Finite BRST Transformations Research Articles

On the Finite Brst Transformations: the Jacobians and the Standard Model with the Gauge-Invariant Gribov Horizon

We review the concept and properties of finite field-dependent BRST and BRST-antiBRST transformations introduced in our recent study (A. Reshetnyak, IJMPA 29 (2014) 1450128, P. Moshin, A. Reshetnyak, Nucl. Phys. B 888 (2014) 92, Phys. Lett B 739 (2014) 110, IJMPA 29 (2014) 1450159, IJMPA 30 (2015) 1550021, IJMPA 31 (2016) 1650111, [arxiv:1604.03027 [hep-th]]) for gauge theories. Exact rules for calculating the Jacobian of a corresponding change of variables in the partition function are presented. Infrared peculiarities under $R_\xi$-gauges in the Yang--Mills theory and Standard Model are examined in a gauge-invariant way with an appropriate horizon functional and unaffected local $N=1,2$ BRST symmetries.

On gauge independence for gauge models with soft breaking of BRST symmetry

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

Finite BRST transformations for the Bagger–Lambert–Gustavsson theory

In this Letter we analyse the Bagger–Lambert–Gustavsson (BLG) theory in N=1 superspace. Furthermore, we will construct the BRST transformations for this theory. These BRST transformations will be integrated out to obtain the finite field dependent version of BRST (FFBRST) transformations. We will also analyse the effect of the FFBRST transformations on the effective action. We will thus show that the FFBRST transformations can be used to relate generating functionals of the BLG theory in two different gauges.

Finite BRST transformation and constrained systems

We establish the connection between the generating functional for the first class theories and the generating functional for the second class theories using the finite field dependent BRST (FFBRST) transformation. We show this connection with the help of explicit calculations in two different models. The generating functional of the Proca model is obtained from the generating functional of the Stueckelberg theory for massive spin 1 vector field using FFBRST transformation. In the other example we relate the generating functionals for gauge invariant and gauge variant theories for a self-dual chiral boson.