Weyl anomaly and the $C$-function in $λ$-deformed CFTs

Eftychia Sagkrioti; Konstantinos Sfetsos; Konstantinos Siampos

doi:10.1016/j.nuclphysb.2018.11.024

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arXiv · 1810.04189

Weyl anomaly and the $C$-function in $λ$-deformed CFTs

Eftychia Sagkrioti·Konstantinos Sfetsos·Konstantinos Siampos

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Abstract

For a general $λ$-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 $β$-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 $SU(2)$ 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.

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Eftychia Sagkrioti, Konstantinos Sfetsos, Konstantinos Siampos. 2018-12-03. Weyl anomaly and the $C$-function in $λ$-deformed CFTs. https://doi.org/10.1016/j.nuclphysb.2018.11.024

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