scholarly journals COMMENTS ON THE BACKGROUND FIELD METHOD IN HARMONIC SUPERSPACE: NON-HOLOMORPHIC CORRECTIONS IN N=4 SYM

1998 ◽  
Vol 13 (20) ◽  
pp. 1623-1635 ◽  
Author(s):  
IOSEPH L. BUCHBINDER ◽  
SERGEI M. KUZENKO
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Vector Multiplet ◽  
Harmonic Superspace ◽  
Background Field Method ◽  
Field Formalism ◽  
The One

We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU (2) SYM effective action.

scholarly journals Consistent higher order $$ \sigma \left(\mathcal{GG}\to h\right) $$, $$ \Gamma \left(h\to \mathcal{GG}\right) $$ and Γ(h → γγ) in geoSMEFT

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Tyler Corbett ◽  
Adam Martin ◽  
Michael Trott
Keyword(s):  
Background Field ◽  
Field Method ◽  
Effective Field ◽  
Leading Order ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Complete Set ◽  
Background Field Method ◽  
The One ◽  
Geometric Formulation

Abstract We report consistent results for Γ(h → γγ), $$ \sigma \left(\mathcal{GG}\to h\right) $$ σ GG → h and $$ \Gamma \left(h\to \mathcal{GG}\right) $$ Γ h → GG in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections $$ \mathcal{O}\left({\overline{\upsilon}}_T^2/16{\pi}^2{\Lambda}^2\right) $$ O υ ¯ T 2 / 16 π 2 Λ 2 in the Background Field Method (BFM) approach to gauge fixing, and to $$ \mathcal{O}\left({\overline{\upsilon}}_T^4/{\Lambda}^4\right) $$ O υ ¯ T 4 / Λ 4 using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasize calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.

scholarly journals Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Chris L. Lin ◽  
Carlos R. Ordóñez
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Scale Dependence ◽  
Classical Action ◽  
Loop Expansion ◽  
Background Field Method

We show the equivalence between Fujikawa’s method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for anO(N)symmetric scalar field theory. Fujikawa’s method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to scale-dependence of the couplings, whereas, in terms of the effective action, the anomaly is the result of the breakdown of Noether’s theorem due to explicit symmetry breaking terms of the effective potential.

A MODEL LAGRANGIAN FOR STRONG INTERACTIONS AT LARGE DISTANCES

1989 ◽  
Vol 04 (03) ◽  
pp. 293-302 ◽  
Author(s):  
MEIUN SHINTANI
Keyword(s):  
Background Field ◽  
String Tension ◽  
Field Method ◽  
Strong Interactions ◽  
Coupling Constant ◽  
Running Coupling ◽  
Free Region ◽  
Running Coupling Constant ◽  
Background Field Method ◽  
The One

On the basis of the massive vector dipole theory as a model for strong interactions at large distances, we compute the counterterm Lagrangian at the one-loop level in the background field method. By smoothly relating the running coupling constant in the confining region to that in the asymptotically free region, we deduce a relationship between the string tension and the QCD scale parameter Λ QCD . With an input data of the string tension, we evaluate the value of Λ QCD . The lower bound to the distances where the dipole theory is valid relies on the number of flavors. The theory seems to be meaningful for six generations or less.

Evolution of Coupling Constant in Hot QCD

1997 ◽  
Vol 06 (01) ◽  
pp. 45-64
Author(s):  
M. Chaichian ◽  
M. Hayashi
Keyword(s):  
Finite Temperature ◽  
Lorentz Invariance ◽  
Background Field ◽  
Field Method ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Time Formalism ◽  
Background Field Method ◽  
The One

The evolution of QCD coupling constant at finite temperature is considered by making use of the finite temperature renormalization group equation up to the one-loop order in the background field method with the Feynman gauge and the imaginary time formalism. The results are compared with the ones obtained in the literature. We point out, in particular, the origin of the discrepancies between different calculations, such as the choice of gauge, the breakdown of Lorentz invariance, imaginary versus real time formalism and the applicability of the Ward identities at finite temperature.

scholarly journals Super heat kernel and one-loop divergence of super Yang–Mills theory in conformal supergravity

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Ka-Hei Leung
Keyword(s):  
Heat Kernel ◽  
Iterative Scheme ◽  
Kernel Method ◽  
Background Field ◽  
Field Method ◽  
Conformal Supergravity ◽  
Quantum Theories ◽  
Yang Mills ◽  
Background Field Method ◽  
The One

