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

J. M. Isidro
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Abstract

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 $C^{\star}$-algebra of functions on $Σ$ to a noncommutative $C^{\star}$-algebra. Our construction provides an explicit example of the $N'\to\infty$ 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.

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J. M. Isidro. 2001-11-16. Twisted K-theory in $g>1$ from D-branes. https://doi.org/10.1016/s0393-0440(01)00095-x

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