Peacock patterns and resurgence in complex ChernSimons theory
@article{Garoufalidis2020PeacockPA, title={Peacock patterns and resurgence in complex ChernSimons theory}, author={Stavros Garoufalidis and Jie Gu and Marcos Mari{\~n}o}, journal={arXiv: Geometric Topology}, year={2020} }
The partition function of complex ChernSimons theory on a 3manifold with torus boundary reduces to a finite dimensional stateintegral which is a holomorphic function of a complexified Planck's constant $\tau$ in the complex cut plane and an entire function of a complex parameter $u$. This gives rise to a vector of factorially divergent perturbative formal power series whose Stokes rays form a peacocklike pattern in the complex plane. We conjecture that these perturbative series are…
6 Citations
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References
SHOWING 110 OF 80 REFERENCES
The Resurgent Structure of Quantum Knot Invariants
 Medicine, PhysicsCommunications in mathematical physics
 2021
It is conjectured that for a hyperbolic knot, a distinguished entry of those matrices equals to the Dimofte–Gaiotto–Gukov 3Dindex, and thus is given by a counting of BPS states.
Holomorphic blocks in three dimensions
 Physics
 2012
A bstractWe decompose sphere partition functions and indices of threedimensional N$$ \mathcal{N} $$ = 2 gauge theories into a sum of products involving a universal set of “holomorphic blocks”. The…
The quantum content of the gluing equations
 Mathematics, Physics
 2012
The gluing equations of a cusped hyperbolic 3manifold $M$ are a system of polynomial equations in the shapes of an ideal triangulation $\calT$ of $M$ that describe the complete hyperbolic structure…
ThreeDimensional Quantum Gravity, ChernSimons Theory, and the APolynomial
 Physics, Mathematics
 2003
We study threedimensional ChernSimons theory with complex gauge group SL(2,ℂ), which has many interesting connections with threedimensional quantum gravity and geometry of hyperbolic 3manifolds.…
ChernSimons theory, analytic continuation and arithmetic
 Mathematics
 2007
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…
Divergent Series, Summability and Resurgence I: Monodromy and Resurgence
 Mathematics
 2016
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential…
Analytic Continuation Of ChernSimons Theory
 Physics, Mathematics
 2010
The title of this article refers to analytic continuation of threedimensional ChernSimons gauge theory away from integer values of the usual coupling parameter k, to explore questions such as the…
Exact eigenfunctions and the open topological string
 Physics, Mathematics
 2016
Mirror curves to toric CalabiYau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the…
Generalized volume conjecture and the Apolynomials: The Neumann–Zagier potential function as a classical limit of the partition function
 Mathematics
 2006
Resurgence in complex ChernSimons theory
 Physics, Mathematics
 2016
We study resurgence properties of partition function of SU(2) ChernSimons
theory (WRT invariant) on closed threemanifolds. We check explicitly that in
various examples Borel transforms of…