Quantum sheaf cohomology

General Introduction
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Search results
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Online References
A Mathematical Theory of Quantum Sheaf Cohomology: http://front.math.ucdavis.edu/1110.3751
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
Talk by Prof. Eric Sharpe of Virginia Tech
TITLE:
An introduction to quantum sheaf cohomology
ABS:
In this talk, I will give an introduction to `quantum sheaf cohomology,'
an analogue of ordinary quantum cohomology determined by a space $X$
plus a holomorphic vector bundle ${\cal E} \rightarrow X$ satisfying
certain consistency conditions. Physically, this structure encodes
alpha'nonperturbative corrections to charged matter couplings in
heterotic strings, such as (27*)^3 couplings. Just as ordinary quantum
cohomology gives nonperturbative corrections to classical cohomology
rings, quantum sheaf cohomology gives nonperturbative corrections to
sheaf cohomology rings $H^(X, \wedge^ {\cal E}^*)$, and reduces to
ordinary quantum cohomology in the special case ${\cal E} = TX$. Just as
ordinary quantum cohomology arises in the study of the A model
topological field theory, quantum sheaf cohomology arises in the A/2
model holomorphic field theory, and plays a role in a generalization of
mirror symmetry known as (0,2) mirror symmetry. After giving a brief
introduction to general aspects of (0,2) mirrors and formal aspects of
quantum sheaf cohomology, we will explain general results for $X$ a
toric variety and ${\cal E}$ a deformation of the tangent bundle, and
give a detailed derivation for an example on $\mathbb{P}^1 \times
\mathbb{P}^1$.
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