BPS spectrum on AdS₃×S³×S³×S¹

The BPS spectrum of string theory on AdS₃×S³×S³×S¹ is determined using a world-sheet description in terms of WZW models. It is found that the theory only has BPS states with j⁺=j⁻ where j^± refer to the spins of the su(2) algebras of the large N=4 superconformal algebra. We then re-examine the BPS spectrum of the corresponding supergravity and find that, contrary to previous claims in the literature, also in supergravity only the states with j⁺=j⁻ are BPS. This resolves a number of long-standing puzzles regarding the BPS spectrum of string theory and supergravity in this background.