TY - JOUR

T1 - OPE for null Wilson loops and open spin chains

AU - Belitsky, Andrei

N1 - Funding Information:
We would like to thank Benjamin Basso for interest in the project at its very early stage and Gregory Korchemsky for reading the manuscript and instructive remarks. This work was supported by the National Science Foundation under grants PHY-0757394 and PHY-1068286 .

PY - 2012/3/19

Y1 - 2012/3/19

N2 - Maximal helicity-violating scattering amplitudes in N= 4 supersymmetric Yang-Mills theory are dual to Wilson loops on closed null polygons. We perform their operator product expansion analysis in two-dimensional kinematics in the soft-collinear approximation which corresponds to the case when some light-cone distances vanish. We construct the expansion in terms of multi-particle "heavy"-light operators, where the "heavy" fields are identified with the Wilson lines defining the OPE channel and the light fields emerge from the curvature of the contour. The correlation function of these define the remainder function. We study the dilatation operator for these operators at one-loop order and find that it corresponds to a non-compact open spin chain. This provides an alternative view on elementary excitations propagating on the GKP string at weak coupling, which now correspond to particles traveling along an open spin chain. The factorized structure of the Wilson loop in the soft limit allows one to represent the two-loop correction to the octagon Wilson loop as a convolution formula and find the corresponding remainder function.

AB - Maximal helicity-violating scattering amplitudes in N= 4 supersymmetric Yang-Mills theory are dual to Wilson loops on closed null polygons. We perform their operator product expansion analysis in two-dimensional kinematics in the soft-collinear approximation which corresponds to the case when some light-cone distances vanish. We construct the expansion in terms of multi-particle "heavy"-light operators, where the "heavy" fields are identified with the Wilson lines defining the OPE channel and the light fields emerge from the curvature of the contour. The correlation function of these define the remainder function. We study the dilatation operator for these operators at one-loop order and find that it corresponds to a non-compact open spin chain. This provides an alternative view on elementary excitations propagating on the GKP string at weak coupling, which now correspond to particles traveling along an open spin chain. The factorized structure of the Wilson loop in the soft limit allows one to represent the two-loop correction to the octagon Wilson loop as a convolution formula and find the corresponding remainder function.

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U2 - 10.1016/j.physletb.2012.02.027

DO - 10.1016/j.physletb.2012.02.027

M3 - Article

AN - SCOPUS:84857793803

VL - 709

SP - 280

EP - 284

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3

ER -