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The closed state space of affine Landau-Ginzburg April 19, 2011
 

Summary: The closed state space of affine Landau-Ginzburg
B-models
Ed Segal
April 19, 2011
Abstract
We study the category of perfect cdg-modules over a curved algebra,
and in particular the category of B-branes in an affine Landau-Ginzburg
model. We construct an explicit chain map from the Hochschild complex
of the category to the closed state space of the model, and prove that this
is a quasi-isomorphism from the Borel-Moore Hochschild complex. Using
the lowest-order term of our map we derive Kapustin and Li's formula for
the correlator of an open-string state over a disc.
Contents
1 Introduction 2
2 Curved algebras 4
2.1 Curved algebras and cdg-modules . . . . . . . . . . . . . . . . . 5
2.2 Some non-commutative geometry . . . . . . . . . . . . . . . . . 6
2.2.1 Curved A-structures and polynomial curved A-structures 6
2.2.2 Differential forms . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 The infinite-dimensional case . . . . . . . . . . . . . . . . . . 10

  

Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield

 

Collections: Mathematics