scholarly journals AN EXACT RG FORMULATION OF QUANTUM GAUGE THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 1899-1911 ◽  
Author(s):  
T. R. MORRIS
Keyword(s):  
Gauge Theory ◽  
Flow Equation ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Quantum Gauge Theory ◽  
Supergauge Theory ◽  
Gauge Fixing ◽  
Β Function ◽  
The One ◽  
First Time

A gauge invariant Wilsonian effective action is constructed for pure SU(N) Yang-Mills theory by formulating the corresponding flow equation. Manifestly gauge invariant calculations can be performed i.e. without gauge fixing or ghosts. Regularisation is implemented in a novel way which realises a spontaneously broken SU(N|N) supergauge theory. As an example we sketch the computation of the one-loop β function, performed for the first time without any gauge fixing.

scholarly journals Background independent exact renormalisation

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Kevin Falls
Keyword(s):  
Path Integral ◽  
Effective Action ◽  
Beta Function ◽  
Background Field ◽  
Flow Equation ◽  
Renormalisation Group ◽  
Gauge Invariant ◽  
Yang Mills ◽  
The One ◽  
Group Flow

AbstractA geometric formulation of Wilson’s exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent approach to quantum gravity and gauge theories in the continuum. The regularisation is a geometric variant of Slavnov’s scheme consisting of a modified action, which suppresses high momentum modes, supplemented by Pauli–Villars determinants in the path integral measure. An exact renormalisation group flow equation for the Wilsonian effective action is derived by requiring that the path integral is invariant under a change in the cutoff scale while preserving quasi-locality. The renormalisation group flow is defined directly on the space of gauge invariant actions without the need to fix the gauge. We show that the one-loop beta function in Yang–Mills and the one-loop divergencies of General Relativity can be calculated without fixing the gauge. As a first non-perturbative application we find the form of the Yang–Mills beta function within a simple truncation of the Wilsonian effective action.

scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

scholarly journals Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

2014 ◽  
Vol 92 (9) ◽  
pp. 1033-1042 ◽  
Author(s):  
S. Gupta ◽  
R. Kumar ◽  
R.P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Point Of View ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

scholarly journals ON THE β-FUNCTION AND CONFORMAL ANOMALY OF NONCOMMUTATIVE QED WITH ADJOINT MATTER FIELDS

2003 ◽  
Vol 18 (15) ◽  
pp. 2591-2607 ◽  
Author(s):  
NÉDA SADOOGHI ◽  
MOJTABA MOHAMMADI
Keyword(s):  
Gauge Theory ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Adjoint Representation ◽  
Conformal Anomaly ◽  
Loop Order ◽  
Path Integral Method ◽  
Β Function ◽  
The One ◽  
Matter Fields

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop β-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part, the conformal anomaly of the same theory is calculated using Fujikawa's path integral method. The value of the one-loop β-function calculated in both methods coincides. As it turns out, noncommutative QED with matter fields in the adjoint representation is asymptotically free for the number of flavor degrees of freedom Nf < 3.

FIELD-ANTIFIELD QUANTIZATION OF THE YANG-MILLS THEORY WITH EXTENDED BRST INVARIANCE IN THE COLLECTIVE FIELD APPROACH

1996 ◽  
Vol 11 (20) ◽  
pp. 3761-3771
Author(s):  
NELSON R.F. BRAGA ◽  
SERGIO M. DE SOUZA
Keyword(s):  
Gauge Theory ◽  
Yang Mills ◽  
Field Approach ◽  
Gauge Fixing ◽  
Judicious Choice ◽  
Brst Invariance

The collective field procedure is an interesting way of deriving the field-antifield formalism from a standard BRST approach. Trivial shift symmetries are introduced in the original gauge theory and then a judicious choice of gauge-fixing leads to the identification of the antighosts of these extra symmetries as the antifields. When explicit extended BRST invariance (BRST and anti-BRST invariance) is required, two collective fields are necessary, and the gauge-fixing structure is more complex. In this article, with the purpose of clarifying some aspects of this procedure, we consider in detail the example of the Yang–Mills theory.

scholarly journals FROM PEIERLS BRACKETS TO A GENERALIZED MOYAL BRACKET FOR TYPE-I GAUGE THEORIES

2007 ◽  
Vol 04 (03) ◽  
pp. 349-360 ◽  
Author(s):  
GIAMPIERO ESPOSITO ◽  
COSIMO STORNAIOLO
Keyword(s):  
Vector Fields ◽  
Field Operator ◽  
Functional Integral ◽  
Gauge Fields ◽  
Order Differential Operator ◽  
Type I ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group Invariant ◽  
Gauge Fixing

