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Aspects of WZW models at critical level
Author(s) -
Bakas I.,
Sourdis C.
Publication year - 2005
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200510198
Subject(s) - physics , conformal field theory , mathematical physics , virasoro algebra , duality (order theory) , coset , string (physics) , string theory , generator (circuit theory) , conformal map , langlands dual group , current algebra , central charge , pure mathematics , mathematics , quantum mechanics , algebra over a field , conjecture , combinatorics , mathematical analysis , algebra representation , power (physics) , cellular algebra
We consider non‐compact WZW models at critical level (equal to the dual Coxeter number) as tensionless limits of gravitational backgrounds in string theory. Special emphasis is placed on the Euclidean black hole coset SL (2, R ) k / U (1) when k = 2. In this limit gravity decouples in the form of a Liouville field with infinite background charge and the world‐sheet symmetry of the model becomes a truncated version of W ∞ without Virasoro generator. This is regarded as manifestation of Langlands duality for the SL (2, R ) k current algebra that relates small with large values of the level in the two extreme limits. However, the physical interpretation of the SL (2, R ) k / U (1) coset model below the self‐dual value k = 3 remains elusive including the non‐conformal theory at k = 2.