Instantons in AdS$_4$ From (anti)Membranes Wrapping $S^7$ To Bose-Fermi Duality in CFT$_3$'s

TL;DR

This paper constructs non-supersymmetric instanton solutions in AdS4 from wrapped membranes, explores their dual CFT3 descriptions, and confirms Bose-Fermi duality and AdS/CFT correspondence through explicit boundary analysis.

Contribution

It introduces new SO(4)-invariant, non-supersymmetric instantons in AdS4 from wrapped membranes, linking bulk configurations to boundary CFT3 dualities and stability analyses.

Findings

Instantons break all supersymmetries and parity.

Boundary effective potential is unbounded, indicating instability.

Dual boundary theories exhibit Bose-Fermi duality and match instanton solutions.

Abstract

We present new SO(4)-invariant and non-supersymmetric instanton solutions for the conformally coupled m^2=-2 and massive m^2=+4 (pseudo)scalars arising from a consistent truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is a S^1 Hopf fibration on CP^3, and we consider backreaction. In fact, the bulk configurations associate with (anti)membranes wrapped around mixed internal (and external) directions, which in turn probe the Wick-rotated or skew-whiffed background, break all supersymmetries as well as parity invariance. From near the boundary behavior of the closed solution for the coupled bulk (pseudo)scalar, we get a marginal triple-trace deformation with mixed boundary condition (valid also for the bulk massless m^2=0 (pseudo)scalar, raised when considering the external space backreaction, with Dirichlet boundary condition) and as a result, the corresponding boundary effective potential is unbounded from below and causes an instability because of the Fubini-like instanton. Presenting dual effective actions, we see that the boundary solutions and counterparts realize in singlet sectors of three-dimensional U(N) and O(N) Chern--Simons-matter field theories. In particular, we use versions of massless and mass-deformed regular and critical boson and fermion models, find instantons and confirm state-operator AdS_4/CFT_3 correspondence and also Bose-Fermi duality at the level of the solutions. In addition, we discuss on relations of our setups with Vasiliev's Higher-Spin theories, deformations of the Aharony-Bergman-Jafferis-Maldacena model and other related studies.