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On self-dualities for scalar $φ^4$ theory

Paul Romatschke

Abstract

Scalar field theory is studied by constructing interacting saddle point expansions in the symmetric and broken phase, respectively. Focusing on analytically tractable saddle expansions, it is found that broken and symmetric phases are related by sign flip of the quartic coupling. Applications to dimensions $d<4$ recover previous results for the phase diagram, whereas $d=4$ is possibly new.

On self-dualities for scalar $φ^4$ theory

Abstract

Scalar field theory is studied by constructing interacting saddle point expansions in the symmetric and broken phase, respectively. Focusing on analytically tractable saddle expansions, it is found that broken and symmetric phases are related by sign flip of the quartic coupling. Applications to dimensions recover previous results for the phase diagram, whereas is possibly new.
Paper Structure (11 sections, 61 equations, 1 figure)

This paper contains 11 sections, 61 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Calculation
  3. Chang duality in $d=2$
  4. Magruder duality in d=3
  5. Self duality in d=4
  6. Summary and Conclusions
  7. Acknowledgments
  8. Expansion around symmetric phase saddle
  9. Expansion around broken phase saddle
  10. Case d=1 aka Quantum Mechanics
  11. Symmetric and Broken Saddle Expansions are Mutually Exclusive

Figures (1)

  • Figure 1: Comparison of lowest lying eigenvalues $E_0,E_1$ of the Hamiltonian to the free energies $\Omega_{R1}^{(1)},\tilde{\Omega}_{R1}^{(1)}$ from the symmetric and broken saddles obtained in the R1-level resummation. See text for details.