Stress-tensor OPE in N=2 Superconformal Theories

TL;DR

This work analyzes the ${\mathcal{N}}=2$ stress-tensor multiplet OPE via a detailed superspace approach and its connection to a protected 2d chiral algebra. The authors derive an analytic lower bound on the 4d central charge $c$ from the 2d holomorphic stress-tensor sector, finding saturation at the Argyres-Douglas point ${H_0}$, which aligns with a null state in the associated Yang-Lee model. They classify the allowed ${\mathcal{N}}=2$ multiplets appearing in ${\hat{\mathcal{C}}}_{0(0,0)}\times{\hat{\mathcal{C}}}_{0(0,0)}$, construct explicit three-point-function solutions, and reveal nilpotent invariants that complicate the superconformal block structure. A partial analysis of the ${\mathcal{N}}=2$ superconformal blocks for the highest-weight scalar is provided, including a practical ${\mathcal{N}}=1$ decomposition that paves the way for full bootstrap studies of stress-tensor correlators and potential bounds on the $a$-anomaly. Overall, the paper bridges 4d ${\mathcal{N}}=2$ dynamics with a 2d chiral-algebra perspective, establishing groundwork for a complete stress-tensor bootstrap and its phenomenological implications.

Abstract

We carry out a detailed superspace analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.