A Monopole Instanton-Like Effect in the ABJM Model

TL;DR

This paper constructs a monopole instanton-like solution in the Euclidean ABJM model using supergravity ansatzs, showing its topological and energetic properties, and matching it with a dual gauge field configuration in the boundary theory.

Contribution

It introduces a novel monopole instanton-like solution in the ABJM model and analyzes its properties and duality with boundary gauge fields.

Findings

The solution is (anti) self-dual at a special limit.

Energy-momentum tensors vanish exactly, indicating negligible back-reaction.

The boundary gauge field is a dynamic U(1) without a kinetic term, matching the bulk solution.

Abstract

Making use of ansatzs for the form fields in the 10d type IIA supergravity version of the ABJM model, we come with a solution in the Euclidean signature recognized as a monopole instanton-like object. Indeed we will see that we can have a (anti) self-dual solution at a special limit. While as a topological object, its back-reaction on the original background should be ignorable, we show the energy-momentum tensors vanish exactly. On the field theory side, the best counterpart is an U(1) gauge field of a gauge transformation. To adjust with bulk, the gauge field must prompt to a dynamic one without adding any kinetic term for this dual photon except a marginal, abelian AB-type Chern-Simons term on the boundary. We will see how both side solutions match next to another confirmation from some earlier works of this vortex-particle duality.