• Corpus ID: 21707053

The Structure of 2 D Semisimple Field Theories

@inproceedings{Teleman2010TheSO,
  title={The Structure of 2 D Semisimple Field Theories},
  author={Constantin Teleman},
  year={2010}
}
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 GromovWitten 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, confirming Givental’s higher-genus reconstruction conjecture… 

Tables from this paper

Local Moduli of Semisimple Frobenius Coalescent Structures
We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms,
Vertex algebras of CohFT-type
Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show
Gromov-Witten theory and cycle-valued modular forms
In this paper, we proved generating functions of Gromov-Witten cycles of the elliptic orbifold lines with weights (3,3,3), (4,4,2), and (6,3,2) are cycle-valued quasi-modular forms. This is a
KP hierarchy for Hurwitz-type cohomological field theories
Abstract. We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting
Frobenius manifolds and quantum groups
We introduce an isomonodromic Knizhnik-Zamolodchikov connection with respect to the quantum Stokes matrices, and prove that the semiclassical limit of the KZ type connection gives rise to the
3 0 D ec 2 01 7 Frobenius manifolds and quantum groups
We introduce an isomonodromic Knizhnik–Zamolodchikov connection with respect to the quantum Stokes matrices, and prove that the semiclassical limit of the KZ type connection gives rise to the
Topological recursion for Gaussian means and cohomological field theories
We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich–Penner matrix model (KPMM), which is the
Givental Action and Trivialisation of Circle Action
In this paper, we show that the Givental group action on genus zero cohomological field theories, also known as formal Frobenius manifolds or hypercommutative algebras, naturally arises in the
Open WDVV Equations and Virasoro Constraints
In their fundamental work, B. Dubrovin and Y. Zhang, generalizing the Virasoro equations for the genus 0 Gromov-Witten invariants, proved the Virasoro equations for a descendent potential in genus 0
...
...

References

SHOWING 1-10 OF 26 REFERENCES
A Change of Coordinates on the Large Phase Space¶of Quantum Cohomology
Abstract: The Gromov–Witten invariants of a smooth, projective variety V, when twisted by the tautological classes on the moduli space of stable maps, give rise to a family of cohomological field
Semisimple Frobenius structures at higher genus
In the context of equivariant Gromov-Witten theory of tori actions with isolated fixed points, we compute genus g > 1 Gromov-Witten potentials and their generalizations with gravitational
ON THE QUANTUM COHOMOLOGY OF SOME FANO THREEFOLDS AND A CONJECTURE OF DUBROVIN
In the present paper the small quantum cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from ℙ3 or the quadric Q3 is explicitely computed. Because of
Gromov-Witten classes, quantum cohomology, and enumerative geometry
The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic
GROMOV - WITTEN INVARIANTS AND QUANTIZATION OF QUADRATIC HAMILTONIANS
We describea formalism based on quantizationof quadratichamil- tonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about
Two-dimensional Topological Quantum Field Theories and Frobenius Algebras
We characterize Frobenius algebras A as algebras having a comultiplication which is a map of A-modules. This characterization allows a simple demonstration of the compatibility of Frobenius algebra
Semisimple Quantum Cohomology and Blow-ups
Using results of Gathmann, we prove the following theorem: If a smooth projective variety X has generically semisimple (p,p)-quantum cohomology, then the same is true for the blow-up of X at any
On the WDVV equation in quantum K-theory.
0. Introduction. Quantum cohomology theory can be described in general words as intersection theory in spaces of holomorphic curves in a given Kahler or almost Kahler manifold X. By quantum K-theory
On the homotopy of the stable mapping class group
Abstract. By considering all surfaces and their mapping class groups at once, it is shown that the classifying space of the stable mapping class group after plus construction, BΓ∞+, has the homotopy
...
...