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I give a rigorous construction of a 2-dimensional quantum field theory of maps from an elliptic curve to a compact complex manifold X, and I show that the partition function of this theory is the Witten genus of X.
Ann. of Math. (2) 90
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S. A. Merkulov, Strong homotopy algebras of a Kähler manifold · 1999
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V. Gorbounov, F. Malikov and V. Schechtman, Gerbes of chiral differential operators · 2000
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J. Pure Appl. Algebra 162
V. Hinich, DG coalgebras as formal stacks · 2001
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(2001), math.SG/0011041
M. Kontsevich and Y. Soibelman, Homological mirror symmetry and torus fibrations · 2001
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(2006), arXiv:math/0604504
B. Toën, Higher and derived stacks: a global overview · 2006
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J. Lurie, Derived Algebraic Geometry V: Structured Spaces · 2009
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J. Lurie, On the classification of topological field theories · 2009
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A geometric construction of the Witten genus, I,
K. Costello, · 2010
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D. Calaque and M. Van den Bergh, Hochschild cohomology and Atiyah classes · 2010
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Available at http://math.northwestern.edu/~costello/renormalization.html (2011)
K. Costello and O. Gwilliam, Factorization algebras in perturbative quantum field theory · 2011
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Renormalization and effective field theory
K. Costello, · 2011
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R. Grady and O. Gwilliam, One-dimensional Chern-Simons theory and the A ^ \widehat{A} genus · 2011
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MIT thesis (2011)
N. Rozenblyum, Connections on conformal blocks · 2011
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