Instantons on a Non-commutative $T^4$ from Twisted (2,0) and Little-String Theories

Details Instantons on a Non-commutative $T^4$ from Twisted (2,0) and Little-String Theories Instantons on a Non-commutative $T^4$ from Twisted (2,0) and Little-String Theories

1998-12-18

arxiv.org/abs/hep-th/9812172v2

Nucl.Phys. B564 (2000) 259-284

Physics

High Energy Physics

High Energy Physics - Theory

32pp TeX, minor corrections

Scientific paper

We show that the moduli space of the $(2,0)$ and little-string theories compactified on $T^3$ with R-symmetry twists is equal to the moduli space of U(1) instantons on a non-commutative $T^4$. The moduli space of $U(q)$ instantons on a non-commutative $T^4$ 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 $T^4$.

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