A Quantum Check of Non-Supersymmetric AdS/dCFT

TL;DR

This paper confirms supergravity predictions for a non-supersymmetric D3-D7 system by performing complex field theory calculations, including one-loop corrections, and finds exact agreement with the supergravity results in a specific limit.

Contribution

It introduces a novel field-theory computation method that verifies supergravity predictions for a non-supersymmetric defect conformal field theory involving flux-stabilized probe branes.

Findings

One-loop scalar VEV corrections are UV finite and non-zero.

Calculated one-point functions match supergravity predictions in the double-scaling limit.

Extended fuzzy spherical harmonics technique to diagonalize the mass matrix.

Abstract

Via a challenging field-theory computation, we confirm a supergravity prediction for the non-supersymmetric D3-D7 probe-brane system with probe geometry AdS_4 x S^2 x S^2, stabilized by fluxes. Supergravity predicts, in a certain double-scaling limit, the value of the one-point functions of chiral primaries of the dual defect version of N=4 SYM theory, where the fluxes translate into SO(3) x SO(3)-symmetric, Lie-algebra-valued vacuum expectation values for all six scalar fields. Using a generalization of the technique based on fuzzy spherical harmonics developed for the related D3-D5 probe-brane system, we diagonalize the resulting mass matrix of the field theory. Subsequently, we calculate the planar one-loop correction to the vacuum expectation values of the scalars in dimensional reduction and find that it is UV finite and non-vanishing. We then proceed to calculating the one-loop correction to the planar one-point function of any single-trace scalar operator and explicitly evaluate this correction for a 1/2-BPS operator of length L at two leading orders in the double-scaling limit, finding exact agreement with the supergravity prediction.