Related papers: Beta functions and anomalous dimensions up to thre…
We propose a new method to quantize gauge theories formulated on a canonical noncommutative spacetime with fields and gauge transformations taken in the enveloping algebra. We show that the theory is renormalizable at one loop and compute…
We compute template formulae of all four-loop $\beta$-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $\overline{\text{MS}}$ scheme. Using these results, novel…
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…
We study conformal quantum mechanics by first considering the perturbative $S$-matrix in various dimensions. The model has two couplings and we study perturbatively the degree of ultraviolet divergences arising in the interplay between the…
We present a new approach to calculation of anomalous dimensions in the framework of $\epsilon$-expansion and renormalization group method. This approach allows one to skip the calculation of renormalization constants and express anomalous…
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…
The two point integrals contributing to the self energy of a particle in a three dimensional quantum field theory are calculated to two loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to…
We compute the one-loop beta-functions for renormalisable quantum gravity coupled to scalars using the co-ordinate space approach and generalised Schwinger De Witt technique. We resolve apparent contradictions with the corresponding…
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
We present a two-loop computation of the beta functions and the anomalous dimensions of a $\gamma_5$-Yukawa model using differential renormalization. The calculation is carried out in coordinate space without modifying the space-time…
A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quantum field theory having broken symmetry. We calculate the…
We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop…
We calculate all contributions $\propto T_F$ to the polarized three-loop anomalous dimensions in the M-scheme using massive operator matrix elements and compare to results in the literature. This includes the complete anomalous dimensions…
Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and…
We derive the full set of beta functions for the marginal essential couplings of projectable Horava gravity in (3 + 1)-dimensional spacetime. To this end we compute the divergent part of the one-loop effective action in static background…
We renormalize six dimensional phi^3 theory in the modified minimal subtraction (MSbar) scheme at four loops. From the resulting beta-function, anomalous dimension and mass anomalous dimension we compute four loop critical exponents…
We derive a systematic treatment of one-loop effective potentials for interacting scalar fields in curved spacetimes, providing a general formula valid in arbitrary geometries and explicit results for de Sitter and anti-de Sitter…
For ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives in the general $\xi$-gauge we calculate the three-loop anomalous dimension of the matter superfields defined in terms of the bare coupling constant and demonstrate…
Three-loop quantum corrections to the effective action are calculated for N=1 supersymmetric electrodynamics, regularized by higher derivatives. Using the obtained results we investigate the anomaly puzzle in the considered model.