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Holomorphic fermions in AdS2

  • Calvin Y. -R. Chen
  • Lukas W. Lindwasser
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Abstract

On two-dimensional Anti-de Sitter space, Majorana fermions with a discrete set of finely tuned, non-zero mass parameters possess conserved spinor--tensors that are symmetric and traceless. In complex coordinates, these correspond to pairs of holomorphic and anti-holomorphic half-integer spin currents and admit Laurent series mode expansions reminiscent of standard two-dimensional conformal field theories. We exploit this fact in order to fully parameterise the classical phase space associated with the equation of motion in terms of arbitrary (anti-)holomorphic functions. We further show that this parameterisation can be written covariantly in terms of a conformal Killing spinor--tensor, hinting at a hidden conformal symmetry. We also show they possess chiral algebras which are strict subalgebras of the one present in the corresponding theory on flat space.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026holomorphic,
  title = {{Holomorphic fermions in $\textAdS_2$}},
  author = {Calvin Y. -R. Chen and Lukas W. Lindwasser},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37762},
  eprint = {2610.37762},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37762},
}
RIS
TY  - UNPB
TI  - Holomorphic fermions in AdS_2
AU  - Calvin Y. -R. Chen
AU  - Lukas W. Lindwasser
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37762
UR  - https://arxiv.org/abs/2610.37762
AB  - On two-dimensional Anti-de Sitter space, Majorana fermions with a discrete set of finely tuned, non-zero mass parameters possess conserved spinor--tensors that are symmetric and traceless. In complex coordinates, these correspond to pairs of holomorphic and anti-holomorphic half-integer spin currents and admit Laurent series mode expansions reminiscent of standard two-dimensional conformal field theories. We exploit this fact in order to fully parameterise the classical phase space associated with the equation of motion in terms of arbitrary (anti-)holomorphic functions. We further show that this parameterisation can be written covariantly in terms of a conformal Killing spinor--tensor, hinting at a hidden conformal symmetry. We also show they possess chiral algebras which are strict subalgebras of the one present in the corresponding theory on flat space.
ER  -