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.