Volume 98B, number 1,2 PHYSICS LETTERS 1 January 1981 SUPERFIELD FORMULATION OF EXTENDED BRS SYMMETRY L. BONORA and M. TONIN lstituto di Fisica dell' Universitd di Padova, Istituto Nazionqle di Fisica Nucleare, Sezione di Padova, Italy Received 11 August 1980 In the light of a recently discovered new BRS-like symmetry in gauge theories, we reformulate a superfield treatment of lagrangian gauge theories supplemented by gauge-fixingand Faddeev-Popov terms. In a recent interesting paper [1 ] Quirbs et al., fol- lowing a previous attempt by Theirry-Mieg [2], have found a geometrical interpretation of the FP ghost fields in the fibre bundle language. In this context, they found a new (super)symmetry of gauge theories [1,3] in addition to the well-known BRS one. This symmetry was discovered earlier by Curci and Ferrari [4]. A superfield treatment of BRS-invariant theories was already carried out in ref. [5]. Motivated by the results of ref. [ 1 ], we have developed a superfield for- mulation of gauge theories in which both BRS sym- metries are explicitly used. This formulation contains some amusing features that in our opinion are worth mentioning. The standard Yang-Mills lagrangian density, sup- plemented by the gauge fixing term, and the FP term is *1 £ = _(4g2)-lFuv. FUr - A u • Ou B - i 3uO" DUe + ½aB" B , (1) where F~v = OuA ~ - OvA ~ + (A u × Av) c~ , DucC~ = Ouca + (A u × c) c~ . Similarly we shall write Duea = buea + (A u × e-)C~ and DuBC' = buBC~+ (A u × e)'L Here a vector notation is used, i.e. • 1 For sake of simplicity we do not take into account matter fields in this paper, although it is straightforward to extend our treatment to the general ease. 48 a . b = aab c' , (a X b) c~ = fa~ra~b'y , Where the f~t~'s are the structure constants of the gauge group (which is supposed simple). The FP fields e a and ~ are assumed to be hermitian. The lagrangian (1) is invariant under the BRS trans- formations generated by the hermitian charge QB, and under the new BRS transformations generated by the hermitian charge QB, where [iQB,Au] =Duc [iQB,C]+ x _ , = -~c X c , [laB, (] + =iB, [iQB,B ]_ =0, (2) and [i0B,Au] =DuE [i(~B,e] + 1 - _ , =--~c×e, [i(~B, c]+ =i/~, [iQB,B ]_ =0. (3) The fields B and/~ are related by: B+/~-icX e=0. (4) The charges QB and (~B are nilpotent and anticom- muting. The lagrangian (1) is also invariant under the ghost scale transformation, generated by Qc: [iQc, c] =c , [iQc, e]=-e, [iQc,A,] = [iQc,B] =0. At this point we remark that the Kugo-Ojima [6] physicality condition QBla) = 0 for the physical states la) may be extended to QBIa)'=O, ~)Bla) =0. (5) 0 031 --9163/81/0000--0000/$ 02.50 © North-Holland Publishing Company