Topological string theory and integrable structures

Klemm, Albrecht

doi:10.1002/prop.200410235

Cited by 1 publication

(1 citation statement)

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“…However, for the rest of this work we will mostly need only the explicit form of the holomorphic anomaly equations. For a more detailed introduction to topological string theory the reader might want to consult references [30,60,51,44,39].…”

Section: The Holomorphic Anomaly Equationsmentioning

confidence: 99%

Direct integration of the topological string

Grimm¹,

Klemm²,

Mariño³

et al. 2007

J. High Energy Phys.

132

235

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We present a new method to solve the holomorphic anomaly equations governing the free energies of type B topological strings. The method is based on direct integration with respect to the non-holomorphic dependence of the amplitudes, and relies on the interplay between non-holomorphicity and modularity properties of the topological string amplitudes. We develop a formalism valid for any Calabi-Yau manifold and we study in detail two examples, providing closed expressions for the amplitudes at low genus, as well as a discussion of the boundary conditions that fix the holomorphic ambiguity. The first example is the non-compact Calabi-Yau underlying Seiberg-Witten theory and its gravitational corrections. The second example is the Enriques Calabi-Yau, which we solve in full generality up to genus six. We discuss various aspects of this model: we obtain a new method to generate holomorphic automorphic forms on the Enriques moduli space, we write down a new product formula for the fiber amplitudes at all genus, and we analyze in detail the field theory limit. This allows us to uncover the modularity properties of SU(2), N = 2 super Yang-Mills theory with four massless hypermultiplets.

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Section: The Holomorphic Anomaly Equationsmentioning

confidence: 99%