Twisted K-theory in g>1 from D-branes
Isidro, J. M.
Original · EN
We study the wrapping of N type IIB Dp-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 Dp'-brane/antibrane pairs, with p'>p. A background Neveu-Schwarz field B deforms the commutative C⋆-algebra of functions on Σ to a noncommutative 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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