Structure of large spin expansion of anomalous dimensions at strong coupling

Abstract

The anomalous dimensions of planar N=4 SYM theory operators like tr(Phi D^S Phi) expanded in large spin S have the asymptotics γ= f ln S + f_c + 1/S (f_11 ln S + f_10) + ..., where f (the universal scaling function or cusp anomaly), f_c and f_mn are given by power series in the `t Hooft coupling λ. The subleading coefficients appear to be related by the so called functional relation and parity invariance (or reciprocity) property of the function expressing γin terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS_5. The large spin expansion of the classical string energy happens to have the same structure as that of γin the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f_c, f_11, f_10 and verify the functional/reciprocity relations at subleading λ^{-1/2} order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions.

43 pages. v2: minor comments added, misprints corrected; v3: one-loop coefficients are expressed in terms of one constant not fixed by our method of computation, conclusion about parity invariance is unchanged, note added; v4: minor correctionsin eq (3.34) and below (3.37)

References in corpus (27)

• Gluon scattering amplitudes at strong coupling
• Comments on operators with large spin
• Spinning strings and AdS/CFT duality
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Dressing and Wrapping
• Logarithmic scaling in gauge/string correspondence
• Anomalous dimensions of high-spin operators beyond the leading order
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections
• 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
• N=4 SUSY Yang--Mills: three loops made simple(r)
• Exact expressions for quantum corrections to spinning strings
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• 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
• Quantum corrections to energy of short spinning string in AdS5
• 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
• Universality of three gaugino anomalous dimensions in N=4 SYM
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM

Cited by in corpus (15)

• On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT
• Twist-three at five loops, Bethe Ansatz and wrapping
• Quark-antiquark potential in AdS at one loop
• The virtual scaling function of AdS/CFT
• Four loop reciprocity of twist two operators in N=4 SYM
• Spiky strings in Bethe Ansatz at strong coupling
• On the Spectrum of the AdS_5xS^5 String at large lambda
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• One-loop spectroscopy of semiclassically quantized strings: bosonic sector
• Semiclassical Strings in AdS_5 x S^5 and Automorphic Functions
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• On the short string limit of the folded spinning string in AdS5 x S5
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Universal structure of subleading infrared poles at strong coupling
• A semiclassical analysis of the fluctuation eigenvalues and the one-loop energy of the folded spinning superstring in AdS_5 x S^5