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Weyl anomaly and the \(C\)-function in \(\lambda\)-deformed CFTs. (English) Zbl 1405.81139

Summary: For a general \(\lambda\)-deformation of current algebra CFTs we compute the exact Weyl anomaly coefficient and the corresponding metric in the couplings space geometry. By incorporating the exact \(\beta\)-function found in previous works we show that the Weyl anomaly is in fact the exact Zamolodchikov’s \(C\)-function interpolating between exact CFTs occurring in the UV and in the IR. We provide explicit examples with the anisotropic \(\operatorname{SU}(2)\) case presented in detail. The anomalous dimension of the operator driving the deformation is also computed in general. Agreement is found with special cases existing already in the literature.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T50 Anomalies in quantum field theory
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
14D15 Formal methods and deformations in algebraic geometry
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
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References:

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