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

Andreas W. W. Ludwig (1) , Kay Joerg Wiese (1, 2)

1 CS-UCSB - Department of Computer Science [Santa Barbara]
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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.

Domaines: Autre [cond-mat.other]; Physique des Hautes Energies - Théorie [hep-th]

Andreas W. W. Ludwig, Kay Joerg Wiese. The 4-loop beta-function in the 2D Non-Abelian Thirring model, and comparison with its conjectured "exact" form. 2002. ⟨hal-00283819⟩