scholarly journals Renormalization Transformations of the 4-D BFYM Theory

1997 ◽  
Vol 12 (31) ◽  
pp. 2353-2366 ◽  
Author(s):  
Alberto Accardi ◽  
Andrea Belli
Keyword(s):  
Perturbative Calculation ◽  
Preliminary Step ◽  
Yang Mills ◽  
First Order ◽  
Bf Theory ◽  
Starting Point ◽  
Brst Cohomology

We study the most general renormalization transformations for the first-order formulation of the Yang–Mills theory. We analyze, in particular, the trivial sector of the BRST cohomology of two possible formulations of the model: the standard one and the extended one. The latter is a promising starting point for the interpretation of the Yang–Mills theory as a deformation of the topological BF theory. This work is a necessary preliminary step towards any perturbative calculation, and completes some recently obtained results.

scholarly journals Chiral perturbation theory for GR

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Kirill Krasnov ◽  
Yuri Shtanov
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation ◽  
Perturbative Calculation ◽  
New Formalism ◽  
Yang Mills ◽  
First Order ◽  
Starting Point ◽  
Gauge Fixing ◽  
New Perturbation ◽  
Effective Description

Abstract We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.

scholarly journals CONSISTENT INTERACTIONS BETWEEN GAUGE FIELDS AND LOCAL BRST COHOMOLOGY: THE EXAMPLE OF YANG-MILLS MODELS

1994 ◽  
Vol 03 (01) ◽  
pp. 139-144 ◽  
Author(s):  
G. BARNICH ◽  
M. HENNEAUX ◽  
R. TATAR
Keyword(s):  
Vector Fields ◽  
Jacobi Identity ◽  
Second Order ◽  
Gauge Fields ◽  
Coupling Constant ◽  
Yang Mills ◽  
First Order ◽  
Gauge Symmetries ◽  
Brst Cohomology ◽  
Structure Constants

Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the Yang-Mills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the Yang-Mills coupling is therefore rederived through cohomological arguments.

ANOMALY FREE SUPERGRAVITY IN D=10: I) THE BIANCHI IDENTITIES AND THE BOSONIC LAGRANGIAN

1988 ◽  
Vol 03 (04) ◽  
pp. 953-1021 ◽  
Author(s):  
RICCARDO D’AURIA ◽  
PIETRO FRÉ ◽  
MARIO RACITI ◽  
FRANCO RIVA
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Variational Equation ◽  
Second Order ◽  
Effective Theory ◽  
Spin Connection ◽  
Bianchi Identities ◽  
First Order ◽  
Interaction Terms ◽  
Starting Point

Using a theorem by Bonora-Pasti and Tonin on the existence of a solution for D=10N=1 Bianchi identities in the presence of a Lorentz Chern Simons term, we find an explicit parametrization of the superspace curvatures. Our solution depends only on one free parameter which can be reabsorbed in a field redefinition of the dilaton and of the gravitello. We emphasize that the essential point which enables us to obtain a closed form for the curvature parametrizations and hence for the supersymmetry transformation rules is the use of first order formalism. The spin connection is known once the torsion is known. This latter, rather than being identified with Hµνρ as it is usually done in the literature, is related to it by a differential equation which reduces to the algebraic relation Hµνρ = - 3Tµνρ e4/3σ only at γ1=0 (γ1 being proportional to κ/g2). The solution of the Bianchi identities exhibited in this paper corresponds to a D=10 anomaly free supergravity (AFS). This theory is unique in first order formalism but corresponds to various theories in second order formalism. Indeed the torsion equation is a differential equation which, in order to be solved must be supplemented with boundary conditions. One wonders whether supplemented with a judicious choice of boundary conditions for the torsion equation, AFS yields all the interaction terms found in the effective theory of the heterotic string (ETHS). In this respect two remarks are in order. Firstly it appears that solving the torsion equation iteratively with Tµνρ = -1/3Hµνρ e-4/3σ as starting point all the terms of ETHS except those with a ζ(3) coefficient show up. (Whether the coefficient agree is still to be checked.) Secondly, as shown in this paper the rheonomic solution of the super Poincaré Bianchi identities is unique. Hence additional interaction terms can be added to the Lagrangian only by modifying the rheonomic parametrization of the [Formula: see text]-curvature. The only assumption made in our paper is that [Formula: see text] has at most ψ∧ψ∧V components (sector (1,2)). Correspondingly the only room left for a modification of the present theory is the addition of a (0, 3) part in the rheonomic parametrization of [Formula: see text]. When this work was already finished a conjecture was published by Lechner Pasti and Tonin that such a generalization of AFS might exist and be responsible for the ζ(3) missing term. Indeed if we were able to solve the [Formula: see text]-Bianchi with this new (0, 3)-part then the torsion equation would be modified via new terms which, in second order formalism, lead to additional gravitational interactions. The equation of motion of Anomaly Free Supergravity can be worked out from the Bianchi identities: we indicate through which steps. The corresponding Lagrangian could be constructed with the standard procedures of the rheonomy approach. In this paper we limit ourselves to the bosonic sector of such a Lagrangian and we show that it can indeed be constructed in such a way as to produce the relation between Hµνρ and Tµνρ as a variational equation.

