Related papers: Effect of Scheme Transformations on a Beta Functio…
We analyse quantum properties of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric gauge theories formulated in terms of ${\cal N}=1$ superfields and investigate the conditions imposed on a renormalization prescription under which the…
We determine the three-loop $\overline{\text{MS}}$ quartic $ \beta $-function for the most general renormalisable four-dimensional theories. A general parametrization of the $ \beta $-function is compared to known $ \beta $-functions for…
Nonrenormalizable scalar fields, such as \varphi^4_n, n\ge5, require infinitely many distinct counter terms when perturbed about the free theory, and lead to free theories when defined as the continuum limit of a lattice regularized theory…
We study the three-loop gauge $\beta$-functions in general $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives (HCD) supplemented with Pauli--Villars subtraction. The all-structure three-loop form of…
The QCD coupling, $\alpha_s$, is not a physical observable since it depends on conventions related to the renormalization procedure. Here we discuss a redefinition of the coupling where changes of scheme are parametrised by a single…
Field theories with weakly coupled holographic duals, such as large N gauge theories, have a natural separation of their operators into `single-trace operators' (dual to single-particle states) and `multi-trace operators' (dual to…
We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space-time scaling, with critical exponent $z=2$, including both scalar and gauge fields. Depending on the relative strength of…
We investigate whether the beta function of the finite-$N$ Gross-Neveu model, as calculated up to the four-loop level, exhibits evidence for an infrared zero. As part of our analysis, we calculate and analyze Pad\'e approximants to this…
We claim that if by a choice of the couplings the theory can be made conformally invariant (vanishing of the beta functions) it is automatically finite and vice versa. This is demonstrated by explicit example in supersymmetric gauge theory.…
We discuss the long term behaviour of trap models on the integers with asymptotically vanishing drift, providing scaling limit theorems and ageing results. Depending on the tail behaviour of the traps and the strength of the drift, we…
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 investigate some higher-loop structural properties of the $\beta$ function in asymptotically free vectorial gauge theories. Our main focus is on theories with fermion contents that lead to an infrared (IR) zero in $\beta$. We present…
We study regularization scheme dependence of K\"ahler ($N=2$) supersymmetric sigma models. At the one-loop order the metric $\beta$ function is the same as in non-supersymmetric case and coincides with the Ricci tensor. First correction in…
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…
Well-known and newly developed renormalization schemes for $\tan\beta$ are analyzed in view of three desirable properties: gauge independence, process independence, and numerical stability in perturbation theory. Arguments are provided that…
This article is an overview of the vanishing cycles method in number theory over function fields. We first explain how this works in detail in a toy example, and then give three examples which are relevant to current research. The focus…
In this work, we mainly study the one-loop effective action for real scalar theories in non-homogeneous backgrounds in odd dimensions. It is shown that through the method studied in Ref. [1], it is possible to obtain a unified result for…
Techniques to achieve various forms of test coverage, such as branch coverage, typically do not iterate loops; in other words, they treat a loop as a conditional, executed zero or one time. Existing work by the author and collaborators…
The Thirring model with random couplings is a translationally invariant generalisation of the SYK model to 1+1 dimensions, which is tractable in the large N limit. We compute its two point function, at large distances, for any strength of…
We calculate the one loop beta function for the would-be marginal coupling on the world sheet of the k deformed sigma models associated to a quantum group with q=exp(i pi/k). This includes the bosonic principal chiral models and symmetric…