Related papers: On $\beta$-function of $N=2$ supersymmetric integr…
We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2…
We give the correct analytic expression of a finite integral appearing in the four-loop computation of the renormalization-group functions for the two-dimensional nonlinear sigma-model on the square lattice with standard action, explaining…
We construct "connected" (0,2) sigma models starting from n copies of (2,2) CP(N-1) models. General aspects of models of this type (known as T+O deformations) had been previously studied in the context of heterotic string theories. Our…
Suppose $\alpha$ is a rotationally symmetric norm on $L^{\infty}\left(\mathbb{T}\right) $ and $\beta$ is a "nice" norm on $L^{\infty}\left(\Omega,\mu \right) $ where $\mu$ is a $\sigma$-finite measure on $\Omega$. We prove a version of…
Coupling constant renormalization is investigated in 2 dimensional sigma models related by non Abelian duality transformations. In this respect it is shown that in the one loop order of perturbation theory the duals of a one parameter…
We examine noncommutative Chern Simons theory using operator regularization. Both the zeta-function and the eta-function are needed to determine one loop effects. The contributions to these functions coming from the two point function is…
We report the result of our evaluation of the Feynman diagrams appearing in the determination of the four-loop renormalization group functions in the two-dimensional lattice O($n$) $\sigma$-model by Caracciolo and Pelissetto. In the list of…
Starting from the dual action of $(4,4)$ $2D$ twisted multiplets in the harmonic superspace with two independent sets of $SU(2)$ harmonic variables, we present its generalization which hopefully provides an off-shell description of general…
We compute the one- and two-loop RG flow of integrable $\sigma$-models with Poisson-Lie symmetry. They are characterised by a twist function with $2N$ simple poles/zeros and a double pole at infinity. Hence, they capture many of the known…
We calculate the one loop beta functions for nonlinear sigma models in four dimensions containing general two and four derivative terms. In the O(N) model there are four such terms and nontrivial fixed points exist for all N \geq 4. In 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…
We set up a suitable renormalization programme for the one-loop computation of the decay rate Gamma(H==>hh) in the Minimal Supersymmetric extension of the Standard Model. We then perform an explicit diagrammatic calculation, including the…
We present the supersymmetric standard model three-loop $\beta$-functions for gauge and Yukawa couplings and consider the effect of three-loop corrections on the standard running coupling analyses.
We study the gravitational dressing of renormalizable two-dimensional field theories. Our main result is that the one-loop $\beta$-function is finitely renormalized by the factor ${k+2\over k+1}$, where $k$ is the central charge of the…
The perturbative all-loop derivation of the NSVZ $\beta$-function for ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives is finalized by calculating the sum of singularities produced by quantum…
We present a systematic study of ${\cal N}=(2,2)$ supersymmetric non-linear sigma models on $S^2$ with the target being a K\"ahler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological…
We study the occurrence of spontaneous symmetry breaking (SSB) for O(N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give…
We study the role of categorical symmetries in constraining the renormalisation of couplings in two-dimensional non-linear sigma models with Wess-Zumino term. A large class of these theories admit self-duality symmetries associated with…
We construct and study a generalized one-parameter class of scheme transformations, denoted $S_{R,m,k_1}$ with $m \ge 2$, with the property that an $S_{R,m,k_1}$ scheme transformation eliminates the $\ell$-loop terms in the beta function of…
Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We…