The structure of 2D semi-simple field theories

By C. Teleman. Inventiones Mathematicae, 2007

260 citations recorded by the source corpus.

I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of κ-classes and by an extension datum to the Deligne–Mumford boundary. Their effect on the Gromov–Witten potential is described by Givental’s Fock space formulae. This leads to the reconstruction of Gromov–Witten (ancestor) invariants from the quantum cup-product at a single semi-simple point and the first Chern class of the manifold, confirming Givental’s higher-genus reconstruction conjecture. This in turn implies the Virasoro conjecture for manifolds with semi-simple quantum cohomology. The classification uses the Mumford conjecture, proved by Madsen and Weiss (European Congress of Mathematics, pp. 283–303, 2005).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fc37c339b9a3b54e5ac02c2e6edeab60629dd0c7

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Citations in the corpus

Relations on Mbar_{g,n} via 3-spin structures (2013, unknown): “Using the classiﬁcation of semisimple CohFTs by Givental-Teleman [6, 20], we derive an explicit formula in the tautological ring of M g,n for Witten’s 3-spin class and use the vanishing property to establish the relation set P .”
Relations in the tautological ring of the moduli space of curves (2013, methodology): “Using the classification of semisimple CohFTs by Givental-Teleman [14, 36], we derive an explicit formula in the tautological ring ofMg,n for Witten’s 3-spin class and use the vanishing property to establish the relations Rg,n.”
Identification of the Givental Formula with the Spectral Curve Topological Recursion Procedure (2012, background): “The main theorem of [9] states that this action preserves the property that Z is a generating function of the correlators of a cohomological field theory with target space (V, η) (see also [20,33]).”