Chern-Simons theory, analytic continuation and arithmetic
By Stavros Garoufalidis. 2007
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The purpose of the paper is to introduce some conjectures re- garding the analytic continuation and the arithmetic properties of quantum invariants of knotted objects. More precisely, we package the perturbative and nonperturbative invariants of knots and 3-manifolds into two power series of type P and NP, convergent in a neighborhood of zero, and we postulate their arithmetic resurgence. By the latter term, we mean analytic continuation as a multivalued analytic function in the complex numbers minus a discrete set of points, with restricted singularities, local and global monodromy. We point out some key features of arithmetic resurgence in connection to various problems of asymptotic expansions of exact and perturbative Chern-Simons theory with compact or complex gauge group. Finally, we discuss theoretical and experimental evidence for our conjecture.
View Paper: https://www.semanticscholar.org/paper/ee20e2dced41ad6e34157fd918fd1a2617e79e76
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Citations in the corpus
- Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, background): “Questions on classical asymptotics and Borel summability in CS theory have started to be addressed only recently, see [61, 123] for some results and/or conjectures.”