Volume 20, issue 6 (2016)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Asymptotic formulae for curve operators in TQFT

Renaud Detcherry

Geometry & Topology 20 (2016) 3057–3096
Abstract

The Reshetikhin–Turaev topological quantum field theories with gauge group SU2 associate to any oriented surface Σ a sequence of vector spaces V r(Σ) and to any simple closed curve γ in Σ a sequence of Hermitian operators Trγ on the spaces V r(Σ). These operators are called curve operators and play a very important role in TQFT.

We show that the matrix elements of the operators Trγ have an asymptotic expansion in orders of 1r, and give a formula to compute the first two terms from trace functions, generalizing results of Marché and Paul for the punctured torus and the 4–holed sphere to general surfaces.

Keywords
TQFT, skein calculus, moduli spaces
Mathematical Subject Classification 2010
Primary: 57R56
References
Publication
Received: 3 September 2012
Revised: 11 September 2015
Accepted: 25 March 2016
Published: 21 December 2016
Proposed: Vaughan Jones
Seconded: Robion Kirby, Leonid Polterovich
Authors
Renaud Detcherry
Institut de Mathématiques de Jussieu
Université Paris 6
4 place Jussieu
75005 Paris
France