Matrix quantum mechanics on S 1 / Z 2

Abstract

We study Matrix Quantum Mechanics on the Euclidean time orbifold S1/Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

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BibTeX RIS

BibTeX

@article{betzios2026matrix,
  title = {{Matrix quantum mechanics on S 1 / Z 2}},
  author = {P. Betzios and U. Gürsoy and O. Papadoulaki},
  journal = {Nuclear Physics B},
  year = {2026},
  month = sep,
  doi = {10.1016/j.nuclphysb.2018.01.019},
  eprint = {1612.04792},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05771580v1},
  note = {CC BY},
}

RIS

TY  - JOUR
TI  - Matrix quantum mechanics on S 1 / Z 2
AU  - P. Betzios
AU  - U. Gürsoy
AU  - O. Papadoulaki
PY  - 2026
DA  - 2026/09/30
JO  - Nuclear Physics B
DO  - 10.1016/j.nuclphysb.2018.01.019
UR  - https://hal.science/hal-05771580v1
AB  - We study Matrix Quantum Mechanics on the Euclidean time orbifold S1/Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.
SN  - 0550-3213
SN  - 1873-1562
ER  -

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