A New Class of N=2 Topological Amplitudes

Understand

We describe a new class of N=2 topological amplitudes that compute a particular class of BPS terms in the low energy effective supergravity action.

• Specifically they compute the coupling F^2(\lambda\lambda)^{g-2}(d\phi)^2 where F, \lambda and \phi are gauge field strengths, gaugino and holomorphic vector multiplet scalars.
• The novel feature of these terms is that they depend both on the vector and hypermultiplet moduli.
• The BPS nature of these terms implies that they satisfy a holomorphicity condition with respect to vector moduli and a harmonicity condition as well as a second order differential equation with respect to hypermultiplet moduli.