Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz

Abstract

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.

15 pages, 1 figure; v2:references, typos and clarifications

References in corpus (23)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Finite-size Effects from Giant Magnons
• Quantum corrections to the string Bethe ansatz
• Wrapping interactions at strong coupling -- the giant magnon
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• Towards integrability for AdS3/CFT2
• Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase
• $Ad{S}_3\times S^3\times M^4$ string S-matrices from unitarity cuts
• Gauge invariant finite size spectrum of the giant magnon
• S-matrix for magnons in the D1-D5 system
• Finite-Size Effects for Dyonic Giant Magnons
• Quantum Wrapped Giant Magnon
• Constructing the AdS/CFT dressing factor
• Finite size effects for giant magnons on physical strings
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Macroscopic (and Microscopic) Massless Modes
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• Quantum Scattering of Giant Magnons
• The AdS(n) x S(n) x T(10-2n) BMN string at two loops
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• An improved AFS phase for AdS3 string integrability

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