Bootstrapping Euclidean two-point correlators

Abstract

We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject to the constraints of reflection positivity, the Heisenberg equations of motion, and the Kubo-Martin-Schwinger condition or ground-state positivity. In the dual formulation, the Heisenberg equations of motion become "inequalities of motion" on the Lagrange multipliers that enforce the constraints. This enables us to derive rigorous bounds on continuous-time two-point correlators using a finite-dimensional semidefinite or polynomial matrix program. We illustrate this method by bootstrapping the two-point correlators of the ungauged one-matrix quantum mechanics, from which we extract the spectrum and matrix elements of the low-lying adjoint states. Along the way, we provide a new derivation of the energy-entropy balance inequality and establish a connection between the high-temperature two-point correlator bootstrap and the matrix integral bootstrap.

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BibTeX RIS

BibTeX

@article{cho2026bootstrapping,
  title = {{Bootstrapping Euclidean two-point correlators}},
  author = {Minjae Cho and Barak Gabai and Henry W Lin and Jessica Yeh and Zechuan Zheng},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = aug,
  doi = {10.1007/jhep08(2026)147},
  url = {https://hal.science/hal-05767600v1},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Bootstrapping Euclidean two-point correlators
AU  - Minjae Cho
AU  - Barak Gabai
AU  - Henry W Lin
AU  - Jessica Yeh
AU  - Zechuan Zheng
PY  - 2026
DA  - 2026/08/19
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep08(2026)147
UR  - https://hal.science/hal-05767600v1
AB  - We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject to the constraints of reflection positivity, the Heisenberg equations of motion, and the Kubo-Martin-Schwinger condition or ground-state positivity. In the dual formulation, the Heisenberg equations of motion become "inequalities of motion" on the Lagrange multipliers that enforce the constraints. This enables us to derive rigorous bounds on continuous-time two-point correlators using a finite-dimensional semidefinite or polynomial matrix program. We illustrate this method by bootstrapping the two-point correlators of the ungauged one-matrix quantum mechanics, from which we extract the spectrum and matrix elements of the low-lying adjoint states. Along the way, we provide a new derivation of the energy-entropy balance inequality and establish a connection between the high-temperature two-point correlator bootstrap and the matrix integral bootstrap.
SN  - 1126-6708
SN  - 1029-8479
ER  -

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