A New supersymmetric index

Cecotti, Sergio; Fendley, Paul; Intriligator, Kenneth A.; Vafa, Cumrun

doi:10.1016/0550-3213(92)90572-S

A New supersymmetric index

Sergio Cecotti
(
- SISSA, Trieste
)
,
Paul Fendley
(
- Boston U.
)
,
Kenneth A. Intriligator
(
- Harvard U.
)
,
Cumrun Vafa
(
- Harvard U.
)

Apr, 1992

48 pages

Published in:

Nucl.Phys.B 386 (1992) 405-452

Published: 1992

e-Print:

hep-th/9204102 [hep-th]

DOI:

10.1016/0550-3213(92)90572-S

Report number:

HUTP-92-A021,
SISSA-68-92-EP,
BUHEP-92-14

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Abstract:

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.

talk
supersymmetry: index theorem
dimension: 2
geometry: ground state
quantization
linear space: Hilbert space
energy
entropy
integrability
bibliography

References(44)

Figures(0)

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