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Title: A braided monoidal category for free super-bosons

The chiral conformal field theory of free super-bosons is generated by weight one currents whose mode algebra is the affinisation of an abelian Lie super-algebra h with non-degenerate super-symmetric pairing. The mode algebras of a single free boson and of a single pair of symplectic fermions arise for even|odd dimension 1|0 and 0|2 of h, respectively. In this paper, the representations of the untwisted mode algebra of free super-bosons are equipped with a tensor product, a braiding, and an associator. In the symplectic fermion case, i.e., if h is purely odd, the braided monoidal structure is extended to representations of the Z/2Z-twisted mode algebra. The tensor product is obtained by computing spaces of vertex operators. The braiding and associator are determined by explicit calculations from three- and four-point conformal blocks.
Authors:
 [1]
  1. Fachbereich Mathematik, Universit├Ąt Hamburg, Bundesstra├če 55, 20146 Hamburg (Germany)
Publication Date:
OSTI Identifier:
22250775
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; BOSONS; CHIRALITY; CONFORMAL INVARIANCE; FERMIONS; QUANTUM FIELD THEORY; SPACE; SUPERSYMMETRY; TENSORS