Evaluation of state integrals at rational points

Saturday, 22 November, 2014

Published in: 

arXiv:1411.6062

Multi-dimensional state-integrals of products of Faddeev's quantum dilogarithms arise frequently in Quantum Topology, quantum Teichmuller theory and complex Chern--Simons theory. Using the quasi-periodicity property of the quantum dilogarithm, we evaluate 1-dimensional state-integrals at rational points and express the answer in terms of the Rogers dilogarithm, the cyclic (quantum) dilogarithm and finite state-sums at roots of unity. We illustrate our results with the evaluation of the state-integrals of the 4_1, 5_2 and (−2,3,7) pretzel knots at rational points.

Author(s): 

Stavros Garoufalidis
Rinat Kashaev