Bubble-resummation and critical-point methods for beta -functions at large N

Abstract

We investigate the connection between the bubble-resummation and critical-point methods for computing the beta -functions in the limit of large number of flavours, N, and show that these can provide complementary information. While the methods are equivalent for single-coupling theories, for multi-coupling case the standard critical exponents are only sensitive to a combination of the independent pieces entering the beta -functions, so that additional input or direct computation are needed to decipher this missing information. In particular, we evaluate the beta -function for the quartic coupling in the Gross–Neveu–Yukawa model, thereby completing the full system at mathcal {O}(1/N). The corresponding critical exponents would imply a shrinking radius of convergence when mathcal {O}(1/N^2) terms are included, but our present result shows that the new singularity is actually present already at mathcal {O}(1/N), when the full system of beta -functions is known.