Tailoring three-point functions and integrability IV. Θ-morphism

Nikolay Gromov; Pedro Vieira

doi:10.1007/JHEP04(2014)068

Tailoring three-point functions and integrability IV. Θ-morphism

Nikolay Gromov, Pedro Vieira

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Abstract

We compute structure constants in N= 4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic description called the Θ-morphism. In this approach we introduce impurities at each spin chain site, act with particular differential operators on the standard algebraic Bethe ansatz vectors and generate in this way higher loop eigenvectors. The final results for the structure constants take a surprisingly simple form, recently reported by us in the short note arXiv:1202.4103. These are based on the tree level and one loop patterns together and also on some higher loop experiments involving simple operators.

Original language	English
Article number	068
Pages (from-to)	1-40
Journal	Journal of High Energy Physics
Volume	2014
Issue number	4
Early online date	9 Apr 2014
DOIs	https://doi.org/10.1007/JHEP04(2014)068
Publication status	Published - Apr 2014

Keywords

1/N Expansion
AdS-CFT Correspondence
Supersymmetric gauge theory

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Tailoring three-point function_GROMOV_Acc11Mar2014Epub9Apr2014_GOLD VoR(CC BY)Final published version, 888 KBLicence: CC BY

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AB - We compute structure constants in N= 4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic description called the Θ-morphism. In this approach we introduce impurities at each spin chain site, act with particular differential operators on the standard algebraic Bethe ansatz vectors and generate in this way higher loop eigenvectors. The final results for the structure constants take a surprisingly simple form, recently reported by us in the short note arXiv:1202.4103. These are based on the tree level and one loop patterns together and also on some higher loop experiments involving simple operators.

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KW - Supersymmetric gauge theory

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Tailoring three-point functions and integrability IV. Θ-morphism

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