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Large-N Principal Chiral Model in Arbitrary External Fields.

Vladimir Kazakov1, Evgeny Sobko2, Konstantin Zarembo3

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|April 19, 2024
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Summary
This summary is machine-generated.

We solved the vacuum state for the 2D SU(N) principal chiral model at large N. This unique solution applies to any chemical potential and interaction strength, bridging weak and strong coupling regimes.

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Area of Science:

  • Quantum Field Theory
  • High Energy Physics
  • Condensed Matter Theory

Background:

  • The SU(N) principal chiral model is a fundamental model in quantum field theory.
  • Understanding its vacuum state is crucial for various physical phenomena.
  • Previous solutions were limited to specific coupling regimes or approximations.

Purpose of the Study:

  • To derive an explicit solution for the vacuum state of the 2D SU(N) principal chiral model.
  • To provide a solution valid for arbitrary chemical potentials and interaction strengths.
  • To analyze the model's behavior in both weak and strong coupling limits.

Main Methods:

  • Large N expansion techniques were employed.
  • The study focused on the continuum limit of the SU(N) Dynkin diagram.
  • The solution was validated against one-loop perturbative calculations.

Main Results:

  • An explicit solution for the vacuum state was obtained for large N.
  • The solution is valid for any chemical potential and interaction strength.
  • At strong coupling, an emergent spatial dimension was observed.

Conclusions:

  • This work provides a unique, comprehensive solution for the 2D SU(N) principal chiral model.
  • The findings bridge the gap between weak and strong coupling physics.
  • The emergent spatial dimension offers new insights into quantum field theory at strong coupling.