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 \( \mathcal{N} = 2 \) 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.
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Papadodimas, K. Topological anti-topological fusion in four-dimensional superconformal field theories. J. High Energ. Phys. 2010, 118 (2010). https://doi.org/10.1007/JHEP08(2010)118
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DOI: https://doi.org/10.1007/JHEP08(2010)118