BPS black holes, the Hesse potential, and the topological string

The Hesse potential is constructed for a class of four-dimensional N = 2 supersymmetric effective actions with S- and T-duality by performing the relevant Legendre transform by iteration. It is a function of fields that transform under duality according to an arithmetic subgroup of the classical dua...

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Published inThe journal of high energy physics Vol. 2010; no. 6
Main Authors Cardoso, G. L., de Wit, B., Mahapatra, S.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.06.2010
Springer Nature B.V
Subjects
Black holes
Classical and Quantum Gravitation
Couplings
Elementary Particles
Free energy
High energy physics
Iterative methods
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
Strings
Subgroups
Supersymmetry
Topology
Black Holes in String Theory
Topological Strings
Supersymmetry and Duality
Extended Supersymmetry
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Summary:The Hesse potential is constructed for a class of four-dimensional N = 2 supersymmetric effective actions with S- and T-duality by performing the relevant Legendre transform by iteration. It is a function of fields that transform under duality according to an arithmetic subgroup of the classical dualities reflecting the monodromies of the underlying string compactification. These transformations are not subject to corrections, unlike the transformations of the fields that appear in the effective action which are affected by the presence of higher-derivative couplings. The class of actions that are considered includes those of the FHSV and the STU model. We also consider heterotic N = 4 supersymmetric compactifications. The Hesse potential, which is equal to the free energy function for BPS black holes, is manifestly duality invariant. Generically it can be expanded in terms of powers of the modulus that represents the inverse topological string coupling constant, g s , and its complex conjugate. The terms depending holomorphically on g s are expected to correspond to the topological string partition function and this expectation is explicitly verified in two cases. Terms proportional to mixed powers of g s and are in principle present.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP06(2010)052