Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms

Abstract

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) approach, we discuss only the fermionic (i.e. off-shell nilpotent) (anti-)BRST, (anti-)co-BRST and some discrete dual-symmetries of the appropriate Lagrangian densities for a two (1+1)-dimensional (2D) modified Proca (i.e. a massive Abelian 1-form) theory without any interaction with matter fields. One of the novel observations of our present investigation is the existence of the Curci-Ferrari (CF)-type restrictions in the case of our present Stückelberg-modified version of the 2D Proca theory which are not like the standard CF-condition of a non-Abelian 1-form gauge theory. Some similarities and a few differences between them have been pointed out in our present investigation. To establish the sanctity of the above off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetries, we derive them by using our newly proposed (anti-)chiral superfield formalism where a few specific and appropriate sets of invariant quantities play a decisive role. We express the (anti-)BRST and (anti-)co-BRST conserved charges in terms of the superfields that are obtained after the applications of (anti-)BRST and (anti-)co-BRST invariant restrictions and prove their off-shell nilpotency and absolute anticommutativity properties, too. Finally, we make some comments on (i) the novelty of our CF-type restrictions, and (ii) the physics behind the negative kinetic term associated with the pseudo-scalar field of our present modified 2D Proca theory.

Supervariable and BRST Approaches to a Toy Model of Reparameterization Invariant Theory

“…One of the highlights of our present investigation is the derivation of the CF-type restriction: B + B + Ċ C − C Ċ = 0 by exploiting the power and potential of the modified BT-supervariable approach which has also led to the derivation of the off-shell nilpotent (anti-)BRST symmetries for the target space variables. The (anti-)BRST symmetry transformations for the other dynamical variables of our theory have been derived by using the newly proposed ACSA to BRST formalism [15][16][17][18][19][20] where the (anti-)BRST invariant restrictions, on the supervariables, have played a decisive role. We have also provided the proof of the existence of the CF-type restrictions by considering (i) the symmetry invariance of the coupled (but equivalent) Lagrangians in the ordinary space, (ii) the (anti-)BRST invariance of the super Lagrangians by exploiting the power and potential of the ACSA to BRST formalism in the superspace, and (iii) the requirement of the proof of the absolute anticommutativity of the conserved (anti-)BRST charges.…”

“…where the superscripts (c) and (ac) denote the chiral and anti-chiral super expansions. This observation, in a subtle manner, explains that the (anti-)chiral supervariable approach (ACSA) to BRST formalism [15][16][17][18][19][20] would be useful to us in our further discussions. Second, it can be checked that the absolute anticommutativity properties, for the phase space target variables (i.e.…”

“…Against this backdrop, it is pertinent to point out that we have applied the newly proposed (anti-)chiral superfield/supervariable approach (ACSA) (see, e.g. [15][16][17][18][19][20]) to derive the (anti-)BRST symmetries for all the relevant variables of a set of two reparameterization invariant theories [20]. These theories are the toy models (i.e.…”

“…Our Sec. 4 contains the theoretical material where we derive the rest of the (anti-)BRST symmetries by using the ACSA [15][16][17][18][19][20]. Sec.…”