Stringlike theory in three dimensions and massive higher spins

Evgeny Skvortsov,Tung Tran,Mirian Tsulaia

doi:10.1103/physrevd.102.126010

Abstract

An example of a consistent theory with massive higher spin fields is constructed in flat space-time of dimension three. The action is written in the light-cone gauge. The theory has certain stringy features, e.g. its spectrum is unbounded in spin and mass, the theory admits Chan-Paton factors. The quartic and the higher tree-level amplitudes vanish, which softens the UV behaviour at the loop level and provides a new mechanism of how massive higher spin states can resolve the Quantum Gravity Problem.

Highlights

Higher spin states are of crucial importance for constructing viable models of quantum gravity, at least within certain approaches
The theory has certain stringlike features, e.g., its spectrum is unbounded in spin and mass; the theory admits Chan-Paton factors
Since constructing a quantum gravity model has never been a simple task, many attempts to look for higher spin gravity (HSGRA) s have faced numerous difficulties that can eventually be attributed to many no-go results against field theories with massless higher spin fields both in flat [22] and anti–de Sitter (AdS) spaces [28]

Summary

INTRODUCTION

Higher spin states are of crucial importance for constructing viable models of quantum gravity, at least within certain approaches. The general question we would like to address is whether or not there are consistent theories of quantum gravity that are much smaller than string theory and are as close to field theories as possible These theories, if any, will have to contain infinitely many higher spin states and the spectrum has to be unbounded in spin [11]. Since constructing a quantum gravity model has never been a simple task, many attempts to look for HSGRA s have faced numerous difficulties that can eventually be attributed to many no-go results against field theories with massless higher spin fields both in flat [22] and anti–de Sitter (AdS) spaces [28]. Massless higher spin fields, including the graviton, do not have any local degrees of freedom in 3d They do not exist in the light-cone approach. The outline is that we first review the basics of the lightcone approach and apply it to massive spinning fields in 3d, where an exhaustive classification of cubic vertices has very recently been obtained by Metsaev [56]

LIGHT-FRONT BOOTSTRAP

MICRO STRING THEORY

CONCLUSIONS