Machine Learning the Conformal Manifold of Holographic CFT$_{2}$s

TL;DR

This paper develops a novel symbolic regression algorithm combining Annealed Sequential Monte Carlo samplers to analytically characterize a new family of solutions on the conformal manifold of holographic CFTs near AdS3×S3.

Contribution

It introduces a new symbolic regression method based on Annealed Sequential Monte Carlo samplers for uncovering polynomial relations in high-dimensional spaces.

Findings

Reconstructed explicit polynomial relations for conformal manifold solutions.

Developed a symbolic regression algorithm suitable for high-dimensional parameter spaces.

Provided an analytic parametrization of a new family of holographic CFT solutions.

Abstract

We investigate the structure of conformal manifolds around AdS$_3 \times S^3$ which lift from continuous flat directions in the scalar potential of gauged supergravity resulting from six-dimensional $\mathcal{N}=(1,1)$ supergravity. Our approach combines numerical exploration and symbolic inference. For the latter, we develop a symbolic regression algorithm based on Annealed Sequential Monte Carlo samplers, a combination of Annealed Importance Sampling and Sequential Monte Carlo samplers, well-suited to uncovering polynomial constraints in high-dimensional parameter spaces. The algorithm reconstructs a set of polynomial relations that provides an explicit analytic parametrization of a new family of solutions.