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2011

A Mathematical Theory of Quantum Sheaf Cohomology

Donagi, Ron, Guffin, Josh, Katz, Sheldon et al.

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The purpose of this paper is to present a mathematical theory of the half-twisted $(0,2)$ gauged linear sigma model and its correlation functions that agrees with and extends results from physics.

The theory is associated to a smooth projective toric variety $X$ and a deformation $\sheaf E$ of its tangent bundle $T_X$.
It gives a quantum deformation of the cohomology ring of the exterior algebra of $\sheaf E^*$.
We prove that in the general case, the correlation functions are independent of `nonlinear' deformations.

A Mathematical Theory of Quantum Sheaf Cohomology · Around

Built on

Ann. Sci. École Norm. Sup. (4) 3
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E. Witten, Phases of N = 2 theories in two dimensions · 1993
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Then

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S. H. Katz and E. Sharpe, Notes on certain (0,2) correlation functions · 2006
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(2011), 1110.3752
R. Donagi, J. Guffin, S. Katz and E. Sharpe, Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties · 2011
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