Renormalization aspects of $$\mathcal {N}=1$$ N = 1 Super Yang–Mills theory in the Wess–Zumino gauge

Capri, M. A. L.; Granado, Diego R.; Guimaraes, M. S.; Justo, I. F.; Mihaila, L.; Sorella, S. P.; Vercauteren, David

doi:10.1140/epjc/s10052-014-2844-0

Cited by 29 publications

(45 citation statements)

References 28 publications

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“…As shown in [53], Eq. (29) can be translated into a set of Slavnov-Taylor identities, ensuring the all-order renormalizability of N = 1 Super-Yang-Mills.…”

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 97%

“…We shall follow [53], where an all-order proof of the renormalization of the theory through the BRST symmetry has been given. In the Wess-Zumino gauge, the action of N = 1 Euclidean Super-Yang-Mills is given by the expression 2…”

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 99%

“…It is a Majorana spinor in the adjoint representation of the gauge group. The auxiliary field D a is needed for the off-shell closure of the supersymmetric algebra [53]. Following [53], the most powerful and efficient way to quantize the theory is that of constructing a generalized BRST operator Q which collects both gauge and supersymmetric field transformations, namely…”

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 99%

“…which enables us to quantize the theory in a BRST invariant way [53]. Equation (25) implies that the operator Q is in fact nilpotent when acting on integrated local polynomials in the fields.…”

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 99%

“…Thanks to property (25), the introduction of the gauge-fixing term can be done by following the standard BRST framework. Adopting the Landau gauge condition, ∂ μ A a μ = 0, we have [53] …”

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 99%

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Implementing the Gribov–Zwanziger framework in $$\mathcal {N}=1$$ N = 1 Super-Yang–Mills in the Landau gauge

et al. 2014

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The Gribov-Zwanziger framework accounting for the existence of Gribov copies is extended to N = 1 Super-Yang-Mills theories quantized in the Landau gauge. We show that the restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon can be implemented in a way to recover non-perturbative features of N = 1 Super-Yang-Mills theories, namely the existence of the gluino condensate as well as the vanishing of the vacuum energy.

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“…As shown in [53], Eq. (29) can be translated into a set of Slavnov-Taylor identities, ensuring the all-order renormalizability of N = 1 Super-Yang-Mills.…”

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 97%

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 99%

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 99%

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 99%

Section: The N = 1 Super-yang-mills and Its Quantizationmentioning

confidence: 99%

See 3 more Smart Citations

Implementing the Gribov–Zwanziger framework in $$\mathcal {N}=1$$ N = 1 Super-Yang–Mills in the Landau gauge

et al. 2014

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The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

Stepanyantz

2020

J. High Energ. Phys.

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The contributions of the matter superfields and of the Faddeev-Popov ghosts to the βfunction of N = 1 supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For this purpose we use the recently proved statement that the β-function in these theories is given by integrals of double total derivatives with respect to the loop momenta. These integrals do not vanish due to singularities of the integrands. This implies that the β-function beyond the one-loop approximation is given by the sum of the singular contributions, which is calculated in all orders for singularities produced by the matter superfields and by the Faddeev-Popov ghosts. The result is expressed in terms of the anomalous dimensions of these superfields. It coincides with the corresponding part of the new form of the NSVZ equation, which can be reduced to the original one with the help of the non-renormalization theorem for the triple gauge-ghost vertices.

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The β-function of $$ \mathcal{N} $$ = 1 supersymmetric gauge theories regularized by higher covariant derivatives as an integral of double total derivatives

Stepanyantz

2019

J. High Energ. Phys.

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For a general N = 1 supersymmetric gauge theory regularized by higher covariant derivatives we prove in all orders that the β-function defined in terms of the bare couplings is given by integrals of double total derivatives with respect to loop momenta. With the help of the technique used for this proof it is possible to construct a method for obtaining these loop integrals, which essentially simplifies the calculations. As an illustration of this method, we find the expression for the three-loop contribution to the β-function containing the Yukawa couplings and compare it with the result of the standard calculations made earlier. Also we briefly discuss, how the structure of the loop integrals for the β-function considered in this paper can be used for the all-loop perturbative derivation of the NSVZ relation in the non-Abelian case.1 In the Landau gauge ξ → 0 a similar statement was known earlier for the usual (non-supersymmetric) Yang-Mills theory [15] and for N = 1 SYM formulated in terms of the component fields [16]. In the former case this statement was explicitly verified by the four-loop calculation in Ref. [17].

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Renormalization aspects of $$\mathcal {N}=1$$ N = 1 Super Yang–Mills theory in the Wess–Zumino gauge

Cited by 29 publications

References 28 publications

Implementing the Gribov–Zwanziger framework in $$\mathcal {N}=1$$ N = 1 Super-Yang–Mills in the Landau gauge

Implementing the Gribov–Zwanziger framework in $$\mathcal {N}=1$$ N = 1 Super-Yang–Mills in the Landau gauge

The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

The β-function of $$ \mathcal{N} $$ = 1 supersymmetric gauge theories regularized by higher covariant derivatives as an integral of double total derivatives

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