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- Title
Symplectic Geometry of Character Varieties and SU(2) Lattice Gauge Theory I.
- Authors
Ramadas, T. R.
- Abstract
Associated to any finite graph Λ is a closed surface S = S Λ , the boundary of a regular neighbourhood of an embedding of Λ in any three manifold. The surface retracts to the graph, mapping loops on the surface to loops on the graph. The (SU(2)) character variety M of S has a symplectic structure and associated Liouville measure; on the other hand, the character variety M of Λ carries a natural measure inherited from the Haar measure. Loops on S define functions on the character varieties, the Wilson loops. By the works of W. Goldman, L. Jeffrey and J. Weitsman, the formalism of Duistermaat-Heckman applies to the relevant integrals over M . We develop a calculus for calculating correlations of Wilson loops on M w.r.to the normalised Liouville measure, and present evidence that they approximate—for large graphs—the corresponding integrals over M . Lattice field theory involves integrals over M ; we present “symplectic” analogues of expressions for partition functions, Wilson loop expectations, etc., in two and three space-time dimensions.
- Publication
Communications in Mathematical Physics, 2024, Vol 405, Issue 4, p1
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-024-04968-x