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The 4-loop beta-function in the 2D Non-Abelian Thirring model, and comparison with its conjectured "exact" form

Andreas W. W. Ludwig·Kay Joerg Wiese
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Abstract

Recently, B. Gerganov, A. LeClair and M. Moriconi [Phys. Rev. Lett. 86 (2001) 4753] have proposed an "exact" (all orders) beta-function for 2-dimensional conformal field theories with Kac-Moody current-algebra symmetry at any level k, based on a Lie group G, which are perturbed by a current-current interaction. This theory is also known as the Non-Abelian Thirring model. We check this conjecture with an explicit calculation of the beta-function to 4-loop order, for the classical groups G= SU(N), SO(N) and SP(N). We find a contribution at 4-loop order, proportional to a higher-order group-theoretical invariant, which is incompatible with the proposed beta-function in all possible regularization schemes.

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Andreas W. W. Ludwig, Kay Joerg Wiese. 2002-11-25. The 4-loop beta-function in the 2D Non-Abelian Thirring model, and comparison with its conjectured "exact" form. https://doi.org/10.1016/s0550-3213(03)00249-9

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