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Twist-three at five loops, Bethe Ansatz and wrapping

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Forini,  Valentina
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Zieme,  Stefan
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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jhep032009129.pdf
(Publisher version), 332KB

0901.4864v2.pdf
(Preprint), 263KB

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Citation

Beccaria, M., Forini, V., Lukowski, T., & Zieme, S. (2009). Twist-three at five loops, Bethe Ansatz and wrapping. Journal of High Energy Physics, 2009(3): 129. doi:10.1088/1126-6708/2009/03/129.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-45BE-E
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.