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Journal of High Energy Physics

, 2015:183 | Cite as

On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors

  • Yoichi Kazama
  • Shota Komatsu
  • Takuya Nishimura
Open Access
Regular Article - Theoretical Physics

Abstract

As a step toward uncovering the relation between the weak and the strong coupling regimes of the \( \mathcal{N}=4 \) super Yang-Mills theory beyond the spectral level, we have developed in a previous paper [arXiv:1410.8533] a novel group theoretic interpretation of the Wick contraction of the fields, which allowed us to compute a much more general class of three-point functions in the SU(2) sector, as in the case of strong coupling [arXiv:1312.3727], directly in terms of the determinant representation of the partial domain wall partition function. Furthermore, we derived a non-trivial identity for the three point functions with monodromy operators inserted, being the discrete counterpart of the global monodromy condition which played such a crucial role in the computation at strong coupling. In this companion paper, we shall extend our study to the entire psu(2, 2|4) sector and obtain several important generalizations. They include in particular (i) the manifestly conformally covariant construction, from the basic principle, of the singlet-projection operator for performing the Wick contraction and (ii) the derivation of the monodromy relation for the case of the so-called “harmonic R-matrix”, as well as for the usual fundamental R-matrtix. The former case, which is new and has features rather different from the latter, is expected to have important applications. We also describe how the form of the monodromy relation is modified as psu(2, 2|4) is reduced to its subsectors.

Keywords

Lattice Integrable Models AdS-CFT Correspondence Bethe Ansatz 

Notes

Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Yoichi Kazama
    • 1
  • Shota Komatsu
    • 2
  • Takuya Nishimura
    • 3
  1. 1.Research Center for Mathematical PhysicsRikkyo UniversityTokyoJapan
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  3. 3.Institute of PhysicsUniversity of TokyoTokyoJapan

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