Browsing by Author "Sudhaker Upadhyay"

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A Superspace Description of Chern-Simons Theory in Batalin-Vilkovisky Formulation
(Springer New York LLC, 2015) Sudhaker Upadhyay; Manoj Kumar Dwivedi; Bhabani Prasad Mandal
We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for the Chern-Simons (CS) theories in (2 + 1) spacetime dimensions. Further we develop the superspace description of BV formulation for such theories. Interestingly, the extended BRST invariant CS theories can be described in superspace in covariant manner with the help of one more (Grassmann) coordinate. However, a superspace with two Grassmann coordinates are required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant actions for these theories. © 2014, Springer Science+Business Media New York.
Anti-FFBRST transformations for the BLG theory in presence of a boundary
(World Scientific Publishing Co. Pte Ltd, 2015) Mir Faizal; Sudhaker Upadhyay; Bhabani P. Mandal
In this paper we will analyze the anti-BRST symmetries of Bagger-Lambert-Gustavsson (BLG) theory in presence of a boundary. We will analyze these symmetries in both linear and nonlinear gauges. We will also derive the finite field version of the anti-BRST transformations for the BLG theory in presence of a boundary. These finite field transformations will be used to relate generating functional in linear gauge to the generating functional in the nonlinear gauge. © 2015 World Scientific Publishing Company.
BV formulation of higher form gauge theories in a superspace
(Springer New York LLC, 2012) Sudhaker Upadhyay; Bhabani Prasad Mandal
We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for 2- and 3-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 other hand a superspace with two Grassmann coordinates is required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant BV actions for higher form gauge theories. © 2012 Springer-Verlag / Società Italiana di Fisica.
Comments on interactions in the SUSY models
(Springer New York LLC, 2016) Sudhaker Upadhyay; Alexander Reshetnyak; Bhabani Prasad Mandal
We consider special supersymmetry (SUSY) transformations with m generators s← α, for some class of models and study the physical consequences when making the Grassmann-odd transformations to form an Abelian supergroup with finite parameters and a set of group-like elements with finite parameters being functionals of the field variables. The SUSY-invariant path integral measure within conventional quantization scheme leads to the appearance of the Jacobian under a change of variables generated by such SUSY transformations, which is explicitly calculated. The Jacobian implies, first of all, the appearance of trivial interactions in the transformed action, and, second, the presence of a modified Ward identity which reduces to the standard Ward identities in the case of constant parameters. We examine the case of the N= 1 and N= 2 supersymmetric harmonic oscillators to illustrate the general concept by a simple free model with (1, 1) physical degrees of freedom. It is shown that the interaction terms Utr have a corresponding SUSY-exact form: Utr= (V(1)s← ; V(2)s¯ ← s←) generated naturally under such generalized formulation. We argue that the case of a non-trivial interaction cannot be obtained in such a way. © 2016, The Author(s).
Emergence of Lowenstein-Zimmermann mass terms for QED3
(World Scientific Publishing Co. Pte Ltd, 2015) Sudhaker Upadhyay; Manoj Kumar Dwivedi; Bhabani Prasad Mandal
In this paper we consider a super-renormalizable theory of massless QED in (2 + 1) dimensions and discuss their BRST symmetry transformation. By extending the BRST transformation, we derive the Nielsen identities for the theory. Further, we compute the generalized BRST (so-called FFBRST) transformation by making the transformation parameter field dependent. Remarkably, we observe that the Lowenstein-Zimmermann mass terms, containing Lowenstein-Zimmermann parameter which plays an important role in the BPHZL renormalization program, along with the external sources coupled to the nonlinear BRST variations appear naturally in the theory through an FFBRST transformation. © 2015 World Scientific Publishing Company.
