Overlaps for Matrix Product States of Arbitrary Bond Dimension in ABJM theory

TL;DR

This paper derives a closed formula for overlaps between Bethe eigenstates and matrix product states in ABJM theory, enabling exact computation of one-point functions in defect conformal field theories.

Contribution

It provides the first explicit formula for overlaps involving arbitrary bond dimension MPS in the context of ABJM theory, connecting integrable spin chains with defect CFTs.

Findings

Closed formula for overlaps of Bethe states and MPS of any bond dimension.

Exact expressions for one-point functions in defect ABJM theory.

Enhanced understanding of integrability in supersymmetric gauge theories.

Abstract

We find a closed formula for the overlap of Bethe eigenstates of an alternating $SU(4)$ spin chain, describing the scalar sector of ABJM theory, and matrix product states of any bond dimension representing 1/2 BPS co-dimension one domain walls in the field theory. One point functions of the defect CFTs involved, being directly expressible in terms of these overlaps, are hence completely determined.