surface embedded in an S 2 -fibration over M 3 . We find that the projection of this surface to M 3 can be either a geodesic or a tubular surface around a geodesic. These configurations preserve an extra U(1) symmetry, in addition to the one corresponding to the R-symmetry of the dual 3d N = 2 $$ \mathcal{N}=2 $$ gauge theory. BPS M2-branes can stretch between M5-branes wrapping geodesics. We interpret the addition of probe M5-branes on a closed geodesic in terms of conformal Dehn surgery.

United States

Ibrahima Bah

Germany

Maxime Gabella

BPS M5-branes as defects for the 3d-3d correspondence

We study probe M5-branes in N $$ \mathcal{N} $$ = 1 AdS 5 solutions of M-theory that arise from M5-branes wrapped on a Riemann surface. Using the BPS condition from κ -symmetry, we classify supersymmetric probe M5-branes that extend along all of AdS 5 and intersect the Riemann surface at points. These can be viewed as punctures in the dual N $$ \mathcal{N} $$ = 1 superconformal field theories. We find M5-branes that correspond to the two types of simple punctures previously studied in field theory. In addition, when the central charge is rational, we find a new class of M5-branes with a moduli space that includes two internal dimensions in addition to the Riemann surface. These new M5-branes have the essential characteristic of fractional branes, in that a single one at a generic point of its moduli space becomes multiple M5-branes at special points.