Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-07-28
Nucl.Phys. B591 (2000) 547-583
Physics
High Energy Physics
High Energy Physics - Theory
49pp LaTeX, ref added, last paragraph of section (4.3) deleted
Scientific paper
10.1016/S0550-3213(00)00533-2
We generalize the spectral-curve construction of moduli spaces of instantons on $\MT{4}$ and $K_3$ to noncommutative geometry. We argue that the spectral-curves should be constructed inside a twisted $\MT{4}$ or $K_3$ that is an elliptic fibration without a section. We demonstrate this explicitly for $T^4$ and to first order in the noncommutativity, for $K_3$. Physically, moduli spaces of noncommutative instantons appear as moduli spaces of theories with $\SUSY{4}$ supersymmetry in 2+1D. The spectral curves are related to Seiberg-Witten curves of theories with $\SUSY{2}$ in 3+1D. In particular, we argue that the moduli space of instantons of $U(q)$ Yang-Mills theories on a noncommutative $K_3$ is equivalent to the Coulomb branch of certain 2+1D theories with ${\cal N} = 4$ supersymmetry. The theories are obtained by compactifying the heterotic little-string theory on $T^3$ with global twists. This extends a previous result for noncommutative instantons on $\MT{4}$. We also briefly discuss the instanton equation on generic curved spaces.
Ganor Ori J.
Mikhailov Andrei Yu.
Saulina Natalia
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