Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon

Canfora, Fabrizio; Gomez, A. J.; Sorella, S. P.; Vercauteren, David

doi:10.1016/j.aop.2014.02.017

Cited by 18 publications

(56 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the extension of the Gribov gap equation at finite temperature provides one with a good qualitative understanding, already within the semiclassical approximation, of the deconfinement temperature as well as of a possible intermediate phase in which features of the confining phase coexist with features of the fully deconfined phase, in agreement with different approaches (see [22] and references therein). Furthermore, within this framework the presence of the Higgs field [23,24] as well as of a ChernSimons term in 2 + 1 dimensions [25] can be accounted for as well. 1 We shall work exclusively with the Landau gauge here.…”

Section: Introductionmentioning

confidence: 99%

Effect of the Gribov horizon on the Polyakov loop and vice versa

et al. 2015

View full text Add to dashboard Cite

We consider finite-temperature SU(2) gauge theory in the continuum formulation, which necessitates the choice of a gauge fixing. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy w.r.t. the Polyakov-loop parameter and solving the Gribov gap equation. Inspired by the Casimir energy-style of computation, we illustrate the usage of Zeta function regularization in finite-temperature calculations. Our main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. In this exploratory work we mainly restrict ourselves to the original Gribov-Zwanziger quantization procedure in order to illustrate the approach and the potential direct link between the vacuum structure of the theory (dynamical mass scales) and (de)confinement. We also present a first look at the critical temperature obtained from the refined Gribov-Zwanziger approach. Finally, a particular problem for the pressure at low temperatures is reported. a

show abstract

Section: Introductionmentioning

confidence: 99%

Effect of the Gribov horizon on the Polyakov loop and vice versa

et al. 2015

View full text Add to dashboard Cite

show abstract

“…We know that the solution of the Gribov problem for a Chern-Simons theory is trivial because the theory does not have metric [14]. But now, in this case with two Chern-Simons interacting with bi-fundamental matter, we can have a spontaneous symmetry breaking such that insert a metric [42,43].…”

Section: Some Aspects Of N= 1 Chern-simons-matter Theoriesmentioning

confidence: 99%

“…So the Gribov mechanism is an interesting possibility of the investigation of confinement in YM theories in three dimensions. That is, YM-CS theory with the Gribov mechanism has the possibility of a confined and a de-confined phase, depending on a fine tune between the Gribov mass gap and the usual parameters in the pure YM-CS [14]. In this case we have an interesting model with different phases.…”

Section: Introductionmentioning

confidence: 99%

“…To calculate the gauge propagator we need only the bilinear of S like to calculate (14). Thus, for S SGZ , we have (with 96):…”

Section: The Super Gauge Propagatormentioning

confidence: 99%

“…However as we'll see in the next section the Gribov parameter γ can be determined as a function of coupling constant g such that these propagators will be function of the two parameters, g and m (in the case m = 0), and so it is possible the study of phases involving this theory. The phases for this type of propagator was studied in [14] through the analysis of the poles in this propagator. It is important to note here that due to a Gribov type propagator also for the fermionic partners we have a fermionic condensate defined by lim x1→x2 T r < λ…”

Section: The Super Gauge Propagatormentioning

confidence: 99%

See 2 more Smart Citations

Remarks on Gribov mechanism on N=1 supersymmetric 3D theories and the possibility of obtaining Gribov from one ABJM like Theory

Amaral

Lemes

2015

Annals of Physics

View full text Add to dashboard Cite

show abstract

Field-dependent BRST–antiBRST transformations in Yang–Mills and Gribov–Zwanziger theories

Moshin

Reshetnyak

2014

Nuclear Physics B

View full text Add to dashboard Cite

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet λ a , a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with s a -potential parameters λ a = s a Λ induced by a finite even-valued functional Λ and by the anticommuting generators s a of BRST-antiBRST transformations, amount to a precise change of the gaugefixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary R ξ -like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the YangMills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations.

show abstract

Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon

Cited by 18 publications

References 41 publications

Effect of the Gribov horizon on the Polyakov loop and vice versa

Effect of the Gribov horizon on the Polyakov loop and vice versa

Remarks on Gribov mechanism on N=1 supersymmetric 3D theories and the possibility of obtaining Gribov from one ABJM like Theory

Field-dependent BRST–antiBRST transformations in Yang–Mills and Gribov–Zwanziger theories

Contact Info

Product

Resources

About