Abstract
We study the wrapping of N-type IIB D p-branes on a compact Riemann surface Σ in genus g>1 by means of the Sen–Witten construction, as a superposition of N′-type IIB D p′-brane/antibrane pairs, with p′> p. A background Neveu–Schwarz field B deforms the commutative C ☆ -algebra of functions on Σ to a non-commutative C ☆ -algebra. Our construction provides an explicit example of the N′→∞ 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 ☆ -algebra, by explicitly constructing a family of projective C ☆ -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.
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