Quantum corrections to short folded superstring in AdS_3 x S^3 x M^4

Abstract

We consider integrable superstring theory on AdS_3 x S^3 x M^4 where M^4=T^4 or M^4=S^3 x S^1 with generic ratio of the radii of the two 3-spheres. We compute the one-loop energy of a short folded string spinning in AdS_3 and rotating in S^3. The computation is performed by world-sheet small spin perturbation theory as well as by quantizing the classical algebraic curve characterizing the finite-gap equations. The two methods give equal results up to regularization contributions that are under control. One important byproduct of the calculation is the part of the energy which is due to the dressing phase in the Bethe Ansatz. Remarkably, this contribution E_1^{dressing} turns out to be independent on the radii ratio. In the M^4=T^4 limit, we discuss how E_1^{dressing} relates to a recent proposal for the dressing phase tested in the su(2) sector. We point out some difficulties suggesting that quantization of the AdS_3 classical finite-gap equations could be subtler than the easier AdS_5 x S^5 case.

37 pages, one reference added in v2

References in corpus (10)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Quantum corrections to the string Bethe ansatz
• The all loop AdS4/CFT3 Bethe ansatz
• All-loop Bethe ansatz equations for AdS3/CFT2
• A Universality Test of the Quantum String Bethe Ansatz
• Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase
• S-matrix for magnons in the D1-D5 system
• Constructing the AdS/CFT dressing factor
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Quantum corrections to energy of short spinning string in AdS5

Cited by in corpus (27)

• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Dressing phases of AdS3/CFT2
• Towards integrability for AdS3/CFT2
• Worldsheet scattering in AdS(3)/CFT(2)
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• Spinning strings and minimal surfaces in $Ad{S}_3$ with mixed 3-form fluxes
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Spinning strings in AdS_3 x S^3 with NS-NS flux
• Elliptic solutions in the Neumann-Rosochatius system with mixed flux
• String solutions in AdS_3 x S^3 x T^4 with NS-NS B-field
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• The low energy limit of the AdS(3) x S(3) x M(4) spinning string
• A note on oscillating strings in $Ad{S}_3\times S^3$ with mixed three-form fluxes
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Scattering in AdS(2)/CFT(1) and the BES Phase
• Massless sector of AdS_3 superstrings: a geometric interpretation
• Pulsating strings with mixed three-form flux
• An improved AFS phase for AdS3 string integrability
• One-loop quantization of rigid spinning strings in $Ad{S}_3\times S^3\times T^4$ with mixed flux
• Geometry of Massless Scattering in Integrable Superstring
• N spike D-strings in AdS Space with mixed flux
• String solutions in $Ad{S}_3\times S^3\times S^3\times S^1$ with $B$-field