Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-11-27
Phys.Lett. B555 (2003) 287-295
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, Latex
Scientific paper
10.1016/S0370-2693(03)00077-7
We demonstrate by explicit calculation that the first two terms in the CIV-DV prepotential for the two-cut case satisfy the generalized WDVV equations, just as in all other known examples of hyperelliptic Seiberg-Witten models. The WDVV equations are non-trivial in this situation, provided the set of moduli is extended as compared to the Dijkgraaf-Vafa suggestion and includes also moduli, associated with the positions of the cuts (not only with their lengths). Expression for the extra modulus dictated by WDVV equation, however, appears different from a naive expectation implied by the Whitham theory. Moreover, for every value of the "quantum-deformation parameter" 1/g_3, we actually find an entire one-parameter family of solutions to the WDVV equations, of which the conventional prepotential is just a single point.
Itoyama Hiroshi
Morozov Alexander
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