A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on $S^4$

TL;DR

This paper develops a quantum framework using fuzzy spherical harmonics on S^4 to analyze a non-supersymmetric domain-wall version of N=4 SYM, successfully computing spectra and correlators that match supergravity predictions.

Contribution

It introduces a novel approach employing fuzzy spherical harmonics on S^4 to solve mixing problems and compute quantum spectra and correlators in a non-supersymmetric domain-wall setup.

Findings

Derived the spectrum of excitations at quantum level.

Computed propagators for perturbative calculations.

Matched one-loop one-point functions with supergravity predictions.

Abstract

We consider a non-supersymmetric domain-wall version of $\mathcal{N} = 4$ SYM theory where five out of the six scalar fields have non-zero classical values on one side of a wall of codimension one. The classical fields have commutators which constitute an irreducible representation of the Lie algebra $\mathfrak{so}(5)$ leading to a highly non-trivial mixing between color and flavor components of the quantum fields. Making use of fuzzy spherical harmonics on $S^4$, we explicitly solve the mixing problem and derive not only the spectrum of excitations at the quantum level but also the propagators of the original fields needed for perturbative quantum computations. As an application, we derive the one-loop one-point function of a chiral primary and find complete agreement with a supergravity prediction of the same quantity in a double-scaling limit which involves a limit of large instanton number in the dual D3-D7 probe-brane setup.