Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

Abstract

Light-cone gauge formulation of relativistic dynamics of a continuous-spin field propagating in the flat space is developed. Cubic interaction vertices of continuous-spin massless fields and totally symmetric arbitrary spin massive fields are studied. We consider parity invariant cubic vertices that involve one continuous-spin massless field and two arbitrary spin massive fields and parity invariant cubic vertices that involve two continuousspin massless fields and one arbitrary spin massive field. We construct the complete list of such vertices explicitly. Also we demonstrate that there are no cubic vertices describing consistent interaction of continuous-spin massless fields with arbitrary spin massless fields.

BRST approach to Lagrangian construction for bosonic continuous spin field

“…Here we have made Fourier transform from momentum p µ representation into the coordinates x µ representation. Equations (19) and (20) have a solution in the form of an expansion in ξ andξ…”

“…in the works [9] and in terms of two towers of traceless fields in the works [10] (see also the approaches to Lagrangian constriction in the works [11][12][13][14][15][16] for bosonic and fermionic fields and relation to the string theory in [17,18]). Interaction of continuous spin fields with finite spin massive fields was considered in the papers [19,20]. Model of relativistic particle corresponding to continuous spin field has been constructed in the recent work [21].…”

Supersymmetric continuous spin gauge theory

“…Apart from supersymmetry, a number of papers have studied other aspects of the continuous spin theory in different approaches [20]- [46]. For instance, since an interacting theory is more favored, possible interactions of continuous spin particle with matter have been investigated in [8,33], while interactions of continuous spin tachyon 4 is examined in [41,44].…”

Lagrangian formulation for the infinite spin N = 1 supermultiplets in d = 4

“…A number of different approaches for their description were proposed [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Also the investigations of possible interactions for such fields started [23][24][25]. At the same time there exists just a few results on the supermultiplets containing such particles [11,21,22], while their classification is already known for a long time [1].…”