scholarly journals Calculation of two-loop β-function for general N=1 supersymmetric Yang–Mills theory with the higher covariant derivative regularization

2010 ◽  
Vol 686 (4-5) ◽  
pp. 293-297 ◽  
Author(s):  
A.B. Pimenov ◽  
E.S. Shevtsova ◽  
K.V. Stepanyantz
Keyword(s):  
Covariant Derivative ◽  
Yang Mills ◽  
Higher Covariant Derivative ◽  
Β Function

scholarly journals CONSISTENCY OF THE HYBRID REGULARIZATION WITH HIGHER COVARIANT DERIVATIVE AND INFINITELY MANY PAULI–VILLARS

2001 ◽  
Vol 16 (22) ◽  
pp. 3755-3783
Author(s):  
KOH-ICHI NITTOH
Keyword(s):  
Covariant Derivative ◽  
Vacuum Polarization ◽  
Gauge Theories ◽  
Polarization Tensor ◽  
Logarithmic Divergence ◽  
Yang Mills ◽  
Higher Covariant Derivative ◽  
Group Functions ◽  
Supersymmetric Gauge ◽  
Vacuum Polarization Tensor

We study the regularization and renormalization of the Yang–Mills theory in the framework of the manifestly invariant formalism, which consists of a higher covariant derivative with an infinitely many Pauli–Villars fields. Unphysical logarithmic divergence, which is the problematic point on the Slavnov method, does not appear in our scheme, and the well-known value of the renormalization group functions are derived. The cancellation mechanism of the quadratic divergence is also demonstrated by calculating the vacuum polarization tensor of the order of Λ0 and Λ-4. These results are the evidence that our method is valid for intrinsically divergent theories and is expected to be available for the theory which contains the quantity depending on the space–time dimensions, like supersymmetric gauge theories.

scholarly journals A COMPARISON OF THE PROPER-TIME EQUATION AND THE RENORMALIZATION GROUP β-FUNCTION IN STRING THEORY

1995 ◽  
Vol 10 (21) ◽  
pp. 1565-1575
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Proper Time ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
The Other ◽  
Proportionality Factor ◽  
Yang Mills ◽  
Higher Covariant Derivative ◽  
Full Equation ◽  
Gauge Covariance ◽  
Β Function

It is known that there is a proportionality factor relating the β-function and the equations of motion viz. the Zamolodchikov metric. Usually this factor has to be obtained by other methods. The proper-time equation, on the other hand, is the full equation of motion. We explain the reasons for this and illustrate it by calculating corrections to Maxwell’s equation. The corrections are calculated to cubic order in the field strength, but are exact to all orders in derivatives. We also test the gauge covariance of the proper-time method by calculating higher (covariant) derivative corrections to the Yang-Mills equation.

scholarly journals A NOTE ON THE QUADRATIC DIVERGENCE IN HYBRID REGULARIZATION

2000 ◽  
Vol 15 (15) ◽  
pp. 955-963 ◽  
Author(s):  
KOH-ICHI NITTOH
Keyword(s):  
Covariant Derivative ◽  
Regularization Method ◽  
Explicit Calculation ◽  
Yang Mills ◽  
Higher Derivative ◽  
Higher Covariant Derivative

We consider the quadratic divergence of the Yang–Mills theory when we use the hybrid regularization method consisting of higher covariant derivative terms and the Pauli–Villars fields. By explicit calculation of the diagrams, we show that the higher derivative terms for the ghost fields are necessary for the complete cancellation of the quadratic divergence.

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.

β-Function in a non-covariant Yang-Mills theory

1978 ◽  
Vol 141 (1-2) ◽  
pp. 153-177 ◽  
Author(s):  
H.B. Nielsen ◽  
Masao Ninomiya
Keyword(s):  
Yang Mills ◽  
Β Function

scholarly journals Thermal β function in Yang-Mills theory

1995 ◽  
Vol 51 (2) ◽  
pp. 774-780 ◽  
Author(s):  
Per Elmfors ◽  
Randy Kobes
Keyword(s):  
Yang Mills ◽  
Β Function

The perturbative β-function in the Zumino model

2001 ◽  
Vol 79 (8) ◽  
pp. 1099-1104
Author(s):  
R Clarkson ◽  
D.G.C. McKeon
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Supersymmetric Model ◽  
Yang Mills ◽  
Β Function ◽  
Zumino Model

We consider the perturbative β-function in a supersymmetric model in four-dimensional Euclidean space formulated by Zumino. It turns out to be equal to the β-function for N = 2 supersymmetric Yang–Mills theory despite differences that exist in the two models. PACS No.: 12.60Jv

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