In the space-of-histories approach to gauge fields and their quantization, the Maxwell, Yang–Mills and gravitational field are well known to share the property of being type-I theories, i.e. Lie brackets of the vector fields which leave the action functional invariant are linear combinations of such vector fields, with coefficients of linear combination given by structure constants. The corresponding gauge-field operator in the functional integral for the in-out amplitude is an invertible second-order differential operator. For such an operator, we consider advanced and retarded Green functions giving rise to a Peierls bracket among group-invariant functionals. Our Peierls bracket is a Poisson bracket on the space of all group-invariant functionals in two cases only: either the gauge-fixing is arbitrary but the gauge fields lie on the dynamical sub-space; or the gauge-fixing is a linear functional of gauge fields, which are generic points of the space of histories. In both cases, the resulting Peierls bracket is proved to be gauge-invariant by exploiting the manifestly covariant formalism. Moreover, on quantization, a gauge-invariant Moyal bracket is defined that reduces to iħ times the Peierls bracket to lowest order in ħ.

scholarly journals EMERGENCE OF THE HAAR MEASURE IN THE STANDARD FUNCTIONAL INTEGRAL REPRESENTATION OF THE YANG-MILLS PARTITION FUNCTION

1996 ◽  
Vol 11 (30) ◽  
pp. 2451-2461 ◽  
Author(s):  
H. REINHARDT
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Haar Measure ◽  
Transition Amplitude ◽  
Functional Integral ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Gauge Fixing ◽  
Popov Method

The conventional path integral expression for the Yang–Mills transition amplitude with flat measure and gauge-fixing built in via the Faddeev-Popov method has been claimed to fall short of guaranteeing gauge invariance in the nonperturbative regime. We show, however, that it yields the gauge-invariant partition function where the projection onto gauge-invariant wave functions is explicitly performed by integrating over the compact gauge group. In a variant of maximal Abelian gauge the Haar measure arises in the conventional Yang-Mills path integral from the Faddeev-Popov determinant.

One-loop effects in N = 4 supersymmetry

1996 ◽  
Vol 74 (3-4) ◽  
pp. 176-181
Author(s):  
D. G. C. McKeon
Keyword(s):  
Radiative Corrections ◽  
Loop Order ◽  
Four Dimensions ◽  
Yang Mills ◽  
Yukawa Couplings ◽  
Gauge Fixing ◽  
Component Field ◽  
Β Function ◽  
Supersymmetric Theories ◽  
Invariant Gauge

It has been demonstrated that in massless supersymmetric theories, finite radiative corrections to the superpotential can occur (viz. the nonrenormalization theorems can be circumvented). In this paper, we examine the consequences of this in N = 4 supersymmetric Yang–Mills theory, a model in which the β function is known to be zero. It is shown that radiative corrections to the superpotential arise at one loop order in this theory contrary to the expectations of the nonrenormalization theorem, but that their form depends on which formulation of the model is used. When one uses a superfield formulation involving an N = 1 vector superfield and three N = 1 chiral superfields in conjunction with a supersymmetric (but not SU(4)) invariant gauge fixing, then at one-loop order, the radiative generation of terms in the superpotential means that the equality of the gauge and Yukawa couplings and indeed of different Yukawa couplings is lost. If one uses the component field formulation of the N = 4 model in the Wess–Zumino gauge with a covariant, SU(4) invariant (but not supersymmetric invariant) gauge fixing, then the SU(4) invariance is maintained, but the gauge and Yukawa couplings are no longer equal. We also consider computations in the component field formulation in the Wess–Zumino gauge using an N = 1 super Yang–Mills theory in ten dimensions, dimensionally reduced to four dimensions, with a ten-dimensional covariant gauge fixing condition. This formulation ensures that there is no distinction between gauge and Yukawa couplings and that SU(4) invariance is automatically preserved; however, supersymmetry is broken by the gauge fixing procedure.

scholarly journals A GAUGE INVARIANT REGULATOR FOR THE ERG

2001 ◽  
Vol 16 (11) ◽  
pp. 1989-2001 ◽  
Author(s):  
S. ARNONE ◽  
YU. A. KUBYSHIN ◽  
T. R. MORRIS ◽  
J. F. TIGHE
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Ultra Violet ◽  
Group Approach ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Yang Mills ◽  
Renormalization Group Approach ◽  
Higher Derivatives ◽  
Exact Renormalization Group

A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the regularisation via covariant higher derivatives and includes auxiliary Pauli-Villars fields which amounts to a spontaneously broken SU(N|N) super-gauge theory. We demonstrate perturbatively that the extended theory is ultra-violet finite in four dimensions and argue that it has a sensible limit when the regularization cutoff is removed.

scholarly journals The one-loop effective action of noncommutative super Yang–Mills is gauge invariant

2001 ◽  
Vol 504 (1-2) ◽  
pp. 131-140 ◽  
Author(s):  
Mario Pernici ◽  
Alberto Santambrogio ◽  
Daniela Zanon
Keyword(s):  
Effective Action ◽  
Gauge Invariant ◽  
Yang Mills ◽  
The One
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