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arXiv · 1603.02085

The 2PI effective action at four loop order in $\varphi^4$ theory

M. E. Carrington·B. A. Meggison·D. Pickering
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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 4-dimensions. We calculate the pressure and two different non-perturbative 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 $n\le 3$ 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 not previously been verified numerically.

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M. E. Carrington, B. A. Meggison, D. Pickering. 2016-03-07. The 2PI effective action at four loop order in $\varphi^4$ theory. https://doi.org/10.1103/physrevd.94.025018

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