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The Scaling function at strong coupling from the quantum string Bethe equations

Matteo Beccaria
(
- Salento U. and
- INFN, Lecce
)
,
Gian Fabrizio De Angelis
(
- Salento U. and
- INFN, Lecce
)
,
Valentina Forini
(
- Perugia U. and
- INFN, Perugia and
- Humboldt U., Berlin
)

Mar, 2007

25 pages

Published in:

JHEP 04 (2007) 066

e-Print:

hep-th/0703131 [hep-th]

DOI:

10.1088/1126-6708/2007/04/066

Report number:

HU-EP-07-06

View in:

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Abstract: (arXiv)

We study at strong coupling the scaling function describing the large spin anomalous dimension of twist two operators in

{\cal N}=4

super Yang-Mills theory. In the spirit of AdS/CFT duality, it is possible to extract it from the string Bethe Ansatz equations in the

\mathfrak{sl}(2)

sector of the \ads superstring. To this aim, we present a detailed analysis of the Bethe equations by numerical and analytical methods. We recover several short string semiclassical results as a check. In the more difficult case of the long string limit providing the scaling function, we analyze the strong coupling version of the Eden-Staudacher equation, including the Arutyunov-Frolov-Staudacher phase. We prove that it admits a unique solution, at least in perturbation theory, leading to the correct prediction consistent with semiclassical string calculations.

integrable quantum field theory
integrable spin chains (vertex models)
quantum integrability (Bethe ansatz)
gauge field theory: Yang-Mills
supersymmetry
scaling
approximation: strong coupling
model: spin
model: vertex
integrability

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Figures(0)

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(
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