Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections

Abstract

We continue the investigation of two-loop string corrections to the energy of a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We compute the generalized scaling function at two-loop order f_2(ell) both for small and large values of ell matching the predictions based on the asymptotic Bethe ansatz. In particular, in the small ell expansion, we derive an exact integral form for the ell-dependent coefficient of the Catalan's constant term in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman diagrams we obtain an exact expression for the leading (ln ell) part of f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2) expansion. At large ell the string energy has a BMN-like expansion and the first few leading coefficients are expected to be the same at weak and at strong coupling. We provide a new example of this non-renormalization for the term which is generated at two loops in string theory and at one-loop in gauge theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for the term of maximal transcendentality in f_2(ell) expanded at large ell. In the second part of the paper we initiate the study of 2-loop finite size corrections to the string energy by formally compactifying the spatial world-sheet direction in the string action expanded near long fast-spinning string. We observe that the leading finite-size corrections are of "Casimir" type coming from terms containing at least one massless propagator. We consider in detail the one-loop order (reproducing the leading Landau-Lifshitz model prediction) and then focus on the two-loop contributions to the (1/ln S) term (for J=0). We find that in a certain regularization scheme used to discard power divergences the two-loop coefficient of the (1/ln S) term appears to vanish.

50 pages, 4 figures v2: typos corrected, references added

References in corpus (16)

• Gluon scattering amplitudes at strong coupling
• Comments on operators with large spin
• Logarithmic scaling in gauge/string correspondence
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• A Generalized Scaling Function for AdS/CFT
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• Scaling function in AdS/CFT from the O(6) sigma model
• The virtual scaling function of AdS/CFT
• The 2-loop generalized scaling function from the BES/FRS equation
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• Integrability and the AdS/CFT correspondence

Cited by in corpus (2)

• Large spin expansion of semiclassical 3-point correlators in AdS_5 x S^5
• On the Spectrum of the AdS_5xS^5 String at large lambda