We perform a $mathcal{N}=1$ supersymmetric extension of the replica model quantized in the Landau gauge and compute the gluon and gluino propagators at tree-level, such results display a supersymmetric confined model very similar to the supersymmetric version of the Gribov-Zwanziger approach.
We introduce, within the Refined-Gribov-Zwanziger setup, a composite BRST invariant fermionic operator coupled to the inverse of the Faddeev-Popov operator. As a result, an effective BRST invariant action in Euclidean space-time is constructed, enabl
ing us to pave the first step towards the study of the behaviour of the fermion propagator in the infrared region in the class of the linear covariant gauges. The aforementioned action is proven to be renormalizable to all orders by means of the algebraic renormalization procedure.
The renormalization properties of two local BRST invariant composite operators, $(O,V_mu)$, corresponding respectively to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are scrutinized in the $U(1)$ Higgs
model by means of the algebraic renormalization setup. Their renormalization $Z$s factors are explicitly evaluated at one-loop order in the $overline{text{MS}}$ scheme by taking into due account the mixing with other gauge invariant operators. In particular, it turns out that the operator $V_mu$ mixes with the gauge invariant quantity $partial_ u F_{mu u}$, which has the same quantum numbers, giving rise to a $2 times 2$ mixing matrix. Moreover, two additional powerful Ward identities exist which enable us to determine the whole set of $Z$s factors entering the $2 times 2$ mixing matrix as well as the $Z$ factor of the operator $O$ in a purely algebraic way. An explicit check of these Ward identities is provided. The final setup obtained allows for computing perturbatively the full renormalized result for any $n$-point correlation function of the scalar and vector composite operators.
In this work, we study a gauge invariant local non-polynomial composite spinor field in the fundamental representation in order to establish its renormalizability. Similar studies were already done in the case of pure Yang-Mills theories where a loca
l composite gauge invariant vector field was obtained and an invariant renormalizable mass term could be introduced. Our model consists of a massive Euclidean Yang-Mills action with gauge group $SU(N)$ coupled to fermionic matter in the presence of an invariant spinor composite field and quantized in the linear covariant gauges. The whole set of Ward identities is analysed and the algebraic proof of the renormalizability of the model is obtained to all orders in a loop expansion.
In this work we present an algebraic proof of the renormazibility of the super-Yang-Mills action quantized in a generalized supersymmetric version of the maximal Abelian gauge. The main point stated here is that the generalized gauge depends on a set
of infinity gauge parameters in order to take into account all possible composite operators emerging from the dimensionless character of the vector superfield. At the end, after the removal of all ultraviolet divergences, it is possible to specify values to the gauge parameters in order to return to the original supersymmetric maximal Abelian gauge, first presented in Phys. Rev. D91, no. 12, 125017 (2015), Ref. [1].
We construct a vector gauge invariant transverse field configuration $V^H$, consisting of the well-known superfield $V$ and of a Stueckelberg-like chiral superfield. The renormalizability of the Super Yang Mills action in the Landau gauge is analyzed
in the presence of a gauge invariant mass term $m^2 int dV mathcal{M}(V^H)$, with $mathcal{M}(V^H)$ a power series in $V^H$. Unlike the original Stueckelberg action, the resulting action turns out to be renormalizable to all orders.
The $mathcal{N}=1$ Super Yang-Mills theory in the presence of the local composite operator $A^2$ is analyzed in the Wess-Zumino gauge by employing the Landau gauge fixing condition. Due to the superymmetric structure of the theory, two more composite
operators, $A_mu gamma_mu lambda$ and $bar{lambda}lambda$, related to the susy variations of $A^2$ are also introduced. A BRST invariant action containing all these operators is obtained. An all order proof of the multiplicative renormalizability of the resulting theory is then provided by means of the algebraic renormalization setup. Though, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino.
The dimension two gauge invariant non-local operator $A_{min }^{2}$, obtained through the minimization of $int d^4x A^2$ along the gauge orbit, allows to introduce a non-local gauge invariant configuration $A^h_mu$ which can be employed to built up a
class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both $A_{min }^{2}$ and $A^{h}_mu$ can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of $A_{min }^{2}$ gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as t Hoofts $R_zeta$-gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field.
The Refined Gribov-Zwanziger framework takes into account the existence of equivalent gauge field configurations in the gauge-fixing quantization procedure of Euclidean Yang-Mills theories. Recently, this setup was extended to the family of linear co
variant gauges giving rise to a local and BRST-invariant action. In this paper, we give an algebraic proof of the renormalizability of the resulting action to all orders in perturbation theory.
In this work, we study the propagators of matter fields within the framework of the Refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full an
alogy with the pure gluon sector of the Refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST invariant formulation of the Gribov-Zwanziger framework achieved in [Capri et al 2016], the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.
