Twisted K-theory in $g>1$ from D-branes

Abstract

We study the wrapping of N type IIB Dp-branes on a compact Riemann surface $\Sigma$ in genus $g>1$ by means of the Sen-Witten construction, as a superposition of N' type IIB Dp'-brane/antibrane pairs, with $p^{\prime }>p$. A background Neveu-Schwarz field B deforms the commutative $C^{\star }$-algebra of functions on $\Sigma$ to a noncommutative $C^{\star }$-algebra. Our construction provides an explicit example of the $N^{\prime }\to \infty$ limit advocated by Bouwknegt-Mathai and Witten in order to deal with twisted K-theory. We provide the necessary elements to formulate M(atrix) theory on this new $C^{\star }$-algebra, by explicitly constructing a family of projective $C^{\star }$-modules admitting constant-curvature connections. This allows us to define the $g>1$ analogue of the BPS spectrum of states in $g=1$, by means of Donaldson's formulation of the Narasimhan-Seshadri theorem.

LaTeX, 20 pages

References in corpus (2)

• Branes on Group Manifolds, Gluon Condensates, and twisted K-theory
• Open Strings and Non-commutative Geometry of Branes on Group Manifolds

Cited by in corpus (2)

• Tachyon Dynamics in Open String Theory
• Orientifolds of SU(2)/U(1) WZW Models