Abstract
We investigate the one-loop spectral problem of γ-twisted, planar \( \mathcal{N} \) = 4 Super Yang-Mills theory in the double-scaling limit of infinite, imaginary twist angle and vanishing Yang-Mills coupling constant. This non-unitary model has recently been argued to be a simpler version of full-fledged planar \( \mathcal{N} \) = 4 SYM, while preserving the latter model’s conformality and integrability. We are able to derive for a number of sectors one-loop Bethe equations that allow finding anomalous dimensions for various subsets of diagonalizable operators. However, the non-unitarity of these deformed models results in a large number of non-diagonalizable operators, whose mixing is described by a very complicated structure of non-diagonalizable Jordan blocks of arbitrarily large size and with a priori unknown generalized eigenvalues. The description of these blocks by methods of integrability remains unknown.
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Ipsen, A.C., Staudacher, M. & Zippelius, L. The one-loop spectral problem of strongly twisted \( \mathcal{N} \) = 4 Super Yang-Mills theory. J. High Energ. Phys. 2019, 44 (2019). https://doi.org/10.1007/JHEP04(2019)044
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DOI: https://doi.org/10.1007/JHEP04(2019)044