Equivalence Between Two Different Field-Dependent BRST Formulations
(Springer New York LLC, 2016) Sudhaker Upadhyay; Bhabani Prasad Mandal
Finite field-dependent BRST (FFBRST) transformations were constructed by integrating infinitesimal BRST transformation in a closed form. Such a generalized transformations have been extended in various branch of physics and found many applications. Recently BRST transformation has also been generalized with same goal and motivation in slightly different manner. In this work we have shown that the later formulation is conceptually equivalent to the earlier formulation. We justify our claim by producing the same result of later formulation using earlier FFBRST formulation. © 2015, Springer Science+Business Media New York.
Field dependent nilpotent symmetry for gauge theories
(Springer New York LLC, 2012) Sudhaker Upadhyay; Bhabani Prasad Mandal
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 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 the field/antifield formulation to show that the solutions of quantum master equation remain invariant under these. Our results are supported by several explicit examples. © 2012 Springer-Verlag / Società Italiana di Fisica.
Finite BRST transformation and constrained systems
(2012) Sudhaker Upadhyay; Bhabani Prasad Mandal
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. © 2012 Elsevier Inc..
Finite BRST transformations for the Bagger-Lambert-Gustavsson theory
(2013) Mir Faizal; Bhabani P. Mandal; Sudhaker Upadhyay
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. © 2013 Elsevier B.V.
Finite field-dependent BRST symmetry for ABJM theory in N=1 superspace
(Elsevier, 2014) Mir Faizal; Sudhaker Upadhyay; Bhabani Prasad Mandal
In this paper we analyze the ABJM theory in N=1 superspace. Firstly we study the linear and non-linear BRST transformations for the ABJM theory. Then we derive the finite field dependent version of these BRST (FFBRST) transformations. Further we show that such FFBRST transformations relate the generating functional in linear gauge to the generating functional in the non-linear gauge of ABJM theory. © 2014 The Authors.
Finite nilpotent symmetry in Batalin-Vilkovisky formalism
(2010) Bhabani Prasad Mandal; Sumit Kumar Rai; Sudhaker Upadhyay
We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories in the context of generalized BRST transformations with a finite field-dependent parameter. In the usual Faddeev-Popov (FP) formulation of gauge theories such finite fielddependent BRST (FFBRST) transformations do not leave the generating functionals invariant as the path integral measure changes in a non-trivial way for finite transformations. Here we show that FFBRST transformation, with the appropriate choice of a finite field-dependent parameter, is the 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 finite parameters are constructed. Copyright © EPLA, 2010.
Gaugeon formalism in the framework of generalized BRST symmetry
(Yukawa Institute for Theoretical Physics, 2014) Sudhaker Upadhyay; Bhabani Prasad Mandal
We consider gaugeon formulations that relate to the quantum gauge freedom covariantly in the framework of the generalized BRST transformation for the Yang-Mills theory as well as the BRST-invariant Higgs model. We generalize the BRST symmetries of both the Yang-Mills theory and the Higgs model by making the transformation parameter finite and field-dependent. Remarkably, we observe that the gaugeon Lagrangian that describes the quantum gauge freedom appears automatically in the effective theories, along with a natural shift in gauge parameters under specific finite field-dependent parameters. © The Author(s) 2014.
Generalized BRST symmetry for arbitrary spin conformal field theory
(Elsevier, 2015) Sudhaker Upadhyay; Bhabani Prasad Mandal
We develop the finite field-dependent BRST (FFBRST) transformation for arbitrary spin-s conformal field theories. We discuss the novel features of the FFBRST transformation in these systems. To illustrate the results we consider the spin-1 and spin-2 conformal field theories in two examples. Within the formalism we found that FFBRST transformation connects the generating functionals of spin-1 and spin-2 conformal field theories in linear and non-linear gauges. Further, the conformal field theories in the framework of FFBRST transformation are also analyzed in Batalin-Vilkovisky (BV) formulation to establish the results. © 2015 The Authors.
Generalized brst transformation in Abelian rank-2 antisymmetric tensor field theory
(2010) Sudhaker Upadhyay; Bhabani Prasad Mandal
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 transformations. We show that generalized BRST transformation connects the generating functional corresponding to the different solutions of quantum master equation in field/antifield formulation. © 2010 World Scientific Publishing Company.
