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June 2013 Quantum Riemann surfaces in Chern-Simons theory
Tudor Dimofte
Adv. Theor. Math. Phys. 17(3): 479-599 (June 2013).


We construct from first principles the operators $\hat A_M$ that annihilate the partition functions (or wavefunctions) of three-dimensional Chern-Simons theory with gauge groups $SU(2)$, $SL(2,\mathbb{R})$, or $SL(2,\mathbb{C})$ on knot complements $M$. The operator $\hat A_M$ is a quantization of a knot complement's classical $A$-polynomial $A_M(\ell,m)$. The construction proceeds by decomposing three-manifolds into ideal tetrahedra, and invoking a new, more global understanding of gluing in topological quantum field theory to put them back together. We advocate in particular that, properly interpreted, "gluing $=$ symplectic reduction." We also arrive at a new finite-dimensional state integral model for computing the analytically continued "holomorphic blocks" that compose any physical Chern-Simons partition function.


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Tudor Dimofte. "Quantum Riemann surfaces in Chern-Simons theory." Adv. Theor. Math. Phys. 17 (3) 479 - 599, June 2013.


Published: June 2013
First available in Project Euclid: 20 August 2014

zbMATH: 1304.81143
MathSciNet: MR3250765

Rights: Copyright © 2013 International Press of Boston


Vol.17 • No. 3 • June 2013
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