Exact WKB analysis and cluster algebras
By Kohei Iwaki, Tomoki Nakanishi. 2014
146 citations recorded by the source corpus.
We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/752bb46e4260d0fa5282cc41f32cf52d6f603ed3
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In Algebra and Number Theory
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Citations in the corpus
- The classification of \tau-tilting modules over Nakayama algebras (2013, methodology): “ Theorem 2.27). Moreover, we give a bijection between the set sτ-tiltΛ of isomorphism classes of basic support τ-tilting Λ-modules and the set of signed triangulations introduced recently by [BS] and [IN] (See Corollary 2.18). Note that Theorem A is analogous to known classification 1 2 TAKAHIDE ADAC”