On the counting tensor model observables as U(N) and O(N) classical invariants
| Autor: | Joseph Ben Geloun |
|---|---|
| Přispěvatelé: | Laboratoire d'Informatique de Paris-Nord (LIPN), Université Sorbonne Paris Cité (USPC)-Institut Galilée-Université Paris 13 (UP13)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
model: tensor Pure mathematics graph theory [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences algebra Unitary state group: representation group: Lie Tensor Invariant (mathematics) Tensor theory Mathematical Physics Mathematics Topological quantum field theory symplectic [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Lie group Observable Mathematical Physics (math-ph) O(N) field theory: topological U(N) High Energy Physics - Theory (hep-th) Symplectic geometry |
| Zdroj: | PoS 19th Hellenic School and Workshops on Elementary Particle Physics and Gravity 19th Hellenic School and Workshops on Elementary Particle Physics and Gravity, Aug 2019, Corfu, Greece. pp.175, ⟨10.22323/1.376.0175⟩ |
| DOI: | 10.22323/1.376.0175 |
| Popis: | Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle to study their combinatorial, topological and algebraic properties. We give here an overview of the symmetric group-theoretic formulation of the enumeration of unitary and orthogonal invariant observables which turns out to bear a rich structure. From their counting formulae, one finds a correspondence with topological field theory on 2-cellular complexes that brings other interpretations of the same countings. Furthermore, tensor model observables span an algebra that turns out to be semi-simple. Dealing with complex tensors, we discuss the representation theoretic base of the algebra making explicit its Wedderburn-Artin decomposition. The real case is more subtle as a base of its Wedderburn-Artin decomposition is yet unknown. Contribution to the Corfu Summer Institute 2019, compiling 1907.04668, 1708.03524 and ,1307.6490, 25 pages, 8 figs |
| Databáze: | OpenAIRE |
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