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تسجيل مستخدم جديدTwisted K-theory and K-theory of bundle gerbes
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In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial backgrounds are discussed.
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Equivariant twisted K theory classes on compact Lie groups $G$ can be realized as families of Fredholm operators acting in a tensor product of a fermionic Fock space and a representation space of a central extension of the loop algebra $LG$ using a s
upersymmetric Wess-Zumino-Witten model. The aim of the present article is to extend the construction to higher loop algebras using an abelian extension of a $3D$ current algebra. We have only partial success: Instead of true Fredholm operators we have formal algebraic expressions in terms of the generators of the current algebra and an infinite dimensional Clifford algebra. These give rise to sesquilinear forms in a Hilbert bundle which transform in the expected way with respect to $3D$ gauge transformations but do not define true Hilbert space operators.
In this note we prove the analogue of the Atiyah-Segal completion theorem for equivariant twisted K-theory in the setting of an arbitrary compact Lie group G and an arbitrary twisting of the usually considered type. The theorem generalizes a result b
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