Renormalization for holomorphic field theories

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We introduce the concept of a holomorphic field theory on any complex manifold in the language of the Batalin-Vilkovisky formalism. When the complex dimension is one, this setting agrees with that of chiral conformal field theory. Our main result concerns the behavior of holomorphic theories under renormalization group flow. Namely, we show that holomorphic theories are one-loop finite. We use this to completely characterize holomorphic anomalies in any dimension. Throughout, we compare our approach to holomorphic field theories to more familiar approaches including that of supersymmetric field theories.
Original languageEnglish
Pages (from-to)1693–1742
Number of pages48
JournalCommunications in Mathematical Physics
Issue number3
Early online date13 Feb 2020
Publication statusPublished - 31 Mar 2020

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