Solving N=2 SYM by Reflection Symmetry of Quantum Vacua

Details Solving N=2 SYM by Reflection Symmetry of Quantum Vacua Solving N=2 SYM by Reflection Symmetry of Quantum Vacua

1996-10-06

arxiv.org/abs/hep-th/9610026v3

Phys.Rev. D55 (1997) 6466-6470

Physics

High Energy Physics

High Energy Physics - Theory

12 pg. LaTex, Discussion of the generalization to higher rank groups added. To be published in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.55.6466

The recently rigorously proved nonperturbative relation between u and the prepotential, underlying N=2 SYM with gauge group SU(2), implies both the reflection symmetry $\overline{u(\tau)}=u(-\bar\tau)$ and $u(\tau+1)=-u(\tau)$ which hold exactly. The relation also implies that $\tau$ is the inverse of the uniformizing coordinate u of the moduli space of quantum vacua. In this context, the above quantum symmetries are the key points to determine the structure of the moduli space. It turns out that the functions a(u) and a_D(u), which we derive from first principles, actually coincide with the solution proposed by Seiberg and Witten. We also consider some relevant generalizations.

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