Families of Monads and Instantons from a Noncommutative ADHM Construction
Quantum Algebra
2011-05-19 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We give a \theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families' of SU(2) instantons on the deformed sphere S^4_\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.
Keywords
Cite
@article{arxiv.0901.0772,
title = {Families of Monads and Instantons from a Noncommutative ADHM Construction},
author = {Simon Brain and Giovanni Landi},
journal= {arXiv preprint arXiv:0901.0772},
year = {2011}
}
Comments
v2: 29 pages, minor changes. Final version to appear in a special volume of the Clay Mathematics Institute dedicated to Alain Connes