tt* Geometry and a Twistorial Extension of Topological Strings
arXiv:1402.2674
Abstract
We extend the recent study of 3d tt* geometry to 5d (4d) N=1 (N=2) supersymmetric theories. We show how the amplitudes of tt* geometry lead to an extension of topological strings and Nekrasov partition functions to twistor space, where the north/south poles of the twistor sphere lead to topological/anti-topological string amplitudes. However, the equator of the twistor sphere is the physical region for the amplitudes, where the unitarity of physical amplitudes is respected. We propose that the amplitudes for line operators studied by Gaiotto, Moore and Neitzke lead to difference equations for the twistorial topological string partition function, extending the familiar one for the monodromy of Branes in the context of the standard topological strings. This setup unifies tt* geometry, topological strings and the hyperKahler geometry formulated by GMN into a single framework.
arXiv comment19 pages, the identification of tt* geometry with the parameters of the refined topological string clarified
References in corpus (13)
- Black Hole Attractors and the Topological String
- Topological Strings and Integrable Hierarchies
- Four-dimensional wall-crossing via three-dimensional field theory
- D-Branes And Mirror Symmetry
- Partition functions of N=(2,2) gauge theories on S^2 and vortices
- Exact Results in D=2 Supersymmetric Gauge Theories
- Analytic Continuation Of Chern-Simons Theory
- The Omega Deformation, Branes, Integrability, and Liouville Theory
- Quantum Background Independence In String Theory
- Wall-Crossing in Coupled 2d-4d Systems
- Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
- M-theory and a Topological String Duality
- On a hyperholomorphic line bundle over the Coulomb branch