Nearing extremal intersecting giants and new decoupled sectors in 𝒩 = 4 SYM

Abstract

We study near-horizon limits of near-extremal charged black hole solutions to five-dimensional U(1) 3 gauged supergravity carrying two charges, extending the recent work of Balasubramanian et.al. [1]. We show that there are two nearhorizon decoupling limits for the near-extremal black holes, one corresponding to the near-BPS case and the other for the far from BPS case. Both of these limits are only defined on the 10d IIB uplift of the 5d black holes, resulting in a decoupled geometry with a six-dimensional part (conformal to) a rotating BTZ×S 3 . We study various aspects of these decoupling limits both from the gravity side and the dual field theory side. For the latter we argue that there should be two different, but equivalent, dual gauge theory descriptions, one in terms of the 2d CFT's dual to the rotating BTZ and the other as certain large R-charge sectors of d = 4, N = 4 U(N) SYM theory. We discuss new BMNtype sectors of the N = 4 SYM in the N → ∞ limit in which the engineering dimensions scale as N 3/2 (for the near-BPS case) and as N 2 (for the far from BPS case). Introduction and SummaryAccording to AdS/CFT conjecture [2, 3] any state/physical process in the asymptotically AdS 5 × S 5 geometry can be described by a (perturbative) deformation of N = 4, d = 4 supersymmetric Yang-Mills (SYM) theory. A class of deformations of AdS 5 ×S 5 are solutions to N = 2, d = 5 U(1) 3 gauged supergravity (the "gauged STU model"), for a review e.g. see [4,5]). Among these solutions there are geometries carrying charges under some (or all) of the three U(1)'s. These are generically 5d black hole type solutions. It is possible to uplift these solutions to 10d and obtain the corresponding type IIB solutions which are constant dilaton solutions only involving metric and the (self-dual) five-form field of IIB theory. These solutions which have been extensively studied from the gravity viewpoint (e.g. see [5] and references therein) can be 1/2, 1/4, 1/8 BPS respectively preserving 16, 8, 4 supercharges. The 10d BPS solutions have been called superstars [6].In the 10d picture the 1/2 BPS solutions correspond to smeared (delocalized) spherical D3-branes [6], the giant gravitons [7]. These are branes wrapping a three sphere inside the S 5 part of the background AdS 5 × S 5 geometry while moving on a geodesic along an S 1 ∈ S 5 transverse to the worldvolume S 3 and smeared (delocalized) over the remaining direction. The 1/2 BPS solutions are specified by a single parameter, the value of the charge. In a similar manner the two-charge 1/4 BPS and three-charge 1/8 BPS solutions can be understood as geometries corresponding to intersecting giant gravitons. The nonsupersymmetric cases then correspond to turning on specific open string excitations on the supersymmetric (intersecting) giant gravitons. Besides the (excited intersecting) spherical brane picture the 5d charged black hole type solutions should also have a description in the N = 4 SYM on R × S 3 . The 1/2 BPS case is described by chiral primary operators in the subdetermina...

Quantum tunneling from three-dimensional black holes

“…In the near horizon geometry of higher dimensional black holes, under appropriate limit, the time and radial direction of the black hole, and a circle direction in the extra dimensions, combine into a BTZ geometry [20,21]. It is interesting to see the connection of this to the discussion in this paper.…”

Warped Ricci-flat reductions

“…In this section, we offer an explanation as to why that may be the case. Our observation hinges on a known "far from BPS" near-horizon limit of certain extremal black holes in D = 4 U(1) 4 and D = 5 U(1) 3 gauged supergravity [13,14] (see also [16]), where an AdS 3 near-horizon is formed by incorporating an internal circular direction with the scalars, in this case X i , all scaled appropriately.…”

“…We begin by considering type IIB supergravity on the product R 4 ≡ R 2 × R 2 . It was previously shown in [14] that there is a consistent KK reduction to a six-dimensional theory admitting an AdS 6 vacuum with a single scalar and three-form flux. We recall the ten-dimensional Ansatz 4 but allow for the opposite sign in the warp factor,…”

“…Within an AdS/CFT context, such warped-product solutions have been studied previously in [13,14] (more recently [15,16]), where consistent KK reductions to lower-dimensional theories were constructed. In contrast to usual AdS/CFT setups, the vacua of the lower-dimensional theories are supported exclusively through the warp factor and lift to vacuum solutions in ten and eleven dimensions.…”

“…By constructing lower-dimensional Freund-Rubin type solutions within our AdS p , p = 5, 6, 8 truncations, we show that AdS 3 solutions are stable. On physical grounds, since these arise as the near-horizon of EVH black holes [13,14], they are expected to be classically stable.…”