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

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.

43 pages (29 pages + 4 appendices), 2 figures, harvmac, v2: fixed typos, improved some derivations, numerical coefficients in tt* equations corrected

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