An AdS/EFT correspondence at large charge

TL;DR

This paper explores the AdS/EFT correspondence at large charge, showing that the ground state energy in a 3D CFT matches the mass of a charged black hole, thus linking CFT, EFT, and gravity descriptions.

Contribution

It establishes a novel dictionary connecting CFT, EFT, and holographic descriptions at large charge, including higher-derivative corrections.

Findings

Ground state energy matches black hole mass as a function of charge.

Agreement of higher-derivative corrections on both EFT and gravity sides.

Validates the large-$C_T$ expansion in the holographic duality context.

Abstract

Considering theories in sectors of large global charge $Q$ results in a semiclassical effective field theory (EFT) description for some strongly-coupled conformal field theories (CFTs) with continuous global symmetries. Hence, when studying dualities at large charge, we can have control over the strongly coupled side of the duality and gain perturbative access to both dual pairs. In this work we discuss the AdS/CFT correspondence in the regime $Q \gg C_T \gg 1$ where both the EFT and gravity descriptions are valid and stable ($C_T$ being the central charge). We present the observation that the ground state energy as a function of the Abelian charge $Q$ for a simple EFT in some three-dimensional CFT coincides with the expression for the mass of an anti-de Sitter-Reissner-Nordstr\"om black hole as a function of its charge. This observation allows us to introduce a dictionary relating CFT, EFT and holographic descriptions. We also find agreement for the higher-derivative corrections on both sides, suggesting a large-$C_T$ expansion on the EFT side.