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Superpotentials from singular divisors
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DOI：10.1007/JHEP11(2022)142.png)
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摘要
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We study Euclidean D3-branes wrapping divisors D in Calabi-Yau orientifold compactifications of type IIB string theory. Witten's counting of fermion zero modes in terms of the cohomology of the structure sheaf O-D applies when D is smooth, but we argue that effective divisors of Calabi-Yau threefolds typically have singularities along rational curves. We generalize the counting of fermion zero modes to such singular divisors, in terms of the cohomology of the structure sheaf O-(D) over bar of the normalization (D) over bar of D. We establish this by detailing compactifications in which the singularities can be unwound by passing through flop transitions, giving a physical incarnation of the normalization process. Analytically continuing the superpotential through the flops, we find that singular divisors whose normalizations are rigid can contribute to the superpotential: specifically, h(+)(.) (O-(D) over bar) = (1, 0, 0) and h(-)(.)(O-(D) over bar) = (0, 0, 0) give a sufficient condition for a contribution. The examples that we present feature infinitely many isomorphic geometric phases, with corresponding infinite-order monodromy groups Gamma. We use the action of Gamma on effective divisors to determine the exact effective cones, which have infinitely many generators. The resulting nonperturbative superpotentials are Jacobi theta functions, whose modular symmetries suggest the existence of strong-weak coupling dualities involving inversion of divisor volumes.
Keyword:
D-Branes
Flux Compactifications
String and Brane Phenomenology
Super-string Vacua
期刊
IF:
5.5
论文数:
3.9W
被引数:
13.7W
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