https://doi.org/10.1140/epjc/s10052-019-7190-9
Regular Article - Theoretical Physics
Bubble-resummation and critical-point methods for 
-functions at large N
1
Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117, Heidelberg, Germany
2
CP3-Origins, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark
* e-mail: tommi.alanne@mpi-hd.mpg.de
Received:
18
April
2019
Accepted:
1
August
2019
Published online:
16
August
2019
We investigate the connection between the bubble-resummation and critical-point methods for computing the -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 -functions, so that additional input or direct computation are needed to decipher this missing information. In particular, we evaluate the -function for the quartic coupling in the Gross–Neveu–Yukawa model, thereby completing the full system at 
. The corresponding critical exponents would imply a shrinking radius of convergence when 
terms are included, but our present result shows that the new singularity is actually present already at , when the full system of -functions is known.
© The Author(s), 2019
