Evaluation of state integrals at rational points

Saturday, 22 November, 2014

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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.


Stavros Garoufalidis
Rinat Kashaev