Math @ Duke
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Publications [#221208] of Paul S. Aspinwall
Papers Published
- P.S. Aspinwall, Some Applications of Commutative Algebra to String Theory,
in Commutative Algebra, Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday
(2013)
(last updated on 2013/12/22)
Abstract: The topological B-model, which is a simplified model of string theory, is essentially algebraic
in nature. We describe how some calculations in this model may be performed using methods
of commutative algebra. In particular, we consider the B-model associated with a Calabi–
Yau threefold in the form of a complete intersection in a toric variety. There is a category of
D-branes associated to matrix factorizations, and we show how to compute certain products
and some Hochschild cohomology associated to this category. Mirror symmetry and the
notion of stability lead to a notion of monodromy on this D-brane category. In general this
monodromy can be awkward to compute, but we show how much of the combinatorial data
associated to the monodromy can be accessed using commutative algebra.
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