2017/08/31 by Arghya Chattopadhyay, Parikshit Dutta, Suvankar Dutta · 12 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Chemistry #Computer science #Eigenvalues and eigenvectors #Geometry #Mathematical physics #Mathematics #Matrix (chemical analysis) #Momentum (technical analysis) #Phase (matter) #Phase diagram #Phase space #Physics #Plane (geometry) #Quantum many-body systems #Quantum mechanics #Space (punctuation) #Unitary matrix #Unitary state #hep-th
paper · pdf · doi:10.1007/jhep11(2017)186
published in Journal of High Energy Physics 2017(11) (Springer Nature) · 52 pages, 15 figures, v2 Introduction and discussions extended, References added
openalex publication_date 2017/11/01 · arxiv created 2018/01/29 · arxiv updated 2018/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract We show that large N phases of a 0 dimensional generic unitary matrix model (UMM) can be described in terms of topologies of two dimensional droplets on a plane spanned by eigenvalue and number of boxes in Young diagram. Information about different phases of UMM is encoded in the geometry of droplets. These droplets are similar to phase space distributions of a unitary matrix quantum mechanics (UMQM) ((0 + 1) dimensional) on constant time slices. We find that for a given UMM, it is possible to construct an effective UMQM such that its phase space distributions match with droplets of UMM on different time slices at large N . Therefore, large N phase transitions in UMM can be understood in terms of dynamics of an effective UMQM. From the geometry of droplets it is also possible to construct Young diagrams corresponding to U( N ) representations and hence different large N states of the theory in momentum space. We explicitly consider two examples: single plaquette model with Tr U 2 terms and Chern-Simons theory on S 3 . We describe phases of CS theory in terms of eigenvalue distributions of unitary matrices and find dominant Young distributions for them.