Supersymmetric Partition Functions and a String Theory in 4 Dimensions
arXiv:1209.2425
Abstract
We propose a novel string theory propagating in a non-commutative deformation of the four dimensional space T* T^2 whose scattering states correspond to superconformal theories in 5 dimensions and the scattering amplitudes compute superconformal indices of the corresponding 5d theories. The superconformal theories are obtained by M-theory compactifications on singular CY 3-folds or equivalently from a web of 5-branes of type IIB strings. The cubic interaction of this string theory for primitive winding modes corresponds to the (refined) topological vertex. The oscillator modes of the string theory correspond to off-shell states and carry information about co-dimension 2 defects of the superconformal theory. Particular limits of a subset of scattering amplitudes of this string theory lead to the partition functions of A_n Gaiotto theories for all n, compactified on S^4, i.e., to amplitudes of all Toda theories.
40 pages
References in corpus (5)
- A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
- The Refined Topological Vertex
- 5-dim Superconformal Index with Enhanced En Global Symmetry
- Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
- M-theory and a Topological String Duality