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.

CHIRAL ANOMALY IN d=4, N=1 SUPERGRAVITY

1995 ◽  
Vol 10 (31) ◽  
pp. 2313-2321 ◽  
Author(s):  
SATOSHI YAJIMA ◽  
YOJI HIGASIDA ◽  
HIDEO TAIRA
Keyword(s):  
Heat Kernel ◽  
Explicit Form ◽  
Kernel Method ◽  
Background Field ◽  
Field Method ◽  
Chiral Anomaly ◽  
Minimal Coupling ◽  
Gravitational Fields ◽  
Background Field Method

The chiral U (1) anomaly in d=4, N=1 supergravity is evaluated on the basis of the heat kernel method. We consider all gravitino interactions of the theory, i.e. not only the minimal coupling of gravitino and gravitational fields, but also four-gravitino interactions which are treated as two-gravitino interactions in the background field method. We show the explicit form of a new contribution from the four-gravitino interactions to the anomaly.

scholarly journals FIELD DECOMPOSITION AND THE GROUND STATE STRUCTURE OF SU(2) YANG–MILLS THEORY

2002 ◽  
Vol 17 (25) ◽  
pp. 3681-3688 ◽  
Author(s):  
LISA FREYHULT
Keyword(s):  
Effective Potential ◽  
Ground State ◽  
Scalar Fields ◽  
Background Field ◽  
Field Method ◽  
Gauge Fields ◽  
Ground State Structure ◽  
State Structure ◽  
Yang Mills ◽  
Background Field Method

We compute the effective potential of SU(2) Yang–Mills theory using the background field method and the Faddeev–Niemi decomposition of the gauge fields. In particular, we find that the potential will depend on the values of two scalar fields in the decomposition and that its structure will give rise to a symmetry breaking.

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.

Quantum gauge theories

2021 ◽  
pp. 223-268
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Background Field ◽  
Field Method ◽  
Extensive Discussion ◽  
Functional Integrals ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Background Field Method ◽  
Popov Method

This chapter, which is the last chapter in Part I, is devoted to an extensive discussion of quantum gauge theories, which is based on functional integrals and Lagrangian quantization. After introducing the notion of a Yang-Mills gauge theory, the Faddeev-Popov method (also known as the DeWitt-Faddeev-Popov procedure) is explained. Starting from this point, the BRST symmetry is formulated, and the corresponding Ward identities (called Slavnov-Taylor identities in some cases) established. More specialized subjects, such as the gauge dependence of effective action and the background field method, are dealt with in detail. In addition, Yang-Mills theory is analyzed as a primary example of general theorems concerning the renormalization of gauge theories.

scholarly journals Three-loop Yang–Mills β-function via the covariant background field method

2003 ◽  
Vol 657 ◽  
pp. 257-303 ◽  
Author(s):  
Jan-Peter Börnsen ◽  
Anton E.M. van de Ven
Keyword(s):  
Background Field ◽  
Field Method ◽  
Yang Mills ◽  
Background Field Method ◽  
Β Function

scholarly journals A FORMULATION OF THE YANG–MILLS THEORY AS A DEFORMATION OF A TOPOLOGICAL FIELD THEORY BASED ON THE BACKGROUND FIELD METHOD AND QUARK CONFINEMENT PROBLEM

2001 ◽  
Vol 16 (07) ◽  
pp. 1303-1346 ◽  
Author(s):  
KEI-ICHI KONDO
Keyword(s):  
Field Theory ◽  
Magnetic Monopole ◽  
Background Field ◽  
Field Method ◽  
Quark Confinement ◽  
Mass Generation ◽  
Yang Mills ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Background Field Method

By making use of the background field method, we derive a novel reformulation of the Yang–Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang–Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically nontrivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of field configurations.

scholarly journals RENORMALIZATION OF FUNCTIONAL SCHRÖDINGER EQUATION BY BACKGROUND FIELD METHOD

1998 ◽  
Vol 13 (21) ◽  
pp. 1709-1717 ◽  
Author(s):  
K. ZAREMBO
Keyword(s):  
Renormalization Group ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Background Field ◽  
Field Method ◽  
Asymptotic Freedom ◽  
Yang Mills ◽  
State Wave ◽  
Background Field Method

Renormalization group transformations for Schrödinger equation are performed in both φ4 and Yang–Mills theories. The dependence of the ground state wave functional on rapidly oscillating fields is found. For Yang–Mills theory, this dependence restricts a possible form of variational ansatz compatible with asymptotic freedom.

scholarly journals Two-loop renormalisation of gauge theories in 4D implicit regularisation and connections to dimensional methods

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
A. Cherchiglia ◽  
D. C. Arias-Perdomo ◽  
A. R. Vieira ◽  
M. Sampaio ◽  
B. Hiller
Keyword(s):  
Quantum Electrodynamics ◽  
Dimensional Regularization ◽  
Background Field ◽  
Field Method ◽  
Loop Order ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Lorentz Algebra ◽  
Background Field Method

AbstractWe compute the two-loop $$\beta $$ β -function of scalar and spinorial quantum electrodynamics as well as pure Yang–Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using implicit regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.

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.

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