Black holes with baryonic charge and $$ \mathcal{I} $$ -extremization

Abstract

Recently it was discovered that twisted superconformal index I can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called I-extremization procedure to threedimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold M 1,1,1 . We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS 2 × Y 9 , where Y 9 is a fibration of toric Sasaki-Einstein manifold M 1,1,1 over a twodimensional Riemann surface Σ g . The nine-dimensional variational problem is given in terms of an entropy functional. In order to illustrate the computations as explicitly as possible, we consider cases where either only mesonic or baryonic fluxes are turned on. By employing the operator counting method, we calculate the S 3 free energy and the topologically twisted index I at large-N . The result for I, it turns out, can be also obtained from the variational principle of the entropy functional with mesonic fluxes. We also study asymptotically AdS 4 black holes which are magnetically charged with respect to the vector field in the Betti multiplet. By extremizing the entropy functional with baryonic flux, we compute the entropy and find that it agrees with the entropy of an explicit solution in a four-dimensional gauged supergravity which is a consistent truncation of eleven-dimensional supergravity in AdS 4 × M 1,1,1 . arXiv:1904.05344v2 [hep-th]

Aspects of AdS2 classification in M-theory: solutions with mesonic and baryonic charges

“…Having such full interpolating solutions from the near horizon to the asymptotically AdS 4 region would help clarify various aspects. For example, by evaluating its on-shell action one could potentially clarify the I-extremizaiton procedure [37][38][39] in terms of an attractor mechanism in the bulk extending on previous related work along the lines of [41][42][43].…”

The BPS limit of rotating AdS black hole thermodynamics

“…Although constructing the full asymptotically AdS d solution would be desiderable, for the purpose of studying the extremization principle it may be sufficient to focus on the simpler near-horizon geometry, upon identifying the near-horizon counterpart of our BPS limit. This approach, once promoted to the full ten-or eleven-dimensional supergravity theory, may also lead to a generalization of the extremization principle of [53][54][55] to the case of rotating horizons with no magnetic charge.…”

Euclidean black saddles and AdS4 black holes

“…• Using the explicit formulae in [12] it is possible to uplift our black saddle solutions to backgrounds of eleven-dimensional supergravity. It will be very interesting to do this JHEP10(2020)073 explicitly and to investigate possible relations with the studies of I-extremization in [63][64][65][66][67][68]. A similar question can be posed about the relation between the holographic realization of F -maximization in four-dimensional gauged supergravity [13] and the Sasaki-Einstein volume minimization principle studied in [69,70].…”