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A<sc>bstract</sc> Using the analytic Bethe ansatz, we initiate a study of the scaling limit of the quasi-periodic$$ {D}_3^{(2)} $$ spin chain. Supported by a detailed symmetry analysis, we determine the effective scaling dimensions of a large class of states in the parameter regimeγ∈ (0,$$ \frac{\pi }{4} $$ ). Besides two compact degrees of freedom, we identify two independent continuous components in the finite-size spectrum. The influence of large twist angles on the latter reveals also the presence of discrete states. This allows for a conjecture on the central charge of the conformal field theory describing the scaling limit of the lattice model.
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This content will become publicly available on April 1, 2026
Poincare invariance in discrete gravity
A formulation of discrete gravity was recently proposed based on defining a lattice and a shift operator connecting the cells. Spinors on such a space will have rotational SO(d) invariance which is taken as the fundamental symmetry. Inspired by lattice QCD, discrete analogues of curvature and torsion were defined that go smoothly to the corresponding tensors in the continuous limit. In this paper, we show that the absence of diffeomorphism invariance could be replaced by requiring translational invariance in the tangent space by enlarging the tangent space from SO(d) to the inhomogeneous Lorentz group ISO(d) to include translations. We obtain the ISO(d) symmetry by taking instead the Lie group SO(d+ 1) and perform on it Inonu-Wigner contraction. We show that, just as for continuous spaces, the zero torsion constraint converts the translational parameter to a diffeomorphism parameter, thus explaining the effectiveness of this formulation.
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- Award ID(s):
- 2207663
- PAR ID:
- 10601466
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2025
- Issue:
- 4
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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