arXiv subjects
Publications and source records attributed to H. C. Toledo.
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.
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 renormalization of $\mathcal{N}=1$ Super Yang-Mills theory with the presence of the local composite operators $AA$, $A_μγ_μλ$ and $\barλλ$ is analyzed in the Wess-Zumino gauge, employing the Landau condition. An all-orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field, and gluino renormalization. The non-renormalization theorem of the gluon--ghost--anti-ghost vertex in the Landau gauge is shown to remain valid in $\mathcal{N}=1$ Super Yang-Mills with the presence of the local composite operators. Moreover, 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 $\mathcal{N}=1$ 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, $A_μγ_μλ$ and $\barλλ$, 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 $A^h_μ$ 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 $A^{h}_μ$ 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 Hooft's $R_ζ$-gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field.
We present an N=1 supersymmetric generalization of the Maximal Abelian Gauge (MAG) in its superfield and component-field formulations, and discuss its Faddeev-Popov quantization, the associated BRST symmetry and the corresponding Slavnov-Taylor identity in superspace approach.