New AdS2 backgrounds and $$ \mathcal{N} $$ = 4 conformal quantum mechanics

Abstract

We present a new infinite family of Type IIB backgrounds with an AdS2 factor, preserving $$ \mathcal{N} $$ N = 4 SUSY. For each member of the family we propose a precise dual Super Conformal Quantum Mechanics (SCQM). We provide holographic expressions for the number of vacua (the “central charge”), Chern-Simons terms and other non-perturbative aspects of the SCQM. We relate the “central charge” of the one-dimensional system with a combination of electric and magnetic fluxes in Type IIB. The Ramond-Ramond fluxes are used to propose an extremisation principle for the central charge. Other physical and geometrical aspects of these conformal quantum mechanics are analysed.

The near-horizon geometry of supersymmetric rotating AdS4 black holes in M-theory

“…The final piece of the solution we need to specify is the dependence of the flux on the torus: we takeh (2,2) to have no legs along the torus directions. 16 Note that this is consistent with setting the rotation of the solution along the torus directions to zero, through the condition (2.18). In addition to this, we assume that the scalars B, C are independent of the torus coordinates, and are hence defined on the 6d base.…”

“…It would be interesting to fully work out the details of this more general case, but it deserves more than this small section in this paper and a full treatment of the most general construction. 16 The primitive piece of this part of flux (with legs on the torus) will give rise to a transgression term like in [20,47]. Again for our purposes such a term is an unnecessary complication, and so we set it to zero here, although it is certainly interesting to consider.…”

“…See also[16] for an extremization principle for N = (0, 4) AdS2 solutions in Type IIB 2. There is the nice paper[27] where the embedding of static AdS4 black holes in 11d supergravity were considered.…”

On the planar limit of 3d $$ {\mathrm{T}}_{\rho}^{\sigma}\left[\mathrm{SU}\left(\mathrm{N}\right)\right] $$

“…More generally, long quivers are studied in other dimensions, e.g. [70][71][72][73][74][75][76][77][78][79][80], and it would be interesting to apply similar localization methods to gain further insights.…”

AdS3 gravity and the complex SYK models

“…Slightly away from the horizon throat, warped conformal symmetry is broken and one expects the near horizon dynamics to be captured by JT gravity coupled to a u(1) Maxwell field. Even though such a field does typically arise from the Kaluza-Klein (KK) reduction of higher dimensional gravity [35][36][37][38][39][40], the symmetries preserved at or near the horizon depend on the boundary conditions imposed. In particular, it was shown in [35] that Dirichlet boundary conditions on the u(1) gauge field can be straightforwardly applied both at and near the extremal horizon and in either case result in a global u(1) symmetry.…”