Asymptotic formulas for curve operators in TQFT

Abstract

Topological quantum field theories with gauge group ${\text{SU}}_2$ associate to each surface with marked points $\Sigma$ and each integer $r>0$ a vector space $V_r(\Sigma )$ and to each simple closed curve $\gamma$ in $\Sigma$ an Hermitian operator $T_r^{\gamma }$ acting on that space. We show that the matrix elements of the operators $T_r^{\gamma }$ have an asymptotic expansion in orders of $\frac{1}{r}$, and give a formula to compute the first two terms in terms of trace functions, generalizing results of Marché and Paul.

References in corpus (2)

• Geometric construction of modular functors from Conformal Field Theory
• Abelian Conformal Field theories and Determinant Bundles

Cited by in corpus (1)

• An embedding of skein algebras of surfaces into quantum tori from Dehn-Thurston coordinates