Twist-three at five loops, Bethe Ansatz and wrapping

Abstract

We present a formula for the five-loop anomalous dimension of N=4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Luescher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous dimension at four-loops, wrapping effects are of order log^2 M/M^2 for large values of the spin.

19 pages

References in corpus (26)

• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• On String S-matrix, Bound States and TBA
• String hypothesis for the AdS_5 x S^5 mirror
• Logarithmic scaling in gauge/string correspondence
• Anomalous dimensions of high-spin operators beyond the leading order
• Wrapping at four loops in N=4 SYM
• Wrapping interactions at strong coupling -- the giant magnon
• Four-Loop Cusp Anomalous Dimension From Obstructions
• A Generalized Scaling Function for AdS/CFT
• N=4 SUSY Yang--Mills: three loops made simple(r)
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• Analytic three-loop Solutions for N=4 SYM Twist Operators
• Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory
• Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• The virtual scaling function of AdS/CFT
• Towards Baxter equation in supersymmetric Yang-Mills theories
• Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Reciprocity of gauge operators in N=4 SYM
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• On the origin of the dressing phase in N=4 Super Yang-Mills

Cited by in corpus (12)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Konishi operator at intermediate coupling
• Twisting the Mirror TBA
• Yangians, S-matrices and AdS/CFT
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• Discrete Hirota dynamics for AdS/CFT
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• Finite size corrections for open strings/open chains in planar AdS/CFT
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• On the $Ad{S}_5/CF{T}_4$ TBA and its analytic properties
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM