Dual Localized Objects From M-Branes Over AdS_4 x S^7/Z_k

TL;DR

This paper explores localized objects like instantons and domain walls in 11D supergravity over AdS_4 x S^7/Z_k, analyzing their dual boundary operators and effects on the geometry and supersymmetry.

Contribution

It introduces new localized solutions involving M-branes and boundary deformations, linking bulk supergravity configurations with dual boundary field theories.

Findings

Identification of massless scalars and pseudoscalars matching boundary operators

Construction of instantons and domain walls as localized objects

Analysis of supersymmetry breaking and boundary deformations

Abstract

We consider a few ansatzs for the four and seven forms of 11-dimensional supergravity over AdS_4 x S^7/Z_k while try to keep the geometry unchanged. From the 4-form equations, we arrive at some massless scalars and pseudoscalars in the bulk of Euclidean AdS_4 that match with some boundary $\Delta_+$=3 operators. Indeed, the main objects are instantons and domain walls as the fully and partially localized objects in the external space, respectively. The latter comes from an (anti)M5-brane wrapping partly around three internal directions similar to the fuzzy S^3/Z_k solutions. Except for the first solutions of adding some anti-M2-branes$\mid$(M2-branes) to the original M2-branes, the objects backreact on the geometry although small$\mid$(break all supersymmetries and destabilize the vacua). The dual 3-dimensional field theory solutions are got by the skew-whiffing 8_s $\rightarrow$ 8_v and 8_s $\rightarrow$ 8_c for the scalars and pseudoscalars respectively, while the gauge fields are used mainly for the k=1,2 cases where the R-symmetry and supersymmetry are enhanced as SU(4) x U(1) $\rightarrow$ SO(8) and N=6 $\rightarrow$ N=8 respectively, and also for pseudoscalars. Further, for the pseudoscalars we propose a special boundary deformation, with a fermion field, that is equivalent to a multi-trace deformation already studied for the bulk m^2=-2 conformally coupled pseudoscalar.