Green’s functions in perturbative quantum gravity
(Springer New York LLC, 2015) Sudhaker Upadhyay; Bhabani Prasad Mandal
We show that the Green’s functions in a non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation also holds for operator Green’s functions. We further derive the explicit relation between the Green’s functions in the theory of perturbative quantum gravity in a pair of arbitrary gauges. This process involves some sort of modified FFBRST transformations which are derivable from infinitesimal field-dependent BRST transformations. © 2015, The Author(s).
IR finite graviton propagators in de Sitter spacetime
(Springer New York LLC, 2016) Mir Faizal; Sudhaker Upadhyay; Bhabani Prasad Mandal
The graviton propagator diverges in certain gauges in de Sitter spacetime. We address this problem in this work by generalizing the infinitesimal BRST transformations in de Sitter spacetime to finite field-dependent BRST (FFBRST) transformations. These FFBRST transformations are a symmetry of the classical action, but they do not leave the path integral measure invariant for the graviton theory in de Sitter spacetime. Due to the non-trivial Jacobian of such a finite transformation the path integral measure changes and hence the FFBRST transformation is capable of relating theories in two different gauges. We explicitly construct the FFBRST transformation which relates the theory with a diverging graviton two-point function to a theory with an infrared finite graviton. The FFBRST transformation thus establishes that the divergence in a graviton two-point function may be only a gauge artifact. © 2016, The Author(s).
Noncommutative gauge theories: Model for hodge theory
(2013) Sudhaker Upadhyay; Bhabani Prasad Mandal
The nilpotent Becchi-Rouet-Stora-Tyutin (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. © 2013 World Scientific Publishing Company.
Off-shell nilpotent finite Becchi-Rouet-Stora-Tyutin (BRST)/anti-BRST transformations
(2011) Sudhaker Upadhyay; Sumit Kumar Rai; Bhabani Prasad Mandal
We develop the off-shell nilpotent finite field dependent Becchi-Rouet-Stora-Tyutin (BRST) transformations and show that for different choices of the finite field dependent parameter these transformations connect the generating functionals corresponding to different effective theories. We also construct both on-shell and off-shell finite field dependent anti-BRST transformations 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 nontrivial 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. © 2011 American Institute of Physics.
Phantom BTZ black holes: Thermal properties under perturbative corrections
(Elsevier B.V., 2025) Kumar Sambhav Upadhyay; Sudhaker Upadhyay; Bhabani Prasad Mandal
This study investigates the thermodynamics of phantom BTZ black holes by incorporating leading-order perturbative corrections arising from small statistical fluctuations around equilibrium. Starting from the phantom BTZ black holes review, we describe a modified action in three-dimensional spacetime that includes coupling with a Maxwell or phantom field. The analysis derives the corresponding field equations and obtains exact solutions for the metric and thermodynamic quantities. The corrected entropy is computed using the steepest descent method. It is expressed in terms of the leading-order entropy and Hawking temperature. Standard thermodynamic relations yield the corrected mass, Helmholtz free energy, specific heat, and Gibbs free energy. These corrections reveal significant deviations from classical results, particularly in the small black hole regime where statistical effects become prominent. Graphical analysis shows that the corrected entropy becomes negative for sufficiently small black holes, indicating potential limitations in thermodynamic stability under perturbative corrections. Furthermore, the influence of thermal fluctuations proves substantial for the small black holes and negligible for larger black holes. In this work, we have also calculated critical points and critical compressibility factor (Zc) of the phantom BTZ black hole, treating it as a Van der Waals fluid. This work provides a comprehensive understanding of how statistical fluctuations modify the thermodynamics of phantom BTZ black holes. It underscores the necessity of including such corrections in realistic models of black hole thermodynamics in (2+1) dimensions. © 2025 The Author(s)
Relating Gribov-Zwanziger and Yang-Mills theories in Batalin-Vilkovisky formalism
(2012) Sudhaker Upadhyay; Bhabani Prasad Mandal
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. © 2012 American Institute of Physics.