An AdS/EFT correspondence at large charge


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-Nordström 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.

Nucl.Phys. B934 (2018) 437-458