AdS₃ Solutions with Exceptional Supersymmetry

Abstract

Among the possible superalgebras that contain the AdS 3 isometries, two interesting possibilities are the exceptional F (4) and G(3). Their R-symmetry is respectively SO(7) and G 2 , and the amount of supersymmetry N = 8 and N = 7. We find that there exist two (locally) unique solutions in type IIA supergravity that realize these superalgebras, and we provide their analytic expressions. In both cases, the internal space is obtained by a round six-sphere fibred over an interval, with an O8-plane at one end. The R-symmetry is the symmetry group of the sphere; in the G(3) case, it is broken to G 2 by fluxes. We also find several numerical N = 1 solutions with G 2 flavor symmetry, with various localized sources, including O2-planes and O8-planes.The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/prop.2018000601 The recent work [9] found that these are allowed superalgebras for an AdS 3 solution; see Table 2 there. In older work, superconformal algebras in two dimensions associated with F (4) and G(3) were found and studied, [10][11][12] confirming this possibility from the dual CFT point of view.

AdS3 solutions in massive IIA with small $$ \mathcal{N} $$ = (4, 0) supersymmetry

“…3. Exploit an existing N = 1 AdS 3 classification [37] to obtain sufficient conditions on the geometry and fluxes for a solution with small N = (4, 0) and SU(2)-structure in IIA to exist. 4.…”

AdS3 solutions with from S3 × S3 fibrations

“…[27][28][29][30] These examples, while certainly of great merit, still only cover a small subset of possible superconfromal algebras -see [31] for a complete list that may be embedded into ten-and eleven-dimensional supergravity 1 . Rather less "vanilla" options, were presented in [33] where solutions with F(4) and G(3) supergroups were constructed. In this paper we aim to expand on this story and construct  = (3, 0) solutions in massive IIA preserving the supergroup OSP(3|2) (see [12] for an earlier study in the context of M-theory).…”

“…We also explain why this breaking of symmetry leads to both  = (3, 0) and  = (1, 0) solutions. In section (3) we then use the necessary geometric conditions for AdS 3 solutions in massive IIA to preserve supersymmetry presented in [33]. We arrive at systems of ordinary differential equations (ODEs) whose solutions define supergravity backgrounds preserving  = (3, 0) and  = (1, 0) supersymmetry.…”

“…I.e. F = F 0 + F 2 + F 4 + F 6 + F 8 + F 10 where F 6 = − ⋆ 10 F 4 , F 8 = ⋆ 10 F 2 , F 1 0 = − ⋆ 10 F 0 .3 This is a requirement for non trivial Romans mass F 0 [33]. 4 We refer to[36] for more details about the Clifford algebra decomposition.…”

“…In general this is need be true piece-wise, with discontinuities signaling D8 sources.3. Necessary Conditions for AdS 3 Solutions to ExistRecently[33] provided necessary and sufficient conditions for  = (1, 0) supersymmetry to be preserved by a solution in massive IIA. The fundamental object in terms of which these conditions are formulated is the seven-dimensional bi-spinor defined in terms of two Majorana spinors 1,2 as1 ⊗ † 2 =…”