# Sudhaker Upadhyay - Banaras Hindu University, Varanasi, India

## Contact Details

NameSudhaker Upadhyay |
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AffiliationBanaras Hindu University, Varanasi, India |
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CityVaranasi |
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CountryIndia |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesHigh Energy Physics - Theory (49) General Relativity and Quantum Cosmology (17) Mathematics - Mathematical Physics (11) Mathematical Physics (11) Cosmology and Nongalactic Astrophysics (2) High Energy Physics - Lattice (1) Astrophysics of Galaxies (1) Physics - General Physics (1) |

## Publications Authored By Sudhaker Upadhyay

In this paper, we study thermodynamics of the cluster of galaxies under the effect of dynamical dark energy. We evaluate the configurational integral for interacting system of galaxies in an expanding universe by including the effects produced by the varying $\Lambda$. The gravitational partition function is obtained using this configuration integral. Read More

Based on thermodynamics, we study the galactic clustering of an expanding Universe by considering the logarithmic and volume (quantum) corrections to Newton's law along with the repulsive effect of a harmonic force induced by the cosmological constant ($\Lambda$) in the formation of the large scale structure of the Universe. We derive the $N$-body partition function for extended-mass galaxies (galaxies with halos) analytically. For this partition function, we compute the exact equations of states, which exhibit the logarithmic, volume and cosmological constant corrections. Read More

A massive Aharony-Bergman-Jafferis-Maldacena (ABJM) model in $\mathcal{N} =1$ superspace is analysed by considering a Proca type mass term into the most general Faddeev-Popov action in a covariant gauge. The presence of mass term breaks the original BRST and anti-BRST invariance of the model. Further, the symmetry of the massive ABJM model is restored by extending the BRST and anti-BRST transformations. Read More

In this paper, we study the various cylindrical solutions (cosmic strings) in gravity's rainbow scenario. In particular, we calculate the gravitational field equations corresponding to energy-dependent background. Further, we discuss the possible Kasner, quasi-Kasner and non-Kasner exact solutions of the field equations. Read More

Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance due to an intrinsic preferred direction. We study the VSR modified extended BRST and anti-BRST symmetry of the Batalin-Vilkovisky (BV) actions corresponding to the $p=1,2,3$-form gauge theories. Within VSR framework, we discuss the extended BRST invariant and extended BRST and anti-BRST invariant superspace formulations for these BV actions. Read More

In this paper, we analyse the effect of the expansion of the universe on the clustering of galaxies. We evaluate the configurational integral for interacting system of galaxies in an expanding universe by including effects produced by the cosmological constant. The gravitational partition function is obtained using this configuration integral. Read More

In this paper, we extend the Gribov-Zwanziger framework accounting for the existence of Gribov copies to the mass deformed Bagger--Lambert--Gustavsson (BLG) theory in $\mathcal{N} =1 $ superspace. The restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon is implemented, by adding a non-local horizon term to the effective action. Furthermore, the soft breaking of the BRST symmetry due to horizon term is restored with the help of external sources. Read More

We demonstrate Yokoyama gaugeon formalism for the Abelian one-form gauge (Maxwell) as well as for Abelian two-form gauge theory in the very special relativity (VSR) framework. In VSR scenario, the extended action due to introduction of gaugeon fields also possesses form invariance under quantum gauge transformations. It is observed that the gaugeon field together with gauge field naturally acquire mass, which is different from the conventional Higgs mechanism. Read More

The structures and the associated gauge algebra of ABJM theory in ${\cal N}=1$ superspace are reviewed. We derive the Ward identities of the theory in the class of Lorentz-type gauges at quantum level to justify the renormalizability of the model. We compute the Nielsen identities for the two-point functions of the theory with the help of enlarged BRST transformation. Read More

In this paper, we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation, we establish connection between the two different solutions of the quantum master equation within the BV formulation. Read More

We consider special supersymmetry (SUSY) transformations with $m$ generators $\overleftarrow{s}_{\alpha }$ for a certain class of models and study some physical consequences of Grassmann-odd transformations which form an Abelian supergroup with finite parameters and respective group-like elements being functionals of field variables. The SUSY-invariant path integral measure within conventional quantization implies the appearance, under a change of variables related to such SUSY transformations, of a Jacobian 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. Read More

In this paper, we consider a $D$-dimensional massive Thirring model with
($2

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 symmetry of the classical action, but do not leave path integral measure invariant for the graviton theory in de Sitter spacetime. Read More

