arXiv subjects

Sudhaker Upadhyay

Publications and source records attributed to Sudhaker Upadhyay.

122 records · Page 7Linked to original sources

arXiv2013

Noncommutative Gauge Theories: Model for Hodge theory

The nilpotent BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on the Moyal plane are shown to satisfy the same algebra as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.

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arXiv2013

Finite field dependent BRST transformations and its applications to gauge field theories

The Becchi-Rouet-Stora and Tyutin (BRST) transformation plays a crucial role in the quantization of gauge theories. The BRST transformation is also very important tool in characterizing the various renormalizable field theoretic models. The generalization of the usual BRST transformation, by making the infinitesimal global parameter finite and field dependent, is commonly known as the finite field dependent BRST (FFBRST) transformation. In this thesis, we have extended the FFBRST transformation in an auxiliary field formulation and have developed both on-shell and off-shell FF-anti-BRST transformations. The different aspects of such transformation are studied in Batalin-Vilkovisky (BV) formulation. FFBRST transformation has further been used to study the celebrated Gribov problem and to analyze the constrained dynamics in gauge theories. A new finite field dependent symmetry (combination of FFBRST and FF-anti-BRST) transformation has been invented. The FFBRST transformation is shown useful in connection of first-class constrained theory to that of second-class also. Further, we have applied the Batalin-Fradkin-Vilkovisky (BFV) technique to quantize a field theoretic model in the Hamiltonian framework. The Hodge de Rham theorem for differential geometry has also been studied in such context.

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arXiv2013

Perturbative quantum gravity in Batalin-Vilkovisky formalism

In this Letter we consider the perturbative quantum gravity on the super-manifold which remains invariant under absolutely anticommuting BRST and anti-BRST transformations. In addition to that the theory posses one more symmetry known as shift symmetry. The BRST invariant Batalin-Vilkovisky (BV) action for perturbative quantum gravity is realized as a translation in Grassmann coordinate. Further we show that the quantum master equation of the BV quantization method at one-loop order can be translated to have a superfield structure for the action. However, the BRST as well as anti-BRST invariant BV action is constructed in superspace with the help of two Grassmann coordinates.

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arXiv2013

The noncovariant gauges in 3-form theories

We study the 3-form gauge theory in the context of generalized BRST formulation. We construct the finite field-dependent BRST (FFBRST) symmetry for such a theory. The generating functional for 3-form gauge theory in noncovariant gauge is obtained from that of in covariant gauge. We further extend the results by considering 3-form gauge theory in the context of Batalin-Vilkovisky (BV) formulation.

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arXiv2013

Finite BRST Transformations for the Bagger-Lambert-Gustavasson Theory

In this paper we analyse the Bagger-Lambert-Gustavsson (BLG) theory in $\mathcal{N} =1$ 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.

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arXiv2012

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 Proca model is obtained from the generating functional of 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 theory for self-dual chiral boson.

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arXiv2012

Field dependent nilpotent symmetry for gauge theories

We construct the field dependent mixed BRST (combination of BRST and anti-BRST) transformations for pure gauge theories. These are shown to be an exact nilpotent symmetry of both the effective action as well as the generating functional for certain choices of the field dependent parameters. We show that the Jacobian contributions for path integral measure in the definition of generating functional arising from BRST and anti-BRST part compensate each other. The field dependent mixed BRST transformations are also considered in field/antifield formulation to show that the solutions of quantum master equation remain invariant under these. Our results are supported by several explicit examples.

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arXiv2012

BV formulation of higher form gauge theories in a superspace

We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for two and three form gauge theories. Further we develop the superspace formulation for the BV actions for these theories. We show that the extended BRST invariant BV action for these theories can be written manifestly covariant manner in a superspace with one Grassmann coordinate. On the hand a superspace with two Grassmann coordinates are required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant BV actions for higher form gauge theories.

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arXiv2011

Relating Gribov-Zwanziger theory and Yang-Mills theory in Batalin-Vilkovisky formalism

We consider the BRST invariant Gribov-Zwanziger theory with appropriate horizon term in Batalin-Vilkovisky formalism. The usual infinitesimal BRST transformation is generalized by considering the parameter finite and field dependent. We show that such finite field dependent BRST transformation with suitable choice of finite parameter relates the generating functional of Gribov-Zwanziger theory to that of the Yang-Mills theory.

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arXiv2011

The model for self-dual chiral bosons as a Hodge theory

We consider (1+1) dimensional theory for a single self-dual chiral boson as classical model for gauge theory. Using Batalin-Fradkin-Vilkovisky (BFV) technique the nilpotent BRST and anti BRST symmetry transformations for this theory have been studied. In this model other forms of nilpotent symmetry transformations like co-BRST and anti co-BRST which leave the gauge-fixing part of the action invariant, are also explored. We show that the nilpotent charges for these symmetry transformations satisfy the algebra of de Rham cohomological operators in differential geometry. The Hodge decomposition theorem on compact manifold is also studied in the context of conserved charges.

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arXiv2011

Relating Gribov-Zwanziger theory to effective Yang-Mills theory

We consider the Gribov-Zwanziger (GZ) theory with appropriate horizon term which exhibits the nilpotent BRST invariance. This infinitesimal BRST transformation has been generalized by allowing the parameter to be finite and field dependent (FFBRST). By constructing appropriate finite field dependent parameter we show that the generating functional of GZ theory with horizon term is related to that of Yang-Mills (YM) theory through FFBRST transformation.

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arXiv2010

Generalized BRST transformation in Abelian rank-2 antisymmetric tensor field theory

We generalize the BRST transformations in Abelian rank-2 tensor field theory by allowing the parameter to be finite and field dependent and show that such transformations play crucial role in studying the Abelian 2-form gauge theory in noncovariant gauges. The generating functionals in different effective theories are connected through these generalized BRST transformations with different choice of finite parameter. We further consider the generalization of the anti-BRST transformations and show that even anti-BRST transformations with the finite field dependent parameter relate the generating functional for different effective theories. Such generalized BRST/anti-BRST transformations are useful in connecting generating functionals corresponding to different effective theories. Field/antifield formulation of this Abelian 2-form gauge theory is also studied in the context of generalized BRST transormations. We show that generalized BRST transformation connects the generating functional corresponding to the different solutions of quantum master equation in field/antifield formulation.

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arXiv2010

Finite nilpotent symmetry in Batalin-Vilkovisky formalism

We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories, in the context of generalized BRST transformations with finite field dependent parameter. In the usual Faddeev-Popov formulation of gauge theories such finite field dependent BRST (FFBRST) transformations do not leave the generating functionals invariant as the path integral measure changes in a non-trivial way for a finite transformations. Here we show that FFBRST transformation, with appropriate choice of finite field-dependent parameter, is symmetry of the generating functionals in the Batalin-Vilkovisky formalism. The finite parameter is chosen in such a way that the contribution from the Jacobian of the path integral measure is adjusted with gauge fixed fermions which do not change the generating functionals. Several examples for such a finite parameters are constructed.

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arXiv2010

Off-shell nilpotent finite BRST/anti-BRST transformations

We develop the off-shell nilpotent finite field dependent BRST transformations and show that for different choices of the finite field dependent parameter these connect the generating functionals corresponding to different effective theories. We also construct both on-shell and off-shell finite field dependent anti-BRST tranformations for Yang Mills theories and show that these transformations play the similar role in connecting different generating functionals of different effective theories. Analogous to the finite field dependent BRST transformations, the non-trivial Jacobians of the path integral measure which arise due to the finite field dependent anti-BRST transformations are responsible for the new results. We consider several explicit examples in each case to demonstrate the results.

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