Double excitations in the AdS(5)/CFT(4) integrable system and the Lagrange operator

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  • Burkhard Eden
  • Dennis le Plat
  • Anne Spiering
It is argued that the integrable model for the planar spectrum of the AdS/CFT correspondence can accommodate for the full spectrum of excitations 𝐷𝛼 ̇ 𝛼 ,𝜙[𝐼𝐽],𝜓𝐼 ,𝜓̄ 𝐼 ,𝐹𝛼𝛽 ,𝐹̃ 𝛼̇ 𝛽̇(with 𝐼, 𝐽 ∈ 1…4)if double excitations are allowed for all three lowering operators of the internal SU(4) group aswell as the supersymmetries. We present a tree-level analysis of related creation amplitudes inthe nested Bethe ansatz as well as in the original level-1 picture in which excitations of variousflavours scatter by a true 𝑆-matrix. In the latter case, the creation amplitudes for all doubleexcitations we encounter take a perfectly universal form.Building on these ideas we work out Bethe solutions and states relevant in the mixing problemconcerning the on-shell Lagrangian of  = 4 super Yang-Mills theory. Owing to the veryexistence of double excitations, the chiral Yang-Mills field strength tensor can be represented bythe four fermions {𝜓31,𝜓32,𝜓41,𝜓42} moving on a spin chain of length two. Our analysis remainsrestricted to leading order in the coupling, where the conformal eigenstate corresponding to theon-shell Lagrangian only comprises the pure Yang-Mills action. It should eventually be possible toaugment our analysis to higher loop orders by incorporating coupling corrections in the relevantingredients from the Bethe ansatz.Finally, it was recently realised how structure constants for operators containing the hithertohidden half of the excitations can be computed by the hexagon formalism. We use this for a firsttest of our conjecture for the on-shell Lagrangian, namely that its three-point function with twohalf-BPS operators of equal length ought to vanish.
OriginalsprogEngelsk
Artikelnummer116489
TidsskriftNuclear Physics B
Vol/bind1001
Antal sider16
ISSN0550-3213
DOI
StatusUdgivet - apr. 2024

Bibliografisk note

Funding Information:
We are grateful to T. McLoughlin, A. Sfondrini and M. Staudacher for discussions clarifying some aspects of the material here presented. B. Eden is supported by Heisenberg funding of the Deutsche Forschungsgemeinschaft , grant Ed 78/7-1 or 441791296 . D. le Plat is supported by the Stiftung der Deutschen Wirtschaft . A. Spiering is supported by the research grant 00025445 from Villum Fonden , as well as by the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 847523 ‘INTERACTIONS’.

Funding Information:
B. Eden reports financial support was provided by German Research Foundation. D. le Plat reports financial support was provided by Stiftung der Deutschen Wirtschaft. A. Spiering reports financial support was provided by Villum Fonden, grant 00025445. A. Spiering reports financial support was provided by ERC Horizon program, Marie Sklodowska-Curie grant 847523. There is a conflict of interest with the inventors of the hexagon formalism that apparently wish to suppress any competing publication. I thought this had been settled in a personal conversation with P. Vieira (who is a great scientist, but apparently not fair on cites or publications) during the conference in Tropea late September 2023. As the last few referee reports show this is apparently not the case. I expect a deliberately bad report from P. Vieira, T. Fleury, V. Goncalves; with B. Basso and S. Komatsu matters may have been settled. I am not sure about T. Bargheer either. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.We are grateful to T. McLoughlin, A. Sfondrini and M. Staudacher for discussions clarifying some aspects of the material here presented. B. Eden is supported by Heisenberg funding of the Deutsche Forschungsgemeinschaft, grant Ed 78/7-1 or 441791296. D. le Plat is supported by the Stiftung der Deutschen Wirtschaft. A. Spiering is supported by the research grant 00025445 from Villum Fonden, as well as by the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 847523 ‘INTERACTIONS’.

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© 2024 The Authors

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