We derive the off-shell nilpotent symmetries of the two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF) type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parameterized by the superspace coordinates Z^{M} = (x^μ, θ, \barθ) where x^{μ} (with μ= 0,1) are the bosonic coordinates and a pair of Grassmannian variables (θ, \barθ) obey the relationships: θ^{2} = \barθ^{2} = 0, θ\barθ+ \barθθ= 0.
Exploiting the theoretical potential of the modified Bonora-Tonin superfield approach (MBTSA) as well as the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the complete set of off-shell nilpotent (anti-)BRST symmetry transformations corresponding to the classical two $(1 + 1)$-dimensional (2D) diffeomorphism symmetry transformations on the world-sheet (that is traced out by the motion of a model of bosonic string). Only the BRST symmetry transformations for this model have been discussed in the earlier literature. We derive the (anti-)BRST inv…
The Landau-gauge gluon and ghost correlation functions obtained in lattice simulations can be reproduced qualitatively and, to a certain extent, quantitatively if a gluon mass is added to the standard Faddeev-Popov action. This has been tested extensively at one loop, for the two and three point correlation functions of the gluons, ghosts and quarks. In this article, we push the comparison to two loops for the gluon and ghost propagators. The agreement between lattice results and the perturbative calculation considerably improves. This validates the Curci-Ferrari action as a good phenomenologi…
We consider a BRST invariant generalization of the "massive background Landau gauge", resembling the original Curci-Ferrari model that saw a revived interest due to its phenomenological success in modeling infrared Yang-Mills dynamics, including that of the phase transition. Unlike the Curci-Ferrari model, however, the mass parameter is no longer a phenomenological input but it enters as a result of dimensional transmutation via a BRST invariant dimension two gluon condensate. The associated renormalization constant is dealt with using Zimmermann's reduction of constants program which fixes th…
In this article we study the unquenched three-gluon and ghost-gluon vertex in all momentum range going from the ultraviolet to the infrared regime using the Curci-Ferrari model at one-loop in Landau gauge as an extension of the results presented in \cite{Pelaez:2013cpa}. Results are compared with recent lattice data for $SU(3)$ in the unquenched case. This calculation is a pure prediction of the model because it does not require fixing any parameter once two-point functions are fitted. An analysis of the influence of dynamical quarks in the position of the zero crossing of the three-gluon vert…
A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges
本文在精化Gribov-Zwanziger理论的框架内研究了物质场的传播子，该理论考虑了Yang-Mills理论规范固定量子化过程中Gribov副本的影响.与精化Gribov-Zwanziger作用量的纯胶子扇区完全类似，在物质扇区中添加了Faddeev-Popov算子逆的非定域长程项。利用最近在[Capri et al 2016]中实现的Gribov-Zwanziger框架的BRST不变公式，在线性协变，Curci-Ferrari和最大Abel规范中明确计算了规范群的伴随和基本表示中标量场和夸克场的传播子。只要晶格数据可用，我们的结果表现出良好的定性协议。
The Curci-Ferrari model has been shown to provide a good grasp on pure Yang-Mills correlation functions in the Landau gauge, already at one-loop order. In a recent work, the robustness of these results has been tested by evaluating the two-loop corrections to the gluon and ghost propagators. We pursue this systematic investigation by computing the ghost-antighost-gluon vertex to the same accuracy in a particular kinematic configuration that makes the calculations simpler. Because both the parameters of the model and the normalizations of the fields have already been fixed in a previous work, t…
Effects of fermions in one-loop propagators in the Curci-Ferrari-Delbourgo-Jarvis gauge
Instituto de Física, Facultad de Ciencias, Universidad de la República（拉普拉塔共和国大学理学院物理研究所）；Instituto de Física, Facultad de Ingeniería, Universidad de la República（拉普拉塔共和国大学工学院物理研究所）；Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC（索邦大学，法国国家科学研究中心，凝聚态物质理论物理实验室）
More on ghost condensation in Yang-Mills theory: BCS versus Overhauser effect and the breakdown of the Nakanishi-Ojima annex SL(2,R) symmetry
We analyze the ghost condensates <f^{abc}c^{b}c^{c}>, <f^{abc} \oc^{b} \oc^{c} > and <f^{abc} \oc^{b} c^{c}> in Yang-Mills theory in the Curci-Ferrari gauge. By combining the local composite operator formalism with the algebraic renormalization technique, we are able to give a simultaneous discussion of <f^{abc}c^{b}c^{c}>, <f^{abc} \oc^{b} \oc^{c} > and <f^{abc} \oc^{b} c^{c}>, which can be seen as playing the role of the BCS, respectively Overhauser effect in ordinary superconductivity. The Curci-Ferrari gauge exhibits a global continuous symmetry generated by the Nakanishi-Ojima (NO) algebr…
We evaluate all two-point correlation functions of the Curci-Ferrari (CF) model in four dimensions and in the presence of mass-degenerate fundamental quark flavors, as a natural extension of an earlier investigation in the quenched approximation. In principle, the proper account of chiral symmetry breaking ($χ$SB) and the corresponding dynamical generation of a quark mass function within the CF model requires one to go beyond perturbation theory \cite{Pelaez:2020ups}. However, it is interesting to assess whether a perturbative description applies to correlation functions that are not directly …
We evaluate the three-gluon vertex with one vanishing external momentum within the Curci-Ferrari (CF) model at two-loop order and compare our results to Landau-gauge lattice simulations of the same vertex function for the SU(2) and SU(3) gauge groups in four dimensions. The parameters of the model being adjusted by fitting the two-point functions to lattice data, our evaluation of the three-gluon vertex arises as a pure prediction. We find that two-loop corrections systematically improve the agreement between the model and the lattice data as compared to earlier one-loop calculations, with a b…
We discuss and derive the continuous Becchi-Rouet-Stora-Tyutin (BRST)and anti-BRST symmetry transformations for the Jackiw-Pi (JP) model of three (2 + 1)-dimensional (3D) massive non-Abelian 1-form gauge theory by exploiting the standard technique of (anti-)chiral superfield approach (ACSA) to BRST formalism where a few appropriate and specific sets of (anti-)BRST invariant quantities (i. e. physical quantities at quantum level) play a very important role. We provide the explicit derivation of the nilpotency and absolute anticommutativity properties of (anti-)BRST conserved charges and the exi…
SU(3) gauge theory in the nonlinear gauge of the Curci--Ferrari type is studied. In the low-energy region, ghost condensation and subsequent gauge field condensation can happen. The latter condensation makes classical gauge fields massive. If the color electric potential with string is chosen as the classical gauge field, it produces the static potential with the linear potential. We apply this static potential to the three-quark system, and show, different from the $Y$-type potential, infrared divergence remains in the $Δ$-type potential. The color electric flux is also studied, and show that…
We derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for any arbitrary D-dimensional St$\ddot u$ckelberg-modified massive Abelian 3-form theory within the framework of augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism where, in addition to the horizontality condition (HC), we exploit the theoretical strength of the gauge invariant restriction (GIR) to deduce the proper transformations for the gauge, associated (anti-)ghost fields, auxiliary fields, St$\ddot u$ckelberg compensating field, etc. In fact, it…
