Path-integral derivation of the superconformal anomaly for theN=1supersymmetric Yang-Mills theory

1991 ◽  
Vol 44 (10) ◽  
pp. 3303-3312 ◽  
Author(s):  
Mayank R. Mehta
Keyword(s):  
Path Integral ◽  
Yang Mills

scholarly journals Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (27) ◽  
pp. 1450159 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Dynamical Systems ◽  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST–anti-BRST transformations for the Yang–Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790 [hep-th]], special field-dependent BRST–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters λaand study the problem of gauge dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary Rξ-like gauges in the Yang–Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790 [hep-th]], which justifies the unitarity of the S-matrix in the Lagrangian approach.

scholarly journals Edge dynamics from the path integral — Maxwell and Yang-Mills

2018 ◽  
Vol 2018 (11) ◽  
Author(s):  
Andreas Blommaert ◽  
Thomas G. Mertens ◽  
Henri Verschelde
Keyword(s):  
Path Integral ◽  
Yang Mills

The physics of meron pairs. I. Introduction, motivation, and formalism

1980 ◽  
Vol 58 (6) ◽  
pp. 845-858 ◽  
Author(s):  
David G. Laughton
Keyword(s):  
Saddle Point ◽  
Path Integral ◽  
Path Integrals ◽  
Field Configuration ◽  
Degree Of Freedom ◽  
Leading Order ◽  
Local Minima ◽  
Yang Mills ◽  
Ordinary Integral

The physics of meron pairs is considered in this series of papers. The first paper presents the motivation for focussing on this particular type of field configuration as an important degree of freedom in the SU(N) Yang–Mills theory. It also outlines the formalism for doing a saddle point expansion of path integrals about configurations which are constrained minima of the action (such as meron pairs) as opposed to local minima (such as instantons). The formalism is illustrated by the treatment of an ordinary integral which is analogous to the meron pair region of the Yang–Mills path integral. It is found that the expansion about constrained minima depends to leading order on the constraints chosen to partition the integral. This means that some criteria must be found for the choice of constraints. This problem is discussed. The actual meron pair calculations are partially described here and done in the second and third papers. Applications are to be considered in any subsequent papers.

Anomalies, instantons and axions

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Standard Model ◽  
Path Integral ◽  
Electric Charge ◽  
Gauge Invariant ◽  
Axial Anomaly ◽  
Yang Mills ◽  
Integral Measure ◽  
The Standard Model ◽  
Electroweak Sector

The axial anomaly is derived both from the non-invariance of the path-integral measure under UA(1) transformations and calculations of specific triangle diagrams. It is demonstrated that the anomalous terms are cancelled in the electroweak sector of the standard model, if the electric charge of all fermions adds up to zero. The CP-odd term F̃μν‎Fμν‎ introduced by the axial anomaly is a gauge-invariant renormalisable interaction which is also generated by instanton transitions between Yang–Mills vacua with different winding numbers. The Peceei–Quinn symmetry is discussed as a possible explanation why this term does not contribute to the QCD action.

scholarly journals TOWARDS THE LOCALIZATION OF SUSY GAUGE THEORY ON A CURVED SPACE

2012 ◽  
Vol 27 (06) ◽  
pp. 1250029 ◽  
Author(s):  
KOICHI NAGASAKI ◽  
SATOSHI YAMAGUCHI
Keyword(s):  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Path Integral ◽  
General Class ◽  
Positive Definite ◽  
Curved Space ◽  
Yang Mills ◽  
Curved Spaces ◽  
Supersymmetric Gauge ◽  
Exact Term

We consider an [Formula: see text] supersymmetric gauge theory on a curved space. We try to generalize Pestun's localization calculation on the four-sphere to a more general class of curved spaces. We calculated the Q-exact term to localize the path-integral, and when it becomes positive-definite, we obtain a configuration where the path-integral localizes. We also evaluate the super-Yang–Mills action in this configuration.

scholarly journals Global path integral quantization of Yang–Mills theory

2000 ◽  
Vol 472 (1-2) ◽  
pp. 101-104 ◽  
Author(s):  
Helmuth Hüffel ◽  
Gerald Kelnhofer
Keyword(s):  
Path Integral ◽  
Yang Mills ◽  
Path Integral Quantization
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