Related papers: Gradient formula for the beta-function of 2d quant…
We investigate Non-Hermitian quantum field theoretic model with $\iota g\phi^3$ interaction in 6 dimension. Such a model is PT-symmetric for the pseudo scalar field $\phi$. We analytically calculate the 2-loop $\beta$ function and analyse…
We present general four-loop template $\beta$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations…
A result from Dodd and Gibbs[1] for the second virial coefficient of particles in 1 dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be…
We suggest a simple algebraic approach to fix the elements of the $\{ \beta \}$-expansion for renormalization group invariant quantities, which uses additional degrees of freedom. The approach is discussed in detail for N$^2$LO calculations…
We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinear sigma models with closed target manifolds supporting a…
Kaluza-Klein reductions of low energy string effective actions possess a continuous $O(d,d) $ symmetry. The non-geometric elements of this group, parameterized by a bi-vector $\beta$, are not inherited from the symmetries of the…
The beta-function is calculated for an SU(N) Yang-Mills theory from an ansatz for the vacuum wavefunctional. Direct comparison is made with the results of calculations of the beta-function of QCD. In both cases the theories are…
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar $\phi$ with…
We consider the convolution equation $(\delta - J) * G = g$ on $\mathbb R^d$, $d>2$, where $\delta$ is the Dirac delta function and $J,g$ are given functions. We provide conditions on $J, g$ that ensure the deconvolution $G(x)$ to decay as…
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…
Threshold effects related to fermion masses are considered for an all-order beta-function based on a background field momentum subtraction scheme. Far away from all thresholds, the suggested beta-function reduces to the conjectured…
We calculate the beta-functions for an open string sigma-model in the presence of a U(1) background. Passing to N=2 boundary superspace, in which the background is fully characterized by a scalar potential, significantly facilitates the…
We have carried out a Schrodinger-functional calculation for the Abelian gauge theory with Nf=2 four-component fermions in three dimensions. We find no fixed point in the beta function, meaning that the theory is confining rather than…
Let $\Omega \subset \mathbb{R}^n$ be a convex domain and let $f:\Omega \rightarrow \mathbb{R}$ be a subharmonic function, $\Delta f \geq 0$, which satisfies $f \geq 0$ on the boundary $\partial \Omega$. Then $$ \int_{\Omega}{f ~dx} \leq…
Explicit formulas for the zeta functions $\zeta_\alpha (s)$ corresponding to bosonic ($\alpha =2$) and to fermionic ($\alpha =3$) quantum fields living on a noncommutative, partially toroidal spacetime are derived. Formulas for the most…
In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…
In this thesis we study two-dimensional supersymmetric non-linear sigma-models with boundaries. We derive the most general family of boundary conditions in the non-supersymmetric case. Next we show that no further conditions arise when…
The exact one-loop beta functions for the four-derivative terms (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet) are derived for the minimal six-derivative quantum gravity (QG) theory in four spacetime dimensions. The…
We consider a univariate beta integral composed from general modular quantum dilogarithm functions and prove its exact evaluation formula. It represents the partition function of a particular $3d$ supersymmetric field theory on the general…
We develop an operator description, much like thermofield dynamics, for quantum field theories on a real time path with an arbitrary parameter $\sigma\,(0\leq\sigma\leq\beta)$. We point out new features which arise when $\sigma\neq…