Instantons on a Non-commutative T⁴ from Twisted (2,0) and Little-String Theories

1998/12/23 by Yeuk-Kwan E. Cheung, Ori J. Ganor, Morten Krogh +1
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP

paper · pdf

published as Nucl.Phys. B564 (2000) 259-284 · 32pp TeX, minor corrections

arxiv created 1998/12/23 · arxiv updated 2009/11/30

Abstract

We show that the moduli space of the (2,0) and little-string theories compactified on T³ with R-symmetry twists is equal to the moduli space of U(1) instantons on a non-commutative T⁴. The moduli space of U(q) instantons on a non-commutative T⁴ is obtained from little-string theories of NS5-branes at A_q-1 singularities with twists. A large class of gauge theories with \cal N=4 SUSY in 2+1D and \cal N=2 SUSY in 3+1D are limiting cases of these theories. Hence, the moduli spaces of these gauge theories can be read off from the moduli spaces of instantons on non-commutative tori. We study the phase transitions in these theories and the action of T-duality. On the purely mathematical side, we give a prediction for the moduli space of 2 U(1) instantons on a non-commutative T⁴.

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