Non-supersymmetric strings on AdS3: a world-sheet perspective

A bstract We explore the quantisation of the tachyonic type 0B superstring and the non-tachyonic Spin(16) × Spin(16) ⋊ ℤ 2 heterotic string on AdS 3 × S 3 × T 4 and AdS 3 × S 3 × S 3 × S 1 backgrounds. Adapting the analysis for the supersymmetric and bosonic string theories to these set-ups, we provide a world-sheet description for a generic level of the SL(2, ℝ ) WZW model, and we read the spectrum through the associated partition functions. Focusing on the low-energy theory, we show that the Spin(16) × Spin(16) ⋊ ℤ 2 heterotic string on both backgrounds accommodates non-trivial Wilson lines that are responsible for the appearance of tachyonic regions in the classical moduli space, hence jeopardising the stability of the vacuum. We show this with a concrete example on the AdS 3 × S 3 × S 3 × S 1 space and provide general formulas for a systematic analysis of the classical moduli space.