Deformations of special geometry: in search of the topological string

• Published in: The journal of high energy physics Vol. 2014; no. 9; p. 1
• Main Authors: Cardoso, G. L., de Wit, B., Mahapatra, S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2014; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Topological Strings; Supersymmetric Effective Theories; Supersymmetry and Duality; Extended Supersymmetry
• DOI: 10.1007/JHEP09(2014)096
• ISSN: 1029-8479

A bstract The topological string captures certain superstring amplitudes which are also encoded in the underlying string effective action. However, unlike the topological string free energy, the effective action that comprises higher-order derivative couplings is not defined in terms of duality covariant variables. This puzzle is resolved in the context of real special geometry by introducing the so-called Hesse potential, which is defined in terms of duality covariant variables and is related by a Legendre transformation to the function that encodes the effective action. It is demonstrated that the Hesse potential contains a unique subsector that possesses all the characteristic properties of a topological string free energy. Genus g ≤ 3 contributions are constructed explicitly for a general class of effective actions associated with a special-Kähler target space and are shown to satisfy the holomorphic anomaly equation of perturbative type-II topological string theory. This identification of a topological string free energy from an effective action is primarily based on conceptual arguments and does not involve any of its more specific properties. It is fully consistent with known results. A general theorem is presented that captures some characteristic features of the equivalence, which demonstrates at the same time that non-holomorphic deformations of special geometry can be dealt with consistently.