A New Supersymmetric Index

Details A New Supersymmetric Index A New Supersymmetric Index

1992-04-30

arxiv.org/abs/hep-th/9204102v1

Nucl.Phys.B386:405-452,1992

Physics

High Energy Physics

High Energy Physics - Theory

60 pages

Scientific paper

10.1016/0550-3213(92)90572-S

We show that ${\rm Tr}(-1)^F F e^{-\beta H}$ 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.

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