Semiclassics of three-dimensional SCFTs from holography

TL;DR

This paper uses holography to analyze the large-$N$ effective field theory of 3D $ ext{SCFTs}$, revealing how large $R$-charge operators correspond to semiclassical bound states of branes, enabling direct scaling dimension calculations.

Contribution

It introduces a semiclassical framework for computing operator dimensions in 3D $ ext{SCFTs}$ with holographic duals, focusing on large $R$-charge sectors and explicit models.

Findings

Spectrum of large $R$-charge operators matches semiclassical solutions.

Explicit semiclassical solutions describe bound states of branes.

Scaling dimensions of operators can be directly computed.

Abstract

We use holography to compute the large-$N$ effective field theory along the moduli space of vacua of an infinite class of three-dimensional $\mathcal{N}=2$ SCFTs admitting a dual M-theory description. We focus in particular on toric models and show how the spectrum of large $R$-charge SCFT chiral scalar operators corresponds to a set of explicit semiclassical solutions of our effective field theory, which describe bound states of backreacting giant gravitons and baryonic-like M5-branes. Our semiclassical description allows for a direct computation of the scaling dimensions of these operators and provides a starting point for a semiclassical investigation of the SCFT data in the large $R$-charge sector. We consider the models corresponding to the $Y^{12}(\mathbb{P}^2)$ and $Q^{111}$ Sasaki-Einstein spaces as explicit examples.