The BV Formalization of Chern—Simons Theory on Deformed Superspace

Abstract

In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.

Novel symmetries in Christ-Lee model

“…In our earlier works [11][12][13][14][15][16][17], we have shown that any arbitrary Abelian p-form (p = 1, 2, 3) gauge theory in D = 2p dimensions of spacetime within the framework of BRST formalism and the N = 2 SUSY quantum mechanical models, turn out to be the tractable model for Hodge theory. It would be interesting to implement this idea in the case of a free particle system on a toric geometry [40], supersymmetric Yang-Mills [24,[41][42][43]. Furthermore, the derivation of proper (anti-)BRST symmetries with the help of superfield formalism would be a nice piece of work in the context of deformed super-Yang-Mills, supersymmetric Chern-Simons, ABJM and BLG theories [43][44][45].…”

“…Furthermore, the perturbative quantum gravity has also been studied in complex and noncommutative spacetime within the framework of the BRST formalism [20][21][22]. The superspace formulation of higherderivative theories [23], Chern-Simons, Yang-Mills theories in the context of Batalin-Vilkovisky formalism [24,25] and ABJM theory on deformed superspace [26,27] have also been analyzed.…”

Nilpotent Symmetries in Jackiw-Pi Model: Augmented Superfield Approach

“…Moreover, the (constant) factors in front of each term are picked for the algebraic convenience. Utilizing the off-shell nilpotent (anti-) BRST transformations from ( 12), ( 13), ( 29) and (30), we obtain the following explicit Lagrangian densities, namely;…”

“…Recently, the (anti-)BRST symmetries for perturbative quantum gravity in curved as well as complex spacetime, in linear as well as in non-linear gauges have been found [27,28] and a superspace formulation of higher derivative theories [29], Chern-Simons and Yang-Mills theories on deformed superspace [30,31] within BV formalism have also been established. Moreover, the study of massless and massive fields with totally symmetric arbitrary spin in AdS space has been carried out in the framework of BRST formalism [32].…”

Conformal to harmonic gauge for bosonic strings

“…(a) E-mail: vipulvaranasi@gmail.com (b) E-mail: bhabani.mandal@gmail.com M theory [28,29], Chern-Simons theory [30][31][32] and ABJM theory [33][34][35]. We indicate how various BRST invariant effective theories are interlinked by considering the finitefield-dependent version of the BRST (FFBRST) transformation, introduced by Joglekar and Mandal [36] about twenty-five years ago.…”