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We consider some applications of the Renormalization Group flow equations obtained by resorting to a specific class of proper time regulators. Within this class a particular limit that corresponds to a sharpening of the effective width of…
We briefly review the calculations of quantum corrections related with the exact NSVZ $\beta$-function in ${\cal N}=1$ supersymmetric theories, paying especial attention to the scheme dependence of the results. It is explained, how the NSVZ…
Geometric Quantization links holomorphic geometry with real geometry, a relation that is a prototype for the modern development of mirror symmetry. We show how to use this treatment to construct a special basis in every space of conformal…
We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this…
All one-loop renormalization constants for Non-Abelian gauge theory are computed in details by using the symmetry-preserving Loop Regularization method proposed in\cite{LR1,LR2}. The resulting renormalization constants are manifestly shown…
A recently proposed renormalization group technique, based on the hierarchical structures present in theories with fluctuating geometry, is implemented in the model of branched polymers. The renormalization group equations can be solved…
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of…
Renormalization group methods are an essential ingredient in the study of nonperturbative problems of quantum field theory. This paper deal with the symmetry constraints on the renormalization group flow for quartic melonic tensorial group…
We calculate the effective action for disordered elastic manifolds in the ground state (equilibrium) up to 3-loop order. This yields the renormalization-group $\beta$-function to third order in $\epsilon=4-d$, in an expansion in the…
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…
Functional renormalization group equations are analytically continued from imaginary Matsubara frequencies to the real frequency axis. On the example of a scalar field with O(N) symmetry we discuss the analytic structure of the flowing…
We show that if the beta functions of a field theory are given by the gradient of a certain potential on the space of couplings, a gravitational background in one more dimension can express the renormalization group (RG) flow of the theory.…
The character of quantum corrections to the gravitational action of a conformally invariant field theory for a self-interacting scalar field on a manifold with boundary is considered at third loop-order in the perturbative expansion of the…
We discuss some implications of the gravitational dressing of the renormalization group for conformal field theories perturbed by relevant operators. The renormalization group flows are defined with respect to the dilatation operator…
I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite…
The functional renormalization group flow of a scalar field theory with quartic couplings and a sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining the entanglement of the IR…
We establish a concrete correspondence between a gradient flow and the renormalization group flow for a generic scalar field theory. We use the exact renormalization group formalism with a particular choice of the cutoff function.
We construct a consistent closure for the beta functions of the cosmological and Newton's constants by evaluating the influence of the fluctuating metric and ghost fields anomalous dimensions on their flow. In this generalized framework we…
We analyze the exact behavior of the renormalization group flow in one-dimensional clock-models which undergo first order phase transitions by the presence of complex interactions. The flow, defined by decimation, is shown to be…
Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not…