BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space

Abstract

We develop a general gauge-invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with a formulation in terms of an auxiliary Fock space, we obtain closed nonlinear symmetry algebras of higher spin fermionic fields in the AdS space and find the corresponding BRST operator. A universal procedure for constructing gauge-invariant Lagrangians describing the dynamics of fermionic fields of any spin is developed. No off-shell constraints for the fields and gauge parameters are imposed from the very beginning. It is shown that all the constraints determining an irreducible representation of the AdS group arise as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive gauge-invariant Lagrangians for massive fermionic fields of spin 1/2 and 3/2 containing the complete set of auxiliary fields and gauge symmetries.

Frame- and Metric-Like Higher-Spin Fermions

“…the ζ-transformation in (22) would relate the mass parameters µ andμ to each other and with the inverse AdS radius. There are a priori three kinds of contributions resulting from the ζ-transformation: 2-derivative, 1-derivative and 0-derivative ones.…”

“…The parameterμ is then also determined from Equation (27). This uniquely fixes the Lagrangian (20), as well as the gauge transformation (22), while the field and gauge parameters mimic their respective flat-space properties. The physical significance of the mass parameter µ will be made clear in the next section as we work out the gauge fixed equations of motion.…”

“…As already mentioned in the Introduction, the γ-trace constraints (A9)-(A10) on the gauge parameter and the higher-spin fermionic field can be avoided by recourse to other formulations. These include the non-local formulation [15], the Becchi-Rouet-Stora-Tyutin (BRST) formulation [17,22], the higher-derivative compensator formulation [20], the quartet formulation [21] and the non-minimal formulation with no higher derivatives [24].…”

Comments on interactions in the SUSY models

“…and Z 0 is determined in (8). Making a change of variable in the integrand of Z 0 generated by FSUSY, we obtain the equation with an accuracy up to the total functional derivative:…”

“…The local or non-linear versions of Lie superalgebra constructions have been extended to various field-theoretic a e-mail: sudhakerupadhyay@gmail.com b e-mail: reshet@ispms.tsc.ru c e-mail: bhabani.mandal@gmail.com models such as superstring theories [1], supergravity [2,3] (for modern developments see Refs. [4,5]) and higher-spin field theories [6][7][8][9][10][11]. SUSY theory provides a bosonic superpartner to each fermion presented in the theory and vice versa.…”