TY - JOUR

T1 - Lüscher formula for GKP string

AU - Basso, B.

AU - Belitsky, Andrei

N1 - Funding Information:
We are most grateful to Gregory Korchemsky for interesting discussions and valuable comments. One of us (B.B.) would like to acknowledge illuminating discussions with Patrick Dorey, Sébastien Leurent, and Vladimir Kazakov, about finite-size corrections, and to Didina Serban and Dmytro Volin, for stimulating discussions. This work (A.B.) was supported by the National Science Foundation under Grant No. PHY-0757394 . Appendix A

PY - 2012/7/1

Y1 - 2012/7/1

N2 - We investigate finite-size corrections to anomalous dimensions of large-spin twist-two operators in the planar maximally supersymmetric Yang-Mills theory. We develop a framework for analysis of these corrections, that is complementary to the conventional spin-chain approach, by making use of the hole rather than the magnon picture. From the dual string theory perspective where the large-spin operator is identified with the Gubser-Klebanov-Polyakov (GKP) string, our approach is equivalent to constructing the first Lüscher correction to the energy of the GKP string by incorporating the contribution of virtual excitations propagating on it. It allows us to propose a formula that controls a particular class of large-spin corrections to the twist-two anomalous dimension and holds at any value of the coupling constant. Compared to wrapping corrections computed with magnons propagating on the spin chain, the finite-size corrections that are encoded in our formalism start at a lower-loop level. Our formalism thus calls for modification of the asymptotic contributions which are conventionally incorporated within the Asymptotic Bethe Ansatz. An educated guess allows us to remedy this pitfall and successfully confront our predictions with known results up to five-loop accuracy at weak coupling. Finally, our formula sheds light on the weak-to-strong coupling transition for the subleading large-spin corrections under study and confirms stringy expectations at strong coupling where they are found to be identical to the first Lüscher correction to the vacuum energy of the O(6) sigma model.

AB - We investigate finite-size corrections to anomalous dimensions of large-spin twist-two operators in the planar maximally supersymmetric Yang-Mills theory. We develop a framework for analysis of these corrections, that is complementary to the conventional spin-chain approach, by making use of the hole rather than the magnon picture. From the dual string theory perspective where the large-spin operator is identified with the Gubser-Klebanov-Polyakov (GKP) string, our approach is equivalent to constructing the first Lüscher correction to the energy of the GKP string by incorporating the contribution of virtual excitations propagating on it. It allows us to propose a formula that controls a particular class of large-spin corrections to the twist-two anomalous dimension and holds at any value of the coupling constant. Compared to wrapping corrections computed with magnons propagating on the spin chain, the finite-size corrections that are encoded in our formalism start at a lower-loop level. Our formalism thus calls for modification of the asymptotic contributions which are conventionally incorporated within the Asymptotic Bethe Ansatz. An educated guess allows us to remedy this pitfall and successfully confront our predictions with known results up to five-loop accuracy at weak coupling. Finally, our formula sheds light on the weak-to-strong coupling transition for the subleading large-spin corrections under study and confirms stringy expectations at strong coupling where they are found to be identical to the first Lüscher correction to the vacuum energy of the O(6) sigma model.

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U2 - 10.1016/j.nuclphysb.2012.02.011

DO - 10.1016/j.nuclphysb.2012.02.011

M3 - Article

AN - SCOPUS:84858279626

VL - 860

SP - 1

EP - 86

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1

ER -