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Quite Discrete for a fermion

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arxiv 2501.03724 v2 pith:2JMTH26X submitted 2025-01-07 hep-th

Vasileios A. Letsios , Ben Pethybridge , Alan Rios Fukelman This is my paper
classification hep-th
keywords discreteeuclideanfermionicfunctionmassseriestwo-pointuirs
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abstract

We study Discrete Series representations of $SL(2,\mathbb{R})$ with half-integer scaling dimension $\Delta$. At the classical level, we show that these UIRs are realised in the space of mode solutions of spinor fields with imaginary mass parameters on a fixed two-dimensional de Sitter, dS$_{2}$, background. Upon such tuning of the mass, the field develops a fermionic shift symmetry that we characterise. We show that in the Euclidean section this manifests itself in the presence of zero-modes which preclude the definition of a Hadamard two-point function for these UIRs. We propose a Euclidean procedure to deal with the zero-modes, define a two-point function with the right singularity structure, and analyse its late-time behaviour. We end this note by proposing two interacting theories containing the fermionic discrete series in their spectrum.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ising the way into de Sitter

    hep-th 2026-07 conditional novelty 8.0 of 10

    The two-dimensional thermal Ising model on de Sitter provides exact cosmological correlators that stay finite at late times, with perturbative secular logarithms resummed into principal-series oscillations.

  2. A discrete series gauge field at the late-time boundary of $dS_4$

    hep-th 2026-07 accept novelty 6.0 of 10

    Both Δ=1 and Δ=2 late-time Maxwell operators on planar dS4 furnish the photon unitary discrete series of SO(4,1), which splits into opposite-helicity summands via self-dual field-strength sectors.

  3. Quasinormal modes and complexity in saddle-dominated SU(N) spin systems

    hep-th 2025-06 conditional novelty 5.0 of 10

    A family of SU(2) and SU(3) Lipkin-Meshkov-Glick-type Hamiltonians reproduces de Sitter quasinormal-mode densities of states, and late-time probes reveal integrability beneath saddle-dominated scrambling.

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