In this paper we analyze the tensor field (reducible gauge) theories in the context of very special relativity (VSR). Particularly, we study the VSR gauge symmetry as well as VSR BRST symmetry of Kalb-Ramond and Abelian 3-form fields involving a fixed null vector. We observe that the Kalb-Ramond and Abelian 3-form fields and corresponding ghosts get masses in VSR framework. Read More

We derive the BRST symmetry, Slavnov-Taylor identities and Nielsen identities for the ABJM theories in ${\cal N}{=}3$ harmonic superspace. Further, the gauge dependence of one-particle irreducible amplitudes in such superconformal Chern-Simons theory is shown to be generated by a canonical flow with respect to the extended Slavnov-Taylor identity, induced by the extended BRST transformations (including the BRST transformations of the gauge parameters). Read More

We illustrate the cosmological Friedmann-Robertson-Walker (FRW) models realized as gauge theory in the extended configuration space with its Becchi-Rouet-Stora-Tyutin (BRST) invariance upto total derivative. To investigate the model in Batalin-Vilkovisky (BV) formalism the Lagrangian density of the models is further extended by introducing shifted fields corresponding to all fields. The extended Lagrangian density having shifted fields admits more general BRST symmetry (including shift symmetry), called as extended BRST symmetry. Read More

We exploit boundary term to preserve the supersymmetric gauge invariance of Bagger--Lambert--Gustavsson (BLG) theory. The fermionic rigid BRST and anti-BRST symmetries are studied in linear and non-linear gauges. Remarkably, for Delbourgo-Jarvis-Baulieu-Thierry-Mieg (DJBTM) type gauge the spontaneous breaking of BRST symmetry occurs in the BLG theory. Read More

The Einstein-Hilbert action in the context of Higher derivative theories is considered for finding out their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et. Read More

We show that the Green's functions in non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation is 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 arbitary gauges. Read More

**Affiliations:**

^{1}IIT Kanpur,

^{2}BHU, Varanasi

**Category:**High Energy Physics - Theory

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. Read More

We consider effective actions of the cosmological Friedmann-Robertson-Walker (FRW) models and discuss their fermionic rigid BRST invariance. Further, we demonstrate the finite field-dependent BRST transformations as a limiting case of continuous field-dependent BRST transformations described in terms of continuous parameter $\kappa$. The Jacobian under such finite field-dependent BRST transformations is computed explicitly, which amounts an extra piece in the effective action within functional integral. Read More

In this paper we study the gauge invariance of the third quantized super-group field cosmology which is a model for multiverse. Further, we propose both the nfinitesimal (usual) as well as the finite superfield-dependent BRST symmetry transformations which leave the effective theory invariant. The effects of finite superfield-dependent BRST transformations on the path integral (so-called void functional in the case of third quantization) are implemented. Read More

In this paper we will analyse the anti-BRST symmetries of Bagger-Lambert-Gustavsson (BLG) theory in presence of a boundary. We will analyses these symmetries in both linear and non-linear gauges. We will also derive the finite field version of the anti-BRST transformations for the BLG theory in presence of a boundary. Read More

The BRST quantizations of worldsheet gravity corresponding to final more acceptable derivative gauge and the standard conformal gauge are studied. We establish a mapping between these two gauges utilizing FFBRST formulation in standard way. Therefore, we are able to declare that the problems associated with Virasoro constraints are the gauge artifact. Read More

In this paper we analyse the ABJM theory in ${\cal N}=1$ 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. Read More

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. Read More

In this paper, we will analyse the ghost condensation in the ABJM theory. We will perform our analysis in ${\cal N}=1$ superspace. We show that in the Delbourgo-Jarvis-Baulieu-Thierry-Mieg gauge the spontaneous breaking of BRST symmetry can occur in the ABJM theory. Read More

**Affiliations:**

^{1}IIT Kanpur,

^{2}Banaras Hindu University,

^{3}Banaras Hindu University

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. Read More

We analyze the quantum ABJM theory on ${\cal N} = 1$ superspace in different gauges. We study the Batalin-Vilkovisky (BV) formulation for this model. By developing field/antifield dependent BRST transformation we establish connection between the two different solutions of the quantum master equation within the BV formulation. Read More

