Chiral primary one-point functions in the D3-D7 defect conformal field theory

TL;DR

This paper calculates one-point functions of chiral primary operators in a defect conformal field theory using both perturbative gauge theory and string theory, finding exact agreement at leading order in the planar limit.

Contribution

It provides the first comparison of one-point functions in a non-supersymmetric defect CFT between weak coupling gauge theory and strong coupling string theory, including cases with non-trivial gauge flux.

Findings

Exact agreement between gauge theory and string theory results at leading order.

Validation of the duality in non-supersymmetric defect setups.

Extension to cases with non-trivial gauge flux configurations.

Abstract

We compute the one-point functions of chiral primary operators in the non-supersymmetric defect conformal field theory that is dual to the IIB string theory on $AdS_5\times S^5$ background with a probe D7 brane with internal gauge field flux, both in perturbative Yang-Mills theory and in the string theory dual. The former is expected to be accurate at weak coupling whereas the latter should be accurate in the planar strong coupling limit of the gauge theory. We consider the distinct cases where the D7 brane has geometry $AdS_4\times S^4$ with an instanton bundle of the worldvolume gauge fields on $S^4$ and $AdS_4\times S^2\times S^2$ with Dirac monopole bundles on each $S^2$. The gauge theory computation and the string theory computation can be compared directly in the planar limit and then a subsequent limit where the worldvolume flux is large. We find that there is exact agreement between the two in the leading order.