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A<sc>bstract</sc> Deformations of the heterotic superpotential give rise to a topological holomorphic theory with similarities to both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. Although the action is cubic, it is only quadratic in the complex structure deformations (the Beltrami differential). Treated separately, for large fluxes, or alternatively at large distances in the background complex structure moduli space, these fields can be integrated out to obtain a new field theory in the remaining fields, which describe the complexified hermitian and gauge degrees of freedom. We investigate properties of this new holomorphic theory, and in particular connections to the swampland distance conjecture in the context of heterotic string theory. In the process, we define a new type of symplectic cohomology theory, where the background complex structure Beltrami differential plays the role of the symplectic form.
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Why Surplus Structure is Not Superfluous
The idea that gauge theory has ‘surplus’ structure poses a puzzle: in one much discussed sense, this structure is redundant; but on the other hand, it is also widely held to play an essential role in the theory. In this article, we employ category-theoretic tools to illuminate an aspect of this puzzle. We precisify what is meant by surplus structure by means of functorial comparisons with equivalence classes of gauge fields, and then show that such structure is essential for any theory that represents a rich collection of physically relevant fields that are ‘local’ in nature.
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- Award ID(s):
- 1734155
- PAR ID:
- 10108280
- Date Published:
- Journal Name:
- British journal for the philosophy of science
- ISSN:
- 0007-0882
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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