Unitarity of supersymmetric SL(2,R)/U(1) and no-ghost theorem for fermionic strings in AdS(3) x N

TL;DR

This work proves the no-ghost theorem for fermionic strings in AdS3 x N by first establishing unitarity of the supersymmetric SL(2,R)/U(1) coset in discrete representations and then applying this to both unflowed and flowed NS-sector states. The key technical advance is a coset unitarity proof for the discrete series with k>2 and j<k/2+1, followed by a careful three-step no-ghost argument that extends to spectral-flowed sectors. The results solidify the consistent spectrum of strings in AdS3 backgrounds and underpin related holographic constructions, with notes on alternative BRST approaches. The paper thus connects coset unitarity, spectral flow, and no-ghost theorems in curved backgrounds relevant to AdS/CFT contexts.

Abstract

The unitarity of the NS supersymmetric coset SL(2,R)/U(1) is studied for the discrete representations. The results are applied to the proof of the no-ghost theorem for fermionic strings in AdS(3) x N in the NS sector. A no-ghost theorem is proved for states in flowed discrete representations.