Extended su(2)_k and restricted U_q sl(2)
Ludmil Hadjiivanov, Paolo Furlan
TL;DR
This paper surveys the mathematical structures of gauge symmetries in low-dimensional quantum field theories, focusing on dualities between braid and quantum group representations in extended su(2)_k models.
Contribution
It introduces a duality between braid and quantum group representations in extended su(2)_k models, advancing understanding of symmetries in low-dimensional QFT.
Findings
Duality between braid and quantum group representations
Extension of the chiral su(2)_k WZNW model
Insights into superselection sectors in low-dimensional QFT
Abstract
Global gauge symmetry becomes more intricate in low dimensional QFT. We survey the mathematical concepts leading to the relevant analogues of the (D=4) Doplicher-Haag-Roberts theory of superselection sectors and internal symmetry. We also review a recently uncovered duality between braid and quantum group representations in an extension of the chiral su(2)_k WZNW model for nonnegative integer level k.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons