Massive fermion model in 3d and higher spin currents

Abstract

Abstract:We analyze the 3d free massive fermion theory coupled to external sources. The presence of a mass explicitly breaks parity invariance. We calculate two-and threepoint functions of a gauge current and the energy momentum tensor and, for instance, obtain the well-known result that in the IR limit (but also in the UV one) we reconstruct the relevant CS action. We then couple the model to higher spin currents and explicitly work out the spin 3 case. In the UV limit we obtain an effective action which was proposed many years ago as a possible generalization of spin 3 CS action. In the IR limit we derive a different higher spin action. This analysis can evidently be generalized to higher spins. We also discuss the conservation and properties of the correlators we obtain in the intermediate steps of our derivation.

One-loop effective actions and higher spins

“…The results obtained in this way, in particular in the even parity sector, transferred to the OLEA, allow us to find the linearized Fronsdal eom's (see [5][6][7][8][9]) for all the source fields we have considered, in the nonlocal form introduced by Francia and Sagnotti, [10,11]. In 3d we consider also the odd parity sector, and confirm the connection with Pope and Townsend's generalizations of Chern-Simons theory, already pointed out in [1].…”

“…But our thesis is that the dynamics generated by the one-loop effective action (OLEA) contains all the information we need to reconstruct complete interacting equations of motion. This paper is a follow-up of [1], which contains a few (mostly parity odd) 3d examples of what has just been said. The present paper is more general and systematic, not limited to 3d, and devoted especially to the parity even sector.…”

One-loop effective actions and higher spins. Part II

“…This is a good point to mention that our research is indebted to several preexisting works, in particular with [17][18][19] as far as the inspiration is concerned, with [20][21][22][23][24][25][26][27][28][29] as far as the methods are concerned and with [4,5,[30][31][32][33][34][35][36][37][38][39][40][41] for HS theories. Other papers of ours, related to the present one are, beside [1,42,43]. For future developments we think that important references are [44][45][46][47].…”

“…The major task of this paper was the completion of the construction of the quadratic part of the higher spin effective action started in [1,42]. We did it in section 4 presenting all two point correlators of symmetric currents of any spin up to 5 and in any dimension between 3 and 6.…”

“…Then we show how to use this material to express the results obtained in [1,42] and in this paper in a geometric language.…”