Constructions of Non Commutative Instantons on $T^4$ and $K_3$

Ori J. Ganor; Andrei Yu. Mikhailov; Natalia Saulina

doi:10.1016/S0550-3213(00)00533-2

paper

Constructions of Non Commutative Instantons on $T^{4}$ and $K_{3}$

arXiv:hep-th/0007236 · doi:10.1016/S0550-3213(00)00533-2

Abstract

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 $N = 4$ 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.

49pp LaTeX, ref added, last paragraph of section (4.3) deleted

Constructions of Non Commutative Instantons on $T^{4}$ and $K_{3}$

Abstract

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Constructions of Non Commutative Instantons on T4 and K3​

Abstract

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Cited by in corpus (9)

Constructions of Non Commutative Instantons on $T^{4}$ and $K_{3}$