The No-ghost Theorem for AdS_3 and the Stringy Exclusion Principle

TL;DR

The paper provides a rigorous no-ghost theorem for bosonic and fermionic strings on AdS3 (SU(1,1)) by restricting the SU(1,1) representations to a spin range tied to the level k. Leveraging coset deconstructions and careful basis arguments, it proves positive-norm physical states in the discrete spectrum, and shows the resulting bound on j matches the stringy exclusion principle observed in the dual CFT. It further shows the supersymmetric extension yields a parallel ghost-free range, and elucidates how these spectral restrictions correspond to the finite set of chiral primaries in the boundary theory, with exact agreement in the K3 case and a stricter bound for T^4. While the restricted spectrum aligns with AdS3/CFT2 expectations, the paper notes that achieving fully interacting, crossing-symmetric, and modular-invariant amplitudes remains an open challenge, requiring a deeper understanding of fusion rules and winding sectors. Overall, the results bolster the consistency of the restricted SU(1,1) string model as a ghost-free sector compatible with holographic duality.

Abstract

A complete proof of the No-ghost Theorem for bosonic and fermionic string theories on AdS_3, or the group manifold of SU(1,1), is given. It is then shown that the restriction on the spin (in terms of the level) that is necessary to obtain a ghost-free spectrum corresponds to the stringy exclusion principle of Maldacena and Strominger.