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Regular Additive Scalar Invariants of š’©=1 Hyperbolic Spin Supertriangles

  • Ilia Gaiur
  • Robert Penner
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Abstract

We classify regular cyclic scalar invariants of non-degenerate hyperbolic š’©=1 spin supertriangles which are additive under geodesic subdivision. After fixing the spin lift, the common-first gauge (introduced in earlier work by the second-named author and further developed here) gives a complete 3|4 modulus of such supertriangles.. The space of additive scalar invariants is proved to have superdimension 3|1: ordinary hyperbolic area in degree zero, two even generators in degree two, and one odd generator in degree three; the degree-one and degree-four sectors vanish. One degree-two generator is the fermionic first variation of body area, equivalently the nilpotent correction from ordinary body angle defect to super angle defect. The degree-three generator changes sign under reversal of the spin lift, while the other generators are fixed, so ordinary supertriangles carry only three even invariants.

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Cite

BibTeXRIS
BibTeX
@misc{gaiur2026regular,
  title = {{Regular Additive Scalar Invariants of $\mathcal N=1$ Hyperbolic Spin Supertriangles}},
  author = {Ilia Gaiur and Robert Penner},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23209},
  eprint = {2610.23209},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23209},
}
RIS
TY  - UNPB
TI  - Regular Additive Scalar Invariants of š’©=1 Hyperbolic Spin Supertriangles
AU  - Ilia Gaiur
AU  - Robert Penner
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23209
UR  - https://arxiv.org/abs/2610.23209
AB  - We classify regular cyclic scalar invariants of non-degenerate hyperbolic š’©=1 spin supertriangles which are additive under geodesic subdivision. After fixing the spin lift, the common-first gauge (introduced in earlier work by the second-named author and further developed here) gives a complete 3|4 modulus of such supertriangles.. The space of additive scalar invariants is proved to have superdimension 3|1: ordinary hyperbolic area in degree zero, two even generators in degree two, and one odd generator in degree three; the degree-one and degree-four sectors vanish. One degree-two generator is the fermionic first variation of body area, equivalently the nilpotent correction from ordinary body angle defect to super angle defect. The degree-three generator changes sign under reversal of the spin lift, while the other generators are fixed, so ordinary supertriangles carry only three even invariants.
ER  -