Supersymmetric Partition Functions and a String Theory in 4 Dimensions

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

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Cited by in corpus (8)

• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Topological strings and 5d T_N partition functions
• BPS Degeneracies and Superconformal Index in Diverse Dimensions
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Refined Black Hole Ensembles and Topological Strings
• Refined Topological Strings on Local ${\mathbb{P}}^2$
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• Some statistics about Tropical Sandpile Model