On supersymmetric AdS3 solutions of Type II

Abstract

We classify supersymmetric warped AdS3×wM7 backgrounds of Type IIA and Type IIB supergravity with non-constant dilaton, generic RR fluxes and magnetic NSNS flux, in terms of a dynamic SU(3)-structure on M7. We illustrate our results by recovering several solutions with various amounts of supersymmetry. The dynamic SU(3)-structure includes a G2-structure as a limiting case, and we show that in Type IIB this is integrable.

${\cal N}=(1,1)$ supersymmetric AdS$_3$ in 10 dimensions

“…We shall now summarise these geometric conditions. First off, similar necessary and sufficient conditions for N = 1 AdS 3 vacua are given in [17,45], and it should be no surprise that when a geometry supports both an N = (1, 0) and an N = (0, 1) set of these one has necessary and sufficient conditions for N = (1, 1): these are…”

“…The first four of these are simply the distinct conditions one would get from an N = (1, 0) and N = (0, 1) 10 dimensional bi-linear respectively (see [45] which shares the conventions taken here for gamma matrices and the SL(2) + portion of 1,2 ). The Bianchi identities and equations of motion of the RR flux away from the loci of sources impose that Here we will work smart rather than hard.…”

“…Here we know that we have sufficient conditions if we are solving two independent copies of their N = 1 conditions, an N = (1, 0) set and an N = (0, 1) set -(B.28a)-(B.28b) already give all the conditions from these independent N = 1 sub-sectors, except the pairing constraints from (3.1c) and (3.1d) of [62]. For N = 1 AdS 3 we can simply extract this from [45]. However, to make use of it, we must now fix Establishing whether this too is redundant is more challenging as (Ψ ++ ∓ − Ψ −− ∓ , Ψ +− ∓ + Ψ −+ ∓ ) 6 = 0 in general.…”

“…An incomplete picture of N = (2, 2) is provided by [35,36] and there are limited examples with N = (3, 0) and N = (3,3) in [37][38][39]. A systematic study of N = (2, 0) in IIB is provided by [40][41][42], and there exist several classifications of N = (1, 0) [17,[43][44][45][46]; for the latter two, many explicit examples exist. We summarize this discussion in Table 1.…”

O6-plane backreaction on scale-separated Type IIA AdS3 vacua

“…Moreover, our analysis here was only the first step that accounts only for the leading order backreaction, and therefore we do not know at this point if some intricate inconsistency can show up at the next order, as the AdS conjecture would imply [2]. One could further check the consistency of the backreacted solutions by matching with the supersymmetric analysis of Type II AdS 3 vacua performed in [38]. These questions and checks are left for future work.…”