Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators

Abstract

We consider folded spinning strings in AdS_5xS^5 (with one spin component S in AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2) sector of the N=4 SYM theory in the special scaling limit in which both the string mass M ~ \sqrt λ\ln S and J are sent to infinity with their ratio fixed. Expanding in the parameter \el= J/M we compute the 2-loop string sigma model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest that a resummation of the logarithmic \el^2 \ln^n \el terms is necessary in order to establish an interpolation to the weakly coupled gauge theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multi-spin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite ``renormalization'' of the relation between the parameters of the classical solution and the fixed spins, i.e. the charges of the SO(2,4) x SO(6) symmetry.

31 pages, Latex. v2:minor corrections; few comments and references added v3: typos corrected

References in corpus (39)

• A semi-classical limit of the gauge/string correspondence
• Transcendentality and Crossing
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Structure functions for large $x$ and renormalization of Wilson loops
• Comments on operators with large spin
• Quantum corrections to the string Bethe ansatz
• Precision Spectroscopy of AdS/CFT
• Gauge/string duality for QCD conformal operators
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• Logarithmic scaling in gauge/string correspondence
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Simplifying superstring action on AdS_5 x S^5
• Dyonic Giant Magnons
• On the highest transcendentality in N=4 SUSY
• 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
• Infinite spin limit of semiclassical string states
• Four-Loop Cusp Anomalous Dimension From Obstructions
• On the Strong Coupling Scaling Dimension of High Spin Operators
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• A Generalized Scaling Function for AdS/CFT
• A Universality Test of the Quantum String Bethe Ansatz
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Strong coupling limit of Bethe Ansatz equations
• Constructing the AdS/CFT dressing factor
• Principal Chiral Field at Large N
• The scaling function at strong coupling from the quantum string Bethe equations
• The Exact Mass-Gap of the Supersymmetric CP^{n-1} Sigam Model
• The Exact Mass-Gap of the Supersymmetric O(N) Sigma Model
• Strong coupling expansion of Baxter equation in N=4 SYM
• Exact Scattering in the SU(n) Supersymmetric Principal Chiral Model
• A Two-loop Test of Buscher's T-duality I

Cited by in corpus (58)

• The all loop AdS4/CFT3 Bethe ansatz
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Four loop twist two, BFKL, wrapping and strings
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• Spinning strings at one-loop in AdS_4 x P^3
• A Generalized Scaling Function for AdS/CFT
• On semiclassical computation of 3-point functions of closed string vertex operators in AdS_5 x S^5
• Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet
• Comment on the Scaling Function in AdS4 x CP3
• Quantum Wrapped Giant Magnon
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Functional BES equation
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Quark-antiquark potential in AdS at one loop
• Scaling function in AdS/CFT from the O(6) sigma model
• Quantum integrability and functional equations
• Quantum AdS_5 x S^5 superstring in the AdS light-cone gauge
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• Quantum corrections to energy of short spinning string in AdS5
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• The virtual scaling function of AdS/CFT
• Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring
• Nonperturbative scales in AdS/CFT
• Spiky strings in AdS_3 x S^1 and their AdS-pp-wave limits
• The generalised scaling function: a note
• The AdS(n) x S(n) x T(10-2n) BMN string at two loops
• From Polygon Wilson Loops to Spin Chains and Back
• Space-like minimal surfaces in AdS x S
• The generalised scaling function: a systematic study
• Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
• The worldsheet low-energy limit of the AdS_4 x CP^3 superstring
• Three-point correlation functions from semiclassical circular strings
• Spiky strings in the SL(2) Bethe Ansatz
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD
• Worldsheet scattering for the GKP string
• On the Spectrum of the AdS_5xS^5 String at large lambda
• Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5
• The 2-loop generalized scaling function from the BES/FRS equation
• The integrable O(6) model and the correspondence: checks and predictions
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
• Green-Schwarz superstring on the lattice
• Two-loop corrections to false vacuum decay in scalar field theory
• From weak coupling to spinning strings
• Two-loop corrections to partition function of Pohlmeyer-reduced theory for AdS_5 x S^5 superstring
• Quantum Giant Magnons
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• On the short string limit of the folded spinning string in AdS5 x S5
• Radiative corrections to false vacuum decay in quantum mechanics
• Topics in Cusped/Lightcone Wilson Loops
• Spiky Strings with Two Spins in AdS5
• NNLO corrections to false vacuum decay rate in thin-wall approximation
• On interpolating anomalous dimension of twist-two operators with general spins