Continuous spin and tensionless strings

Abstract

A classical action is proposed which upon quantisation yields massless particles belonging to the continuous spin representation of the Poincar\'e group. The string generalisation of the action is identical to the tensionless extrinsic curvature action proposed by Savvidy. We show that the BRST quantisation of the string action gives a critical dimension of 28. The constraints result in a number of degrees of freedom which is the same as the bosonic string.