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PreprintCC BY 4.0arXiv

An obstruction to generalised discrete torsion in string theory

  • Carlo Angelantonj
  • Giorgio Leone
  • Diego Perugini
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Abstract

We reconsider the possibility of turning on generalised discrete torsion in orbifold compactifications, whereby different discrete torsion phases are attached to different fixed points of a given twisted sector. By an explicit inspection of the genus one and genus two vacuum amplitudes for the T6/ℤ22 and T7/ℤ23 cases, we show that this is not possible in String Theory. In fact, this generalised discrete torsion, although modular invariant at genus one, leads to an inconsistent interpretation of the spectrum which, in turn, implies a loss of modular invariance on genus-two Riemann surfaces. Our finding is in agreement with a recent classification of allowed topological deformations in equivariant cohomology, which does not include this possibility.

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Cite

BibTeXRIS
BibTeX
@misc{angelantonj2026obstruction,
  title = {{An obstruction to generalised discrete torsion in string theory}},
  author = {Carlo Angelantonj and Giorgio Leone and Diego Perugini},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00209},
  eprint = {2611.00209},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00209},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An obstruction to generalised discrete torsion in string theory
AU  - Carlo Angelantonj
AU  - Giorgio Leone
AU  - Diego Perugini
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00209
UR  - https://arxiv.org/abs/2611.00209
AB  - We reconsider the possibility of turning on generalised discrete torsion in orbifold compactifications, whereby different discrete torsion phases are attached to different fixed points of a given twisted sector. By an explicit inspection of the genus one and genus two vacuum amplitudes for the T^6/ℤ_2^2 and T^7/ℤ_2^3 cases, we show that this is not possible in String Theory. In fact, this generalised discrete torsion, although modular invariant at genus one, leads to an inconsistent interpretation of the spectrum which, in turn, implies a loss of modular invariance on genus-two Riemann surfaces. Our finding is in agreement with a recent classification of allowed topological deformations in equivariant cohomology, which does not include this possibility.
ER  -