Abstract
Totally symmetric continuous spin field propagating in (A)dS is studied. Lagrangian gauge invariant formulation for such field is developed. Lagrangian of continuous spin field is constructed in terms of double traceless tensor fields, while gauge transformations are constructed in terms of traceless gauge transformation parameters. de Donder like gauge condition that leads to simple gauge fixed Lagrangian is found. Gauge-fixed Lagrangian invariant under global BRST transformations is presented. The BRST Lagrangian is used for computation of a partition function. It is demonstrated that the partition function of the continuous spin field is equal to one. Various decoupling limits of the continuous spin field are also studied.
Highlights
Continuous spin field has attracted some interest in recent time
Interesting feature of continuous spin field is that this field is decomposed into infinite chain of coupled scalar, vector, and tensor fields which consists of every field just once
We think that further progress in understanding dynamics of continuous spin field requires, among other things, better understanding of gauge invariant Lagrangian formulation of continuous spin field in (A)dS and flat spaces
Summary
Continuous spin field has attracted some interest in recent time. Such field can be considered as a field theoretical realization of continuous spin representation of Poincarealgebra which was studied many years ago in Ref.[1]. We think that further progress in understanding dynamics of continuous spin field requires, among other things, better understanding of gauge invariant Lagrangian formulation of continuous spin field in (A)dS and flat spaces. This is what we are doing in this paper. Gauge invariant formulation for bosonic continuous spin field in four-dimensional flat space, R3,1, was developed in Ref.[6], while gauge theory of fermionic continuous spin field in R3,1 was studied in Ref.[7]. Lagrangian formulation of continuous spin field in flat space Rd, with arbitrary d ≥ 3 was discussed only in the framework of light-cone gauge approach [2]
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