Coulomb Branch and Integrability

TL;DR

This paper derives a closed-form formula for one-point functions of non-BPS operators on the Coulomb branch of planar N=4 SYM using integrability, validated by field theory computations.

Contribution

It introduces an integrable bootstrap approach to compute one-point functions at finite coupling, providing a new exact determinant formula.

Findings

Derived a finite-coupling determinant expression for one-point functions.

Validated the formula against tree-level and one-loop field theory results.

Assumed integrability preservation by the D-brane boundary state.

Abstract

We study one-point functions of non-BPS single-trace operators on the Coulomb branch of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Holography relates them to overlaps between on-shell closed string states and a boundary state describing a probe D3-brane in $AdS_5\times S^{5}$. Assuming that the D-brane preserves integrability, we formulate and solve integrable bootstrap equations satisfied by the boundary state at finite 't Hooft coupling. This leads to a closed-form determinant expression for one-point functions at finite coupling, valid for sufficiently long operators. We test the result against direct field theory computations at tree level and one loop, finding perfect agreement.