Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories

TL;DR

This paper derives new differential equations for chiral primary correlators in four-dimensional superconformal field theories, revealing quasi-topological properties and extending the tt* equations to four dimensions without using topological twisting.

Contribution

It introduces four-dimensional analogues of the tt* equations via topological anti-topological fusion, providing exact results for N=2 superconformal theories.

Findings

Differential equations for coupling dependence of correlators

Quasi-topological nature of the Zamolodchikov metric and operator mixing

Extension of tt* equations to four dimensions

Abstract

We present some new exact results for general four-dimensional superconformal field theories. We derive differential equations governing the coupling constant dependence of chiral primary correlators. For N=2 theories we show that the Zamolodchikov metric on the moduli space and the operator mixing of chiral primaries are quasi-topological quantities and constrained by holomorphy. The equations that we find are the four-dimensional analogue of the tt* equations in two-dimensions, discovered by the method of "topological anti-topological fusion" by Cecotti and Vafa. Our analysis relies on conformal perturbation theory and the superconformal Ward identities and does not use a topological twist.