Related papers: Gradient formula for the beta-function of 2d quant…
In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we…
A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion…
We start with some methodic remarks referring to purely bosonic quantum systems and then explain how corrections to the leading--order quasiclassical result for the fermion--graded partition function Tr{(-1)^F exp(-\beta H)} can be…
After showing how to prove the integrated c-theorem within the functional RG framework based on the effective average action, we derive an exact RG flow equation for Zamolodchikov's c-function in two dimensions by relating it to the flow of…
Using a calibration method we prove that, if $\Gamma\subset \Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $\Gamma$ and regular outside, then the function $u_{\beta}$ which solves $$ \begin{cases}…
We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or…
We derive an algorithm for automatic calculation of perturbative $\beta$-functions and anomalous dimensions in any local quantum field theory with canonical kinetic terms. The infrared rearrangement is performed by introducing a common mass…
The g-function was introduced by Affleck and Ludwig in the context of critical quantum systems with boundaries. In the framework of the thermodynamic Bethe ansatz (TBA) method for relativistic scattering theories, all attempts to write an…
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…
The Fermi function $F(Z,E)$ accounts for QED corrections to beta decays that are enhanced at either small electron velocity $\beta$ or large nuclear charge $Z$. For precision applications, the Fermi function must be combined with other…
In the joint work of T.Rivoal and the author, a hypergeometric construction was proposed for studing arithmetic properties of the values of Dirichlet's beta function $\beta(s)$ at even positive integers. The construction gives some bonuses…
The $O(d,d)$ invariant worldsheet theory for bosonic string theory with $d$ abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the…
We show irreversibility of the renormalization group flow in non-unitary but ${\cal PT}$-invariant quantum field theory in two space-time dimensions. In addition to unbroken $\mathcal{PT}$-symmetry and a positive energy spectrum, we assume…
In this paper, we define a notion of $\beta$-dimensional mean oscillation of functions $u: Q_0 \subset \mathbb{R}^d \to \mathbb{R}$ which are integrable on $\beta$-dimensional subsets of the cube $Q_0$: \begin{align*}…
We present an elegant exact formula for the gaugino $\beta$-function in a softly-broken supersymmetric gauge theory, of the form $\beta_M = {\cal O}(\beta_g/g)$, where $\beta_g$ is the gauge $\beta$ function and ${\cal O}$ is a simple…
We consider the deformations of a supersymmetric quantum field theory by adding spacetime-dependent terms to the action. We propose to describe the renormalization of such deformations in terms of some cohomological invariants, a class of…
We consider the renormalization group flow equation for the two-dimensional sigma models with the K\"ahler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We…
The new method of nonperturbative calculation of the beta function in the lattice gauge theory is proposed. The method is based on the finite size scaling hypothesis.
In this paper, I compare the generators of the renormalization group flow, or the geometric $\beta$-functions for dimensional regularization and operator regularization. I then extend the analysis to show that the geometric $\beta$-function…
First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG…