Related papers: Seven loops $\phi^4$
The beta function of the vacuum energy density is analytically computed at the five-loop level in O(N)-symmetric phi^4 theory, using dimensional regularization in conjunction with the MSbar scheme. The result for the case of a cubic…
We present the main ideas and techniques of the proof that the duality-covariant four-dimensional noncommutative \phi^4-model is renormalisable to all orders. This includes the reformulation as a dynamical matrix model, the solution of the…
Recently it was shown that the scaling dimension of the operator $\phi^n$ in scale-invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading…
We present an analytic five-loop calculation for the additive renormalization constant A(u,\epsilon) and the associated renormalization-group function B(u) of the specific heat of the O(n) symmetric \phi^4 theory within the minimal…
We reconsider the general constraints on the perturbative anomalous dimensions in conformal invariant QFT and in particular in N=4 SYM with gauge group SU(N_c). We show that all the perturbative corrections to the anomalous dimension of a…
We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner…
It has been previously shown that calculation of renormalization group (RG) functions of the scalar \phi^4 theory reduces to the analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG…
We discuss the renormalizability of Phi-derivable approximations in scalar phi^4 theory in four dimensions. The formalism leads to self-consistent equations for the 2-point and the 4-point functions which are plagued by ultraviolet…
We present four-loop results for the gauge beta-function and the fermion mass anomalous dimension for a gauge theory with a general gauge group and a multiplet of fermions transforming according to an arbitrary representation, calculated…
Three-loop $\beta$-functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous…
We consider a class of singlet operators $(\phi^2)^n$ in the three-dimensional $O(N)$ model with $\lambda^2 \phi^6$ interaction. Recently, the corresponding anomalous dimensions $\gamma_{2n}$ were computed by semiclassical methods and the…
Recently, a new type of renormalizable $\phi^{\star 4}_{4}$ scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a $a/(\theta^2p^2)$ term. We calculate here…
Massive field theory at fixed dimension d<4 is combined with the minimal subtraction scheme to calculate the amplitude functions of thermodynamic quantities for the O(n) symmetric phi^4 model below T_c in two-loop order. Goldstone…
In this paper we give all the details of the calculation that we presented in our previous paper arXiv:0712.3522, concerning the four-loop anomalous dimension of the Konishi descendant tr(\phi Z\phi Z-\phi \phi Z Z) in the SU(2) sector of…
We present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four and three loops, respectively. The essence of our approach is fixing unknown coefficients in the most general ansatz for…
The loop-expansion of the effective potential in the $O(N)$-symmetric $\phi^4$-model contains generically two types of large logarithms. To resum those systematically a new minimal two-scale subtraction scheme $\tMS$ is introduced in an…
We compute the complete $Q$-dependence of anomalous dimensions of traceless symmetric tensor operator $\phi^Q$ in $O(N)$ scalar theory to five-loop. The renormalization factors are extracted from $\phi^Q\rightarrow Q\phi$ form factors, and…
The complete set of one-loop anomalous dimensions for general Effective Field Theories (EFTs) is derived using on-shell methods. Combined with previous findings for the bosonic sector, the obtained results conclude the computation of the…
Perturbation theory and renormalization group methods are used to derive a finite-size scaling theory for the partition function zeroes and thermodynamic functions in the $O(n)$ $\phi^4$ model in four dimensions. The leading power--law…
We study a renormalized coupling g and mass m in four dimensional phi^4 theory on tori with finite size z=mL. Precise numerical values close to the continuum limit are reported for z=1,2,4, based on Monte Carlo simulations performed in the…