A New Supersymmetric Index

Abstract

We show that $\mathrm{Tr}(-1{)}^{F}F{e}^{-\beta H}$ is an index for $N$=2 supersymmetric theories in two dimensions, in the sense that it is independent of almost all deformations of the theory. This index is related to the geometry of the vacua (Berry's curvature) and satisfies an exact differential equation as a function of $\beta$. For integrable theories we can also compute the index thermodynamically, using the exact $S$-matrix. The equivalence of these two results implies a highly non-trivial equivalence of a set of coupled integral equations with these differential equations, among them Painleve III and the affine Toda equations.

60 pages

References in corpus (8)

• Geometry and Integrability of Topological-Antitopological Fusion
• Scattering and Thermodynamics of Fractionally-Charged Supersymmetric Solitons
• Scattering and Thermodynamics of Integrable N=2 Theories
• Exact Results for Supersymmetric Sigma Models
• N=2 Supersymmetry, Painleve III and Exact Scaling Functions in 2D Polymers
• Topological Matter, Integrable Models and Fusion Rings
• Topological Landau-Ginzburg Matter from Sp(N)_{K} Fusion Rings
• Symplectic fusion rings and their metric

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