Abstract We consider super Yang–Mills (SYM) theory in $N=1$ conformal supergravity. Using the background field method and the Faddeev–Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat kernel method. We shall develop a non-iterative scheme, generalizing the non-supersymmetric case, to obtain the super heat kernel coefficients. In particular, the first three coefficients, which govern the one-loop divergence, will be calculated. We shall also demonstrate how to schematically derive the higher-order coefficients. The method presented here can be readily applied to various quantum theories. We shall, as an application, derive the full one-loop divergence of SYM in conformal supergravity.

scholarly journals Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 68 ◽  
Author(s):  
Ioseph Buchbinder ◽  
Evgeny Ivanov ◽  
Boris Merzlikin ◽  
Konstantin Stepanyantz
Keyword(s):  
Effective Action ◽  
Gauge Theories ◽  
Proper Time ◽  
Background Field ◽  
Field Method ◽  
Quantum Corrections ◽  
Supersymmetric Gauge Theories ◽  
Loop Approximation ◽  
Supersymmetric Gauge ◽  
The One

We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

THE BACKGROUND FIELD METHOD AND THE ANOMALIES OF THE HETEROTIC σ-MODEL IN A CURVED (1, 0) SUPERSPACE

1991 ◽  
Vol 06 (17) ◽  
pp. 2971-2998 ◽  
Author(s):  
S.V. KETOV ◽  
O.A. SOLOVIEV
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Low Energy ◽  
Heterotic String ◽  
Explicit Calculation ◽  
Two Dimensional ◽  
Gauge Bosons ◽  
Background Field Method ◽  
Background Fields

The covariant (in the σ-model sense) background field method for calculating the anomalies of the heterotic string propagating on the background of its massless modes is developed in a curved superspace of the two-dimensional (1, 0) supergravity. As the massless background fields, we use a metric, an antisymmetric tensor, a dilaton and gauge bosons. Explicit calculation of the anomalies up to five loops is performed and the results are found to be in agreement with the known facts about the heterotic string low-energy effective action. The dilaton-dependent corrections to the anomalies at the two- and three-loop levels are shown to be absent.

The one-loop θ2 corrections of gauge boson propagator in the noncommutative scalar U(1) theory

2014 ◽  
Vol 29 (34) ◽  
pp. 1450172
Author(s):  
Weijian Wang ◽  
Jia-Hui Huang
Keyword(s):  
Gauge Theory ◽  
Gauge Boson ◽  
Background Field ◽  
Field Method ◽  
Quantum Corrections ◽  
Complex Scalar ◽  
Boson Propagator ◽  
Complex Scalar Field ◽  
Background Field Method ◽  
The One

In this paper, the quantum corrections of gauge field propagator are investigated in the noncommutative (NC) scalar U(1) gauge theory with Seiberg–Witten map (SWM) method. We focus on the simplest case where the gauge boson couples with a massless complex scalar field. The one-loop divergent corrections at θ2-order are calculated using the background field method. It is found that the divergences can be absorbed by making field redefinitions, leading to a good renormalizability at θ2-order.

scholarly journals THE RENORMALIZED LOCALLY COVARIANT DIRAC FIELD

2014 ◽  
Vol 26 (01) ◽  
pp. 1330012 ◽  
Author(s):  
JOCHEN ZAHN
Keyword(s):  
Background Field ◽  
Field Method ◽  
Dirac Field ◽  
Energy Tensor ◽  
Stress Energy ◽  
Background Field Method ◽  
The One ◽  
Definition Of ◽  
Background Fields ◽  
Group Flow

The definition of the locally covariant Dirac field is adapted such that it may be charged under a gauge group and in the presence of generic gauge and Yukawa background fields. We construct renormalized Wick powers and time-ordered products. It is shown that the Wick powers may be defined such that the current and the stress-energy tensor are conserved, and the remaining ambiguity is characterized. We sketch a variant of the background field method that can be used to determine the renormalization group flow at the one loop level from the nontrivial scaling of Wick powers.

scholarly journals The background field method for N=2 super Yang-Mills theories in harmonic superspace

1998 ◽  
Vol 417 (1-2) ◽  
pp. 61-71 ◽  
Author(s):  
I.L. Buchbinder ◽  
E.I. Buchbinder ◽  
S.M. Kuzenko ◽  
B.A. Ovrut
Keyword(s):  
Background Field ◽  
Field Method ◽  
Harmonic Superspace ◽  
Yang Mills ◽  
Background Field Method
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