scholarly journals Renormalon-free definition of the gluon condensate within the large-$\beta_0$ approximation

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Hiroshi Suzuki ◽  
Hiromasa Takaura
Keyword(s):  
Operator Product Expansion ◽  
Density Operator ◽  
Gradient Flow ◽  
Gluon Condensate ◽  
Operator Product ◽  
Clear Definition ◽  
Lattice Data ◽  
Perturbative Calculation ◽  
Yang Mills ◽  
Definition Of

Abstract We propose a clear definition of the gluon condensate within the large-$\beta_0$ approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of $\mathcal{O}(\Lambda^4)$, which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The renormalon uncertainty is absorbed into the gluon condensate in the OPE, which makes the gluon condensate free from the renormalon uncertainty. As a result, we can define the OPE in a renormalon-free way. Based on this renormalon-free OPE formula, we discuss numerical extraction of the gluon condensate using the lattice data of the energy density operator defined by the Yang–Mills gradient flow.

scholarly journals Local BRST cohomology and Seiberg–Witten maps in noncommutative Yang–Mills theory

2004 ◽  
Vol 677 (3) ◽  
pp. 503-534 ◽  
Author(s):  
Glenn Barnich ◽  
Friedemann Brandt ◽  
Maxim Grigoriev
Keyword(s):  
Yang Mills ◽  
Brst Cohomology

scholarly journals EXACT SOLUTIONS TO THE TWO-DIMENSIONAL BF AND YANG–MILLS THEORIES IN THE LIGHT-CONE GAUGE

2002 ◽  
Vol 17 (11) ◽  
pp. 1491-1502 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Quantum Gravity ◽  
Light Cone ◽  
Lagrangian Density ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Bf Theory ◽  
Conformal Gauge

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the [Formula: see text] term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

THE QUANTUM MECHANICS OF AN N=1 SUPERPARTICLE IN AN EXTENDED SUPERSPACE

1990 ◽  
Vol 05 (18) ◽  
pp. 1399-1409 ◽  
Author(s):  
MICHAEL B. GREEN ◽  
CHRISTOPHER M. HULL
Keyword(s):  
Quantum Mechanics ◽  
Finite Number ◽  
Gauge Fields ◽  
Yang Mills ◽  
Brst Cohomology ◽  
Covariant Gauge ◽  
Light Cone Quantization ◽  
Local Symmetries ◽  
Invariant Quantum ◽  
Extended Superspace

A new ten-dimensional superparticle action with local symmetries implemented via gauge fields is formulated in a superspace with an extra anticommuting space-time spinor coordinate. Light-cone quantization gives the spectrum of N=1 super-Yang-Mills. Covariant gauge choices in which the gauge fields are set to constants lead to free BRST-invariant quantum actions. Possible ghost systems include one with only a finite number of ghosts and several with an infinite number. In each case, the BRST cohomology class of zero ghost number gives the spectrum of N=1 super-Yang-Mills.

scholarly journals Local BRST cohomology in Einstein-Yang-Mills theory

1995 ◽  
Vol 455 (1-2) ◽  
pp. 357-408 ◽  
Author(s):  
Glenn Barnich ◽  
Friedemann Brandt ◽  
Marc Henneaux
Keyword(s):  
Yang Mills ◽  
Brst Cohomology

scholarly journals XVII. On the spectrum of nitrogen

1872 ◽  
Vol 20 (130-138) ◽  
pp. 484-487 ◽  
Keyword(s):  
Point Of View ◽  
Band Spectrum ◽  
Oxides Of Nitrogen ◽  
Pure Nitrogen ◽  
First Order ◽  
Gaseous Substance ◽  
Starting Point ◽  
Metallic Compounds ◽  
Band Spectra ◽  
General Fact

1. Introductory .—The formation of the different spectra which one gas is said to exhibit, when examined under different conditions, still remains one of the most obscure points of spectrum analysis. In 1864, when Plücker and Hittorf published their researches “On the Spectra of Ignited Gases and Vapours, with especial regard to the different Spectra of the same elementary gaseous substance”, they drew attention to the close resemblance in character of the band-spectra which certain metals yield at a comparatively low temperature to the band-spectrum of nitrogen and sulphur. Roscoe and Clifton, n their paper “On the effect of increased Temperature upon the nature of the Light emitted by the Vapour of certain Metals or Metallic Compounds”, rendered it probable that the band-spectra of the metals belonged really to the oxides. The two spectra of nitrogen were not, however, examined from that point of view, but, on the contrary, they were made the starting-point of new investigations by Wüllner, who came to the conclusion that certain gases may give even more than two different spectra. Ångström, expressing his doubts about the trustworthiness of Wüllner’s experiments, says in a note: “As regards the spectra which are usually attributed to nitrogen, I mention here, as a general fact, that it is my conviction that the fluted bands which are so characteristic of the oxides of metals are never found in spectra of elementary gases." I propose to show, in the present communication, (1) that pure nitrogen gives only one spectrum; (2) that this is the line-spectrum; (3) that the fluted spectrum of the first order is due to oxides of nitrogen, formed under the influence of the electric spark.

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