scholarly journals GLUON SELF-INTERACTION IN THE POSITION SPACE IN LANDAU GAUGE

2008 ◽  
Vol 23 (25) ◽  
pp. 4145-4204 ◽  
Author(s):  
GORAZD CVETIČ ◽  
IGOR KONDRASHUK
Keyword(s):  
Landau Gauge ◽  
Position Space ◽  
Integral Expression ◽  
Loop Contribution ◽  
Gluon Vertex ◽  
Yang Mills ◽  
Interaction Vertex ◽  
Finite Integral ◽  
Single Integral

We propose a method to treat the three-gluon self-interaction vertex in the position space in D = 4 - 2∊ dimensions. As an example, we calculate a two-loop contribution to auxiliary Lcc vertex in the Landau gauge which contains the three-gluon vertex for SU (N) Yang–Mills theory. We represent the integral expression as a sum of separate contributions so that each of the contributions is a double finite integral or single integral (singular or finite) in the position space. In each double finite integral, we use the freedom to shift exponents in powers in the denominator of integrands by some multiples of ∊, in order to perform at least one of the integrations by the uniqueness technique without corrupting the first term of the decomposition in ∊.

Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
Author(s):  
Yeong-Chuan Kao ◽  
Hsiang-Nan Li
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Landau Gauge ◽  
Quantum Corrections ◽  
Simons Theory ◽  
Loop Correction ◽  
Loop Contribution ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

scholarly journals Infrared behavior of the ghost-gluon vertex in Landau gauge Yang-Mills theory

2005 ◽  
Vol 72 (1) ◽  
Author(s):  
W. Schleifenbaum ◽  
A. Maas ◽  
J. Wambach ◽  
R. Alkofer
Keyword(s):  
Landau Gauge ◽  
Gluon Vertex ◽  
Yang Mills ◽  
Infrared Behavior

scholarly journals TOWARDS THE TWO-LOOP Lcc VERTEX IN LANDAU GAUGE

2007 ◽  
Vol 22 (10) ◽  
pp. 1905-1934 ◽  
Author(s):  
GORAZD CVETIČ ◽  
IGOR KONDRASHUK ◽  
ANATOLY KOTIKOV ◽  
IVAN SCHMIDT
Keyword(s):  
Landau Gauge ◽  
Conformal Structure ◽  
Auxiliary Field ◽  
Position Space ◽  
Yang Mills ◽  
Gegenbauer Polynomial ◽  
Uniqueness Method ◽  
Ghost Field

We are interested in the structure of the Lcc vertex in the Yang–Mills theory, where c is the ghost field and L the corresponding BRST auxiliary field. This vertex can give us information on other vertices, and the possible conformal structure of the theory should be reflected in the structure of this vertex. There are five two-loop contributions to the Lcc vertex in the Yang–Mills theory. We present here calculation of the first of the five contributions. The calculation has been performed in the position space. One main feature of the result is that it does not depend on any scale, ultraviolet or infrared. The result is expressed in terms of logarithms and Davydychev integral J(1, 1, 1) that are functions of the ratios of the intervals between points of effective fields in the position space. To perform the calculation we apply Gegenbauer polynomial technique and uniqueness method.

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

scholarly journals On gauge independence for gauge models with soft breaking of BRST symmetry

2014 ◽  
Vol 29 (30) ◽  
pp. 1450184 ◽  
Author(s):  
Alexander Reshetnyak
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Landau Gauge ◽  
Functional Integral ◽  
Yang Mills ◽  
Gauge Models ◽  
S Matrix ◽  
Gauge Fixing ◽  
Dependent Parameter ◽  
Quantum Treatment

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

scholarly journals Renormalizability of the linearly broken formulation of the BRST symmetry in the presence of the Gribov horizon in Landau gauge Euclidean Yang-Mills theories

2011 ◽  
Vol 83 (10) ◽  
Author(s):  
M. A. L. Capri ◽  
A. J. Gómez ◽  
M. S. Guimaraes ◽  
V. E. R. Lemes ◽  
S. P. Sorella ◽  
...  
Keyword(s):  
Brst Symmetry ◽  
Landau Gauge ◽  
Yang Mills

scholarly journals Three-gluon vertex in Landau gauge

2014 ◽  
Vol 89 (10) ◽  
Author(s):  
Gernot Eichmann ◽  
Richard Williams ◽  
Reinhard Alkofer ◽  
Milan Vujinovic
Keyword(s):  
Landau Gauge ◽  
Gluon Vertex
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