**Affiliations:**

^{1}BHU,

^{2}BHU,

^{3}BHU

**Category:**High Energy Physics - Theory

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. Read More

In this paper the novel features of Yokoyama gaugeon formalism are stressed out for the theory of perturbative quantum gravity in Einstein curved spacetime. The quantum gauge transformations for the theory of perturbative gravity are demonstrated in the framework of gaugeon formalism. These quantum gauge transformations lead to renormalized gauge parameter. Read More

We consider gaugeon formulations which discuss the quantum gauge freedom covariantly in the framework of 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 which describe the quantum gauge freedom appear automatically in the effective theories along with the natural shift in gauge parameters under specific finite field-dependent parameters. Read More

In this paper we consider the gauge invariant third quantized model of supersymmetric group field cosmology. The supersymmetric BRST invariance for such theory in non-linear gauge is also analysed. The path integral formulation to the case of a multiverse made up of homogeneous and isotropic spacetimes filled with a perfect fluid is presented. Read More

In this paper we generalize the quantum gauge transformation of Maxwell theory obtained through gaugeon formalism. The generalization is made by making the bosonic transformation parameter field-dependent. The Jacobian of vacuum functional under field-dependent quantum gauge transformation is calculated explicitly. Read More

We analyse the Abelian $N=1$ super-Chern-Simons model coupled to parity-preserving matter in linear and non-linear gauges with exact BRST invariance. Then we analyse the theory in field/antifield formulation to discuss the model at quantum level. Furthermore, we implement the field/antifield dependent transformation parameter to generalize the BRST symmetry of the theory. Read More

In this paper we investigate the Yokoyama gaugeon formalism for perturbative quantum gravity in a general curved spacetime. Within the gaugeon formalism, we extend the configuration space by introducing vector gaugeon fields describing a quantum gauge degree of freedom. Such an extended theory of perturbative gravity admits quantum gauge transformations leading to a natural shift in the gauge parameter. Read More

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. Read More

In this Letter we consider SU(2) Yang-Mills theory analysed in Cho-Faddeev-Niemi variables which remains invariant under local gauge transformations. The BRST symmetries of this theory is generalized by making the infinitesimal parameter finite and field-dependent. Further, we show that under appropriate choices of finite and field-dependent parameter, the gauge-fixing and ghost terms corresponding to Landau as well as maximal Abelian gauge for such Cho-Faddeev-Niemi decomposed theory appear naturally within functional integral through Jacobian calculation. Read More

In this paper, we discuss the generalizations of exact supersymmetries present in the supersymmetrized sigma models. These generalizations are made by making the supersymmetric transformation parameter field-dependent. Remarkably, the supersymmetric effective actions emerge naturally through the Jacobian associated with the generalized supersymmetry transformations. Read More

We analyse the constraints of an Abelian 2-form gauge theory using Faddeev-Jackiw symplectic formalism. Further, this theory is treated as a constrained system in the context of Batalin-Fradkin-Vilkovisky formalism to retrieve the BRST symmetry. Using the fields decompositions the effective action for Abelian 2-form gauge theory is written in terms of diagonalized uncanonical part and BRST exact one. Read More

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. Read More

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. Read More

In this paper we discuss the (anti-)BRST symmetries and $W$-algebra of higher derivative theories of relativistic particles satisfying general gauge conditions. Using this formalism, the connection between the (anti-)BRST symmetries and $W$-algebra for the rigid relativistic particle is established. Incidentally, the full $W$-algebra emerges only when the anti-BRST transformations are considered in tandem with the BRST ones. Read More

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. Read More

**Affiliations:**

^{1}BHU, Varanasi,

^{2}BHU, Varanasi,

^{3}BHU, Varanasi

**Category:**High Energy Physics - Theory

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. Read More

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. Read More

**Affiliations:**

^{1}Banaras Hindu University, Varanasi, India,

^{2}Banaras Hindu University, Varanasi, India

**Category:**High Energy Physics - Theory

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. Read More

**Affiliations:**

^{1}BHU, Varanasi, India,

^{2}BHU, Varanasi, India

**Category:**High Energy Physics - Theory

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. Read More

**Affiliations:**

^{1}Banaras Hindu University, Varanasi, India,

^{2}Banaras Hindu University, Varanasi, India

**Category:**High Energy Physics - Theory

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. Read More

**Affiliations:**

^{1}Banaras Hindu University, Varanasi, India,

^{2}Banaras Hindu University, Varanasi, India

**Category:**High Energy Physics - Theory

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. Read More