A Quantum Check of AdS/dCFT

TL;DR

This paper develops a framework for loop computations in a defect conformal field theory dual to a D5-D3 brane system, enabling quantum corrections analysis and testing gauge-gravity duality with partial symmetry breaking.

Contribution

It introduces a method to perform loop calculations in a non-trivial defect N=4 super Yang-Mills theory with space-time-dependent VEVs, solving complex mass mixing and propagator problems.

Findings

One-loop correction to scalar one-point functions computed.

Agreement with string theory predictions confirms gauge-gravity duality.

Method handles non-trivial space-time dependence and symmetry breaking.

Abstract

We build the framework for performing loop computations in the defect version of N=4 super Yang-Mills theory which is dual to the probe D5-D3 brane system with background gauge-field flux. In this dCFT, a codimension-one defect separates two regions of space-time with different ranks of the gauge group and three of the scalar fields acquire non-vanishing and space-time-dependent vacuum expectation values. The latter leads to a highly non-trivial mass mixing problem between different colour and flavour components, which we solve using fuzzy-sphere coordinates. Furthermore, the resulting space-time dependence of the theory's Minkowski space propagators is handled by reformulating these as propagators in an effective AdS4. Subsequently, we initiate the computation of quantum corrections. The one-loop correction to the one-point function of any local gauge-invariant scalar operator is shown to receive contributions from only two Feynman diagrams. We regulate these diagrams using dimensional reduction, finding that one of the two diagrams vanishes, and discuss the procedure for calculating the one-point function of a generic operator from the SU(2) subsector. Finally, we explicitly evaluate the one-loop correction to the one-point function of the BPS vacuum state, finding perfect agreement with an earlier string-theory prediction. This constitutes a highly non-trivial test of the gauge-gravity duality in a situation where both supersymmetry and conformal symmetry are partially broken.