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

We explore the quantisation of the tachyonic type 0B superstring and the non-tachyonic Spin(16) × Spin(16) ⋊ ℤ₂ heterotic string on AdS₃ × S³ × T ⁴ and AdS₃ × S³ × S³ × S¹ 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) ⋊ ℤ₂ 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 AdS₃ × S³ × S³ × S¹ space and provide general formulas for a systematic analysis of the classical moduli space.