$\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras

TL;DR

This paper derives a new analytic bound on the $c$-anomaly in $ =2$ SCFTs based on 2d chiral algebra analysis, constraining the theories' parameter space and identifying models with fixed $c$ for given flavor central charge $k$.

Contribution

It introduces a novel bound relating the $c$-anomaly to the flavor central charge $k$ in $ =2$ SCFTs, refining the classification of these theories.

Findings

New bound on $c$ as a function of $k$ for $ =2$ theories.

Constraints on the parameter space of $ =2$ SCFTs.

Identification of models with fixed $c$ given $k$, including Kodaira's rank one SCFTs.

Abstract

We study protected correlation functions in $\mathcal{N} = 2$ SCFT whose description is captured by a two-dimensional chiral algebra. Our analysis implies a new analytic bound for the $c$-anomaly as a function of the flavor central charge $k$, valid for any theory with a flavor symmetry $G$. Combining our result with older bounds in the literature puts strong constraints on the parameter space of $\mathcal{N}=2$ theories. In particular, it singles out a special set of models whose value of $c$ is uniquely fixed once $k$ is given. This set includes the canonical rank one $\mathcal{N}=2$ SCFTs given by Kodaira's classification.