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Modular functors in homotopy quantum field theory and tortile structures

✍ Scribed by Mark Brightwell; Paul Turner

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
296 KB
Volume
185
Category
Article
ISSN
0022-4049

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✦ Synopsis

We study a version of a modular functor for Turaev's homotopy quantum ΓΏeld theories using 2-categories of surfaces. We deΓΏne the homotopy surface 2-category of a space X and deΓΏne an SX -structure to be a monoidal 2-functor from this to the 2-category of idempotent-complete additive k-linear categories. We initiate the study of the algebraic structure arising from these functors. In particular we show that a unitary SX -structure gives rise to a lax tortile -category when the background space is an Eilenberg-Maclane space X = K( ; 1), and to a tortile category with lax 2X -action when the background space is simply connected.

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Modular inclusion, the Hawking temperatu
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A recent result by Borchers connecting geometric modular action, modular inclusion and spectrum condition, is applied in quantum field theory on spacetimes with a bifurcate Killing horizon (these are generalizations of black-hole spacetimes, comprising the familiar black-hole spacetime models). With