The 4-loop beta-function in the 2D Non-Abelian Thirring model, and
comparison with its conjectured "exact" form
Andreas W.W. Ludwig1, Kay Jörg Wiese1,2
1Physics Department, University of California at Santa
Barbara, CA 93106, USA
2KITP, University of California at Santa Barbara, CA 93106,
USA
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.
cond-mat/0211531 [pdf]
Nucl. Phys. B 661 (2003)
577-607 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.