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.
Highlights
Introduction to strongly twistedN =4 Super Yang-MillsThe discovery and exploitation of the integrability of planar N =4 Super Yang-Mills theory (SYM) has been a huge success story
We investigate the one-loop spectral problem of γ-twisted, planar N = 4 Super Yang-Mills theory in the double-scaling limit of infinite, imaginary twist angle and vanishing Yang-Mills coupling constant
The two showcase instances where integrability can be rigorously proved in N =4 SYM are obscured in the double-scaled deformed models
Summary
Prior to turning to specific sectors of the strongly twisted theories, we would like to explain the nilpotency properties of their dilatation operator To this end, we find it convenient to introduce the notion of eclectic spin chains. The {φ1, φ2, φ3} sector is discussed, and its asymptotic Bethe ansatz (ABA) equations are derived In our conventions, this would correspond to eclectic field content. For general excitations, a Bethe ansatz should not work in this sector, since eigenstates in eclectic spin chains are not of the global form given by the Bethe ansatz.
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