BV formulation of higher form gauge theories in a superspace

Abstract

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.

Appendix: Mathematical details of Abelian 3-form gauge theory

1.1 A.1 Extended BRST transformation of fields

(A.1)

where $\varOmega\equiv [L_{\mu\nu\eta}, M_{\mu\nu}, \tilde{M}_{\mu\nu}, N_{\mu\nu}, \tilde{N}_{\mu\nu}, O_{\mu}, \tilde{O}_{\mu}, P_{\mu}, \tilde{P}_{\mu}, Q_{\mu}, \tilde{Q}_{\mu}, R, \tilde{R}, S, \tilde{S}, T_{\mu}, U, V, W]$.

1.2 A.2 Extended BRST transformation of antifields

(A.2)

1.3 A.3 Superfields for the extended BRST invariant theory

(A.3)

1.4 A.4 Superfields for both extended BRST and anti-BRST invariant theory

(A.4)

From the above relations, we calculate

(A.5)