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Related papers: Two-Loop Beta Functions Without Feynman Diagrams

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The proof of the non-renormalization theorem for the gauge anomaly of four-dimensional theories is extended to the case of models with a vanishing one-loop gauge beta function.

High Energy Physics - Theory · Physics 2009-10-22 O. Piguet , S. P. Sorella

Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling $\zeta$ in a generalized Wilson loop operator of the $\mathcal{N}=4$ SYM theory, working in the planar weak-coupling expansion. The beta-function…

High Energy Physics - Theory · Physics 2022-02-02 Matteo Beccaria , Simone Giombi , Arkady A. Tseytlin

Two-loop renormalization group equations in gauge theories with multiple U(1) groups are presented. Instead of normalizing the abelian gauge fields in canonical forms, we retain kinetic-mixing terms and treat the mixing coefficients as free…

High Energy Physics - Phenomenology · Physics 2009-11-07 Mingxing Luo , Yong Xiao

The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…

High Energy Physics - Theory · Physics 2022-02-02 Han Ma , Sung-Sik Lee

We consider N=2 supersymmetric nonlinear sigma-models in two dimensions defined in terms of the nonminimal scalar multiplet. We compute in superspace the one-loop beta function and show that the classical duality between these models and…

High Energy Physics - Theory · Physics 2015-06-26 S. Penati , A. Refolli , A. Van Proeyen , D. Zanon

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph $G$ to evaluate to multiple zeta values. The criterion depends…

Algebraic Geometry · Mathematics 2009-03-24 Francis Brown

We revisit classical "on shell" duality, i.e., pseudoduality, in two dimensional conformally invariant classical sigma models and find some new interesting results. We show that any two sigma models that are "on shell" duals have opposite…

High Energy Physics - Theory · Physics 2015-06-26 Orlando Alvarez

We continue studying regularization scheme dependence of the $\mathcal{N}=2$ supersymmetric sigma models. In the present work the previous result for the four loop $\beta$-function is extended to the five loop order. Namely, we find the…

High Energy Physics - Theory · Physics 2026-04-22 Mikhail Alfimov , Andrey Kurakin

It is known that the $U(2)$ Wess-Zumino-Witten model is dual to the free fermion theory in two dimensions via non-Abelian bosonization. While it is decomposed into the $SU(2)$ Wess-Zumino-Witten model and a free compact boson, the former is…

High Energy Physics - Theory · Physics 2025-02-20 Junichi Haruna , Keito Shimizu , Masatoshi Yamada

We analyze the renormalization group flow in a recently constructed class of integrable sigma-models which interpolate between WZW current algebra models and the non-Abelian T-duals of PCM for a simple group G. They are characterized by the…

High Energy Physics - Theory · Physics 2015-06-19 Georgios Itsios , Konstadinos Sfetsos , Konstadinos Siampos

In this paper, we construct the beta function in the functorial formulation of two-dimensional quantum field theories (FQFT). A key feature of this approach is the absence of ultraviolet divergences. We show that, nevertheless, in the FQFT…

Mathematical Physics · Physics 2025-10-07 Maxim Gritskov , Andrey Losev

Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely…

High Energy Physics - Theory · Physics 2009-02-18 A. Codello , R. Percacci

We argue that in general renormalizable field theories the topological angles may develop an additive beta function starting no earlier than 2-loop order. The leading expression is uniquely determined by a single model-independent…

High Energy Physics - Phenomenology · Physics 2023-02-15 Alessandro Valenti , Luca Vecchi

Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector…

High Energy Physics - Theory · Physics 2016-05-17 Athanasios Chatzistavrakidis , Andreas Deser , Larisa Jonke

By explicit solution of the one-loop finiteness conditions for all dimensionless coupling constants (i.~e., gauge coupling constant as well as Yukawa and quartic scalar-boson self-interaction coupling constants), two classes of grand…

High Energy Physics - Phenomenology · Physics 2015-06-25 Wolfgang Lucha , Franz F. SCHÖberl

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…

High Energy Physics - Theory · Physics 2008-11-26 Ahmed Lakhoua , Fabien Vignes-Tourneret , Jean-Christophe Wallet

We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<\zeta<1$, rendering the…

High Energy Physics - Theory · Physics 2024-11-06 Dario Benedetti , Razvan Gurau , Sabine Harribey , Kenta Suzuki

For various two dimensional non linear $\sigma$ models, we present a direct comparison between the $\beta$ functions computed with the $2+\epsilon$ renormalization group and the $\beta$ functions measured by Monte Carlo simulations. The…

Condensed Matter · Physics 2009-10-28 Gil Zumbach

We define a model of 2 coupled SU(2) doublets of scalar fields in $4$ spacetime dimensions which have a rich structure of renormalization group (RG) flows to 1-loop when the SU(2) is broken to U(1). The model is pseudo-hermitian, $H^\dagger…

High Energy Physics - Theory · Physics 2026-04-07 André LeClair

We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the…

Condensed Matter · Physics 2009-07-10 Pierre Le Doussal , Kay Joerg Wiese , Pascal Chauve