35 research outputs found

    Fusion of implementers for spinors on the circle

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    We consider the space of odd spinors on the circle, and a decomposition into spinors supported on either the top or on the bottom half of the circle. If an operator preserves this decomposition, and acts on the bottom half in the same way as a second operator acts on the top half, then the fusion of both operators is a third operator acting on the top half like the first, and on the bottom half like the second. Fusion restricts to the Banach Lie group of restricted orthogonal operators, which supports a central extension of implementers on a Fock space. In this article, we construct a lift of fusion to this central extension. Our construction uses Tomita-Takesaki theory for the Clifford-von Neumann algebras of the decomposed space of spinors. Our motivation is to obtain an operator-algebraic model for the basic central extension of the loop group of the spin group, on which the fusion of implementers induces a fusion product in the sense considered in the context of transgression and string geometry. In upcoming work we will use this model to construct a fusion product on a spinor bundle on the loop space of a string manifold, completing a construction proposed by Stolz and Teichner.Comment: 49 page

    Transgression of D-branes

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    Closed strings can be seen either as one-dimensional objects in a target space or as points in the free loop space. Correspondingly, a B-field can be seen either as a connection on a gerbe over the target space, or as a connection on a line bundle over the loop space. Transgression establishes an equivalence between these two perspectives. Open strings require D-branes: submanifolds equipped with vector bundles twisted by the gerbe. In this paper we develop a loop space perspective on D-branes. It involves bundles of simple Frobenius algebras over the branes, together with bundles of bimodules over spaces of paths connecting two branes. We prove that the classical and our new perspectives on D-branes are equivalent. Further, we compare our loop space perspective to Moore-Segal/Lauda-Pfeiffer data for open-closed 2-dimensional topological quantum field theories, and exhibit it as a smooth family of reflection-positive, colored knowledgable Frobenius algebras

    Geometric T-duality: Buscher rules in general topology

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    The classical Buscher rules describe T-duality for metrics and B-fields in a topologically trivial setting. On the other hand, topological T-duality addresses aspects of non-trivial topology while neglecting metrics and B-fields. In this article we develop a new unifying framework for both aspects.Comment: 67 pages. In v2 some typos and sign mistakes have been corrected; v2 is the published versio