Dual Instantons in Anti-membranes Theory

TL;DR

This paper explores dual instantons in anti-membrane theory by introducing scalar modes in Euclidean 11d supergravity on a skew-whiffed AdS_4 x S^7 background, linking bulk solutions to boundary operators via a proposed duality.

Contribution

It proposes a new duality framework for anti-membranes by swapping representations in ABJM theory and identifies boundary operators corresponding to bulk scalar modes.

Findings

Exact solutions for scalar equations on skew-whiffed background

Identification of dual boundary operators for scalar modes

Comparison of fermionic solutions in deformed boundary theory

Abstract

We introduce two ansatzs for the 3-form potential of Euclidean 11d supergravity on skew-whiffed AdS_4 X S^7 background which results in two scalar modes with m^2=-2 on AdS_4. Being conformally coupled with a quartic interaction it is possible to find the exact solutions of the scalar equation on this background. These modes turn out to be invariant under SU(4) subgroup of SO(8) isometry group, whereas there are no corresponding SU(4) singlet BPS operators of dimensions one or two on the boundary ABJM theory. Noticing the interchange of 8_s and 8_c representations under skew-whiffing in the bulk, we propose the theory of anti-membranes should similarly be obtained from ABJM theory by swapping these representations. In particular, this enables us to identify the dual boundary operators of the two scalar modes. We deform the boundary theory by the dual operators and examine the fermionic field equations and compare the solutions of the deformed theory with those of the bulk.