2PI effective action at four loop order in φ^{4} theory
Abstract
It is well known that perturbative pressure calculations show poor convergence. Calculations using a twoparticle irreducible (2PI) effective action show improved convergence at the 3 loop level, but no calculations have been done at 4 loops. We consider the 2PI effective theory for a symmetric scalar theory with quartic coupling in four dimensions. We calculate the pressure and two different nonperturbative vertices as functions of coupling and temperature. Our results show that the 4 loop contribution can become larger than the 3 loop term when the coupling is large. This indicates a breakdown of the 2PI approach, and the need for higher order n PI approximations. In addition, our results demonstrate the renormalizability of 2PI calculations at the 4 loop level. This is interesting because the counterterm structure of the 2PI theory at 4 loops is different from the structure at n ≤3 loops. Two vertex counterterms are required at the 4 loop level, but not at lower loop order. This unique feature of the 2PI theory has never been verified numerically.
 Publication:

Physical Review D
 Pub Date:
 July 2016
 DOI:
 10.1103/PhysRevD.94.025018
 arXiv:
 arXiv:1603.02085
 Bibcode:
 2016PhRvD..94b5018C
 Keywords:

 High Energy Physics  Theory
 EPrint:
 15 pages, 6 figures