Quantum Dilogarithm Identities at Root of Unity

Abstract

We study the root of unity degeneration of cluster algebras and quantum dilogarithm identities. We prove identities for the cyclic dilogarithm associated with a mutation sequence of a quiver, and as a consequence new identities for the non-compact quantum dilogarithm at $b=1$.

20 pages

References in corpus (7)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• The quantum dilogarithm and representations quantum cluster varieties
• R-Twisting and 4d/2d Correspondences
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Quivers, YBE and 3-manifolds
• Emergent 3-manifolds from 4d Superconformal Indices
• BPS spectrum, wall crossing and quantum dilogarithm identity

Cited by in corpus (5)

• Comments on Exchange Graphs in Cluster Algebras
• Theta series, wall-crossing and quantum dilogarithm identities
• Integrability As Duality: The Gauge/YBE Correspondence
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• On webs, polylogarithms and cluster algebras