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

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 noncommutative T . The moduli space of U(q) instantons on a non-commutative T 4 is obtained from little-string theories of NS5-branes at Aq−1 singularities with twists. A large class of gauge theories with N = 4 SUSY in 2+1D and 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 .