2003/05/31 by T. A. Ivanova, Tatiana A. Ivanova, Olaf Lechtenfeld · 16 citations
Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Codimension #Cosmology and Gravitation Theories #Gauge theory #Geometry #Instanton #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Scalar (mathematics) #Scalar field #Vortex #hep-th
paper · pdf · open access · doi:10.1016/s0370-2693(03)00868-2
published in Physics Letters B 567(1-2), 107-115 (Elsevier BV) · 1+8 pages, v2: reference added, version published in PLB
arxiv created 2003/06/16 · openalex publication_date 2003/07/07 · arxiv updated 2010/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Generalizing self-duality on R-2 x S-2 to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on R-2n x S-2 and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an Abelian gauge field and a complex scalar on R-theta(2n). For a special S-2-radius R depending on the noncommutativity theta we find explicit solutions in terms of shift operators. These vortex-like configurations on R-theta(2n) determine SO(3)-invariant multi-instantons on R-theta(2n) x S-R(2) for R = R(theta). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S-2 factor of suitable size