AdS₃solutions of IIB supergravity from D3-branes

Abstract

We consider pure D3-brane configurations of IIB string theory which lead to supersymmetric solutions containing an AdS 3 factor. They can provide new examples of AdS 3 /CFT 2 examples on D3-branes whose worldvolume is partially compactified. When the internal 7 dimensional space is non-compact, they can be identified as supersymmetric fluctuations of higher dimensional AdS solutions and are in general dual to 1/8-BPS operators thereof. We find that supersymmetry requires the 7 dimensional space take the form of a U (1) fibration over a 6 dimensional Kahler manifold.

Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

“…A double Wick rotated version of this system (i.e. one with AdS 3 instead of S 3 isometry) was recently investigated in [20], and the results are directly applicable to the present case. The analysis of [20] demonstrated that the seven-dimensional metric may be written as time fibered over a six (real) dimensional Kähler base which satisfies an appropriate geometric condition.…”

“…Backgrounds with S 3 × S 1 isometry were initially examined in [18], and subsequent gauging of the U(1) isometry was considered in [19]. In addition, solutions preserving an S 3 isometry (corresponding to the 1/8 BPS case) may be obtained by double analytic continuation of the AdS 3 solutions investigated in [20], as it was later done in [21]. (Note that 1/4 BPS and 1/8 BPS solutions of a different nature were also investigated in [4] and [22], respectively.)…”

“…(Note that 1/4 BPS and 1/8 BPS solutions of a different nature were also investigated in [4] and [22], respectively.) In both cases of S 3 isometry [20] and S 3 × S 1 isometry [18,19], the invariant tensor analysis and resulting description of the backgrounds are essentially complete. However, unlike for LLM geometries, in these cases the supersymmetry analysis is not particularly constructive.…”

“…However, unlike for LLM geometries, in these cases the supersymmetry analysis is not particularly constructive. For example, it was found in [20] that 1/8 BPS configurations with an S 3 isometry may be written using a metric of the form ds 2 10 = −e 2α (dt + ω) 2 + e −2α h ij dx i dx j + e 2α dΩ 2 3 , ( 8) where h ij is a Kähler metric of complex dimension three. In the end, the invariant tensor analysis does not provide an actual procedure for obtaining this metric short of solving a non-linear equation on its curvature [20] 6 R = −R ij R ij + 1 2 R 2 .…”

“…Finally, to guarantee that the above is a true solution to the equations of motion, we may apply the Bianchi identity and equation of motion for F (2) . From (3.19) along with dJ = 0 the Bianchi identity turns out to be trivial, while the F (2) equation of motion gives 20) where 6 as well as the tensor contraction is with respect to the base metric h ij . Substituting in the expression for e −4α in (3.19) then gives a condition on the curvature…”