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December 2011 Algebraic deformations of toric varieties II: noncommutative instantons
Lucio Cirio, Giovanni Landi, Richard J. Szabo
Adv. Theor. Math. Phys. 15(6): 1817-1907 (December 2011).


We continue our study of the noncommutative algebraic and differential geometry of a particular class of deformations of toric varieties, focusing on aspects pertinent to the construction and enumeration of noncommutative instantons on these varieties. We develop a noncommutative version of twistor theory, which introduces a new example of a noncommutative four-sphere. We develop a braided version of the ADHM construction and show that it parameterizes a certain moduli space of framed torsion free sheaves on a noncommutative projective plane. We use these constructions to explicitly build instanton gauge bundles with canonical connections on the noncommutative four-sphere that satisfy appropriate anti-selfduality equations. We construct projective moduli spaces for the torsion free sheaves and demonstrate that they are smooth. We define equivariant partition functions of these moduli spaces, finding that they coincide with the usual instanton partition functions for supersymmetric gauge theories on $\mathbb{C}2$.


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Lucio Cirio. Giovanni Landi. Richard J. Szabo. "Algebraic deformations of toric varieties II: noncommutative instantons." Adv. Theor. Math. Phys. 15 (6) 1817 - 1907, December 2011.


Published: December 2011
First available in Project Euclid: 12 December 2012

zbMATH: 1262.14002
MathSciNet: MR2989814

Rights: Copyright © 2011 International Press of Boston

Vol.15 • No. 6 • December 2011
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