On non-supersymmetric conformal manifolds: field theory and holography

TL;DR

This paper explores the conditions under which non-supersymmetric conformal field theories can have exactly marginal deformations, using conformal perturbation theory and holography, to understand conformal manifolds beyond supersymmetric cases.

Contribution

It derives sum rules constraining operator spectra and OPE coefficients for non-supersymmetric conformal manifolds, linking conformal perturbation theory with holographic dual descriptions.

Findings

Derived sum rules for operator spectra and OPE coefficients.

Established connections between conformal perturbation theory and bulk loop expansions.

Applied results to non-supersymmetric theories, broadening understanding of conformal manifolds.

Abstract

We discuss the constraints that a conformal field theory should enjoy to admit exactly marginal deformations, i.e. to be part of a conformal manifold. In particular, using tools from conformal perturbation theory, we derive a sum rule from which one can extract restrictions on the spectrum of low spin operators and on the behavior of OPE coefficients involving nearly marginal operators. We then consider conformal field theories admitting a gravity dual description, and as such a large-$N$ expansion. We discuss the relation between conformal perturbation theory and loop expansion in the bulk, and show how such connection could help in the search for conformal manifolds beyond the planar limit. Our results do not rely on supersymmetry, and therefore apply also outside the realm of superconformal field theories.