Four-loop vacuum energy density of the SU(Nc) plus adjoint Higgs theory -: art. no. 036

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 master integrals are evaluated in d = 3 - 2epsilon 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.