Yang-Baxter deformations of the GL(2,R) WZW model and non-Abelian T-duality

By calculating inequivalent classical r-matrices for the g l ( 2 , R ) Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the G L ( 2 , R ) Lie group in twelve inequivalent families. Most importantly,...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2023-10, Vol.83 (10), p.917, Article 917
Main Authors: Eghbali, Ali, Parvizi, Tayebe, Rezaei-Aghdam, Adel
Format: Article
Language:English
Subjects:
Algebra
Astronomy
Astrophysics and Cosmology
Deformation
Elementary Particles
Group theory
Hadrons
Heavy Ions
Lie groups
Matrices (mathematics)
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
String Theory
Symmetry
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Summary:By calculating inequivalent classical r-matrices for the g l ( 2 , R ) Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the G L ( 2 , R ) Lie group in twelve inequivalent families. Most importantly, it is shown that each of these models can be obtained from a Poisson-Lie T-dual σ -model in the presence of the spectator fields when the dual Lie group is considered to be Abelian, i.e. all deformed models have Poisson-Lie symmetry just as undeformed WZW model on the G L ( 2 , R ) . In this way, all deformed models are specified via spectator-dependent background matrices. For one case, the dual background is clearly found.
ISSN:1434-6052
1434-6044
1434-6052
DOI:10.1140/epjc/s10052-023-12084-8