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Xizhi Han1, Sean A Hartnoll1, Jorrit Kruthoff1

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Summary
This summary is machine-generated.

We introduce a numerical bootstrap method to solve complex large N matrix quantum mechanics problems, crucial for holographic duality. This approach successfully determines spectra and expectation values, offering new insights into quantum systems.

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Area of Science:

  • Quantum Field Theory
  • String Theory
  • Holographic Duality

Background:

  • Large N matrix quantum mechanics is fundamental to holographic duality.
  • Exact solutions are often intractable in complex scenarios.
  • Numerical methods are needed to explore these theories.

Purpose of the Study:

  • To develop and apply a numerical bootstrap methodology for solving large N matrix quantum mechanics.
  • To demonstrate the efficacy of this method on known and new problems.
  • To obtain spectra and expectation values in previously unsolvable cases.

Main Methods:

  • Utilizing a bootstrap approach relating operator expectation values through symmetries (time translation, SU(N) gauge invariance).
  • Applying positivity constraints to bound these values.
  • Numerical implementation for solving quantum anharmonic oscillator and large N matrix models.

Main Results:

  • The bootstrap method efficiently solves the quantum anharmonic oscillator.
  • It accurately reproduces known solutions for large N single matrix quantum mechanics.
  • New results are presented for the ground state of large N two matrix quantum mechanics.

Conclusions:

  • The numerical bootstrap methodology provides a powerful tool for tackling complex large N matrix quantum mechanics.
  • This approach offers a viable path to studying holographic dualities in previously inaccessible regimes.
  • The findings open avenues for further research in quantum field theory and related areas.