We compute the dimensionally regularised four-loop vacuum energy density of the SU(N_c) gauge + adjoint Higgs theory, in the disordered phase. ``Scalarisation'', or reduction to a small set of master integrals of the type appearing in scalar field theories, is carried out in d dimensions, employing general partial integration identities through an algorithm developed by Laporta, while the remaining scalar integrals are evaluated in d = 3 - 2\epsilon dimensions, by expanding in \epsilon << 1 and evaluating a number of coefficients. The results have implications for the thermodynamics of finite temperature QCD, allowing to determine perturbative contributions of orders O(g^6 ln(1/g)), O(g^6) to the pressure, while the general methods are applicable also to studies of critical phenomena in QED-like statistical physics systems.
@article{arxiv.hep-ph/0304048,
title = {Four-loop vacuum energy density of the SU(N_c) + adjoint Higgs theory},
author = {K. Kajantie and M. Laine and K. Rummukainen and Y. Schroder},
journal= {arXiv preprint arXiv:hep-ph/0304048},
year = {2009}
}