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Distinguished bases and the braid group action for solutions of the tt*-Toda equations

  • Yudai Hateruma
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Abstract

We implement (in a concrete example) a procedure of Dubrovin which gives a braid group action on spaces of solutions of ordinary differential equations such as the quantum differential equation of complex projective space. Such actions originated in physics for the tt* (topological-antitopological fusion) equations. We make the procedure systematic by utilizing an algebraic description of braid group actions on distinguished bases. We also generalize to the case of (arbitrary) solutions of the tt*-Toda equations, one of which corresponds to the quantum cohomology of complex projective space.

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Cite

BibTeXRIS
BibTeX
@misc{hateruma2026distinguished,
  title = {{Distinguished bases and the braid group action for solutions of the tt*-Toda equations}},
  author = {Yudai Hateruma},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14078},
  eprint = {2610.14078},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14078},
}
RIS
TY  - UNPB
TI  - Distinguished bases and the braid group action for solutions of the tt*-Toda equations
AU  - Yudai Hateruma
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.14078
UR  - https://arxiv.org/abs/2610.14078
AB  - We implement (in a concrete example) a procedure of Dubrovin which gives a braid group action on spaces of solutions of ordinary differential equations such as the quantum differential equation of complex projective space. Such actions originated in physics for the tt* (topological-antitopological fusion) equations. We make the procedure systematic by utilizing an algebraic description of braid group actions on distinguished bases. We also generalize to the case of (arbitrary) solutions of the tt*-Toda equations, one of which corresponds to the quantum cohomology of complex projective space.
ER  -