One-loop finiteness of Chiral Higher Spin Gravity

Evgeny Skvortsov,Tung Tran

doi:10.1007/jhep07(2020)021

Abstract

One of the main ideas behind Higher Spin Gravities is that the higher spin symmetry is expected to leave no room for counterterms, thereby eliminating UV divergences that make the pure gravity non-renormalizable. However, until recently it has not been clear if such a mechanism is realized. We show that Chiral Higher Spin Gravity is one-loop finite, the crucial point being that all one-loop S-matrix elements are UV-convergent despite the fact that the theory is naively not renormalizable by power counting. For any number of legs the one-loop S-matrix elements coincide with all-plus helicity one-loop amplitudes in pure QCD and SDYM, modulo a certain higher spin dressing, which is an unusual relation between the non-gravitational theories and a higher spin gravity.

Highlights

JHEP07(2020)021 massless higher spin fields require higher derivative interactions [9, 25, 26], while higher spin symmetry can mix both spins and derivatives
We show that Chiral Higher Spin Gravity is oneloop finite, the crucial point being that all one-loop S-matrix elements are UV-convergent despite the fact that the theory is naively not renormalizable by power counting
For any number of legs the one-loop S-matrix elements coincide with all-plus helicity one-loop amplitudes in pure QCD and SDYM, modulo a certain higher spin dressing, which is an unusual relation between the non-gravitational theories and a higher spin gravity

Summary

Chiral Higher Spin Gravity

We refer to [1,2,3, 5, 46, 60] for the detailed description of Chiral Theory and e.g. to [61] for the systematical introduction to the light-cone approach. The action contains only the chiral half of each vertex and is missing the conjugate vertices built out of P. Certain higher derivative ‘counterterms’ for low spin fields are present: C+1,+1,+1 is the cubic three-derivative term built out of the self-dual component F + of the Yang-Mills field strength Fμν, Tr[F +F +F +] and we omit the Lorentz indices; C+2,+2,+2 is the chiral half of the Goroff-Sagnotti [71]. For simplicity we will work with the large-N limit of the U(N ) Chiral Theory In the latter case, fields Φλ are taken to be N × N matrices, the spin-one states Φ±1 turn into a U(N ) Yang-Mills field and all other components of the higher spin multiplet become charged with respect to it. The formulas below are valid, up to self-evident N -factors and permutations, for the version of the theory that has all integer spins

One-loop finiteness

Conclusions and discussion