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Massless L\"uscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz
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In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long strings, accurate up to exponentially small corrections. This is no longer true in AdS3, as we demonstrate here by studying Luscher F-terms with a massless particle running in the loop. We apply this to the classic test of Hernandez & Lopez, in which the su(2) sector Bethe equations (including one-loop dressing phase) should match the semiclassical string theory result for a circular spinning string. These calculations did not agree in AdS3xS3xT4, and we show that the sum of all massless Luscher F-terms can reproduce the difference.
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Demystifying the Massless Sector in AdS_3 Quantum Spectral Curve
Massless modes in the AdS3 x S3 x T4 quantum spectral curve are shown to emerge as zeros on the branch cut, yielding Bethe equations and uniquely constrained dressing phases.
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