Prepotential and the Seiberg-Witten theory

Itoyama, H.; Morozov, A.

doi:10.1016/S0550-3213(96)00679-7

Prepotential and the Seiberg-Witten theory

H. Itoyama
(
- Osaka U.
)
,
A. Morozov
(
- Moscow, ITEP
)

Dec, 1995

50 pages

Published in:

Nucl.Phys.B 491 (1997) 529-573

e-Print:

hep-th/9512161 [hep-th]

DOI:

10.1016/S0550-3213(96)00679-7

Report number:

ITEP-M6-95,
OU-HET-230

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Abstract:

Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical

\tau

-functions , which uses as input a family of complex spectral curves with a meromorphic differential

dS

, subject to the constraint

\partial dS/\partial(moduli)= \ holomorphic

, and gives as an output a homogeneous prepotential on extended moduli space. Then reversed construction is discussed, which is straightforwardly generalizable from spectral {\it curves} to certain complex manifolds of dimension

d >1

(like

K3

and

CY

families). Finally, examples of particular

N=2

SUSY gauge models are considered from the point of view of this formalism. At the end we discuss similarity between the

WP~{12}_{1,1,2,2,6}

-\-Calabi-\-Yau model with

h_{21}=2

and the

1d

SL(2)

Calogero/Ruijsenaars model, but stop short of the claim that they belong to the same Whitham universality class beyond the conifold limit.

Note:

50 pages, Latex Report-no: ITEP-M6/95, OU-HET-230

N = 2 supersymmetry
Low-energy prepotential
Quasi-classical τ-function
Elliptic Calogero system
Picard-Fuchs equation
Meromorphic differential
field theory: topological
potential: prepotential
Riemann surface
moduli space

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