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

✍ Scribed by José M. Isidro

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 147 KB
• Volume: 42
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(01)00095-x

✦ Synopsis

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 ଝ -algebra of functions on Σ to a non-commutative C ଝ -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 ଝ -algebra, by explicitly constructing a family of projective C ଝ -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.