2PI effective action at four loop order in φ4 theory
Abstract
It is well known that perturbative pressure calculations show poor convergence. Calculations using a two-particle 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:
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Physical Review D
- Pub Date:
- July 2016
- DOI:
- 10.1103/PhysRevD.94.025018
- arXiv:
- arXiv:1603.02085
- Bibcode:
- 2016PhRvD..94b5018C
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 15 pages, 6 figures