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arXiv · 1810.05842

Effective Action study of $\mathcal{PT}$-Symmetry Breaking for the non-Hermitian $\left( iϕ^{3}\right) _{6-ε}$ Theory and The Yang-Lee Edge Singularity

Abouzeid M. Shalaby
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Abstract

We use the effective potential method to study the $\mathcal{PT}$-symmetry breaking of the non-Hermitian $iϕ^{3}$ field theory in $6-ε$ space-time dimensions. The critical exponents so obtained coincide with the exact values listed in the literature. We showed that at the point of $\mathcal{PT}$-symmetry breaking, the vacuum-vacuum amplitude is certainly zero and the fugacity is one which mimics a Yang-Lee edge singularity in magnetic systems. What makes this work interesting is that it takes into account problems which are always overlooked in the literature for the Yang-Lee model like stability, unitarity and generation of Stokes wedges at space-time dimensions for which divergences occur in the theory . Besides, here we make direct calculation of critical exponents from the dependance of the order parameter on external magnetic field not from the density of zeros of the partition function.

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Abouzeid M. Shalaby. 2018-10-13. Effective Action study of $\mathcal{PT}$-Symmetry Breaking for the non-Hermitian $\left( iϕ^{3}\right) _{6-ε}$ Theory and The Yang-Lee Edge Singularity. https://doi.org/10.1142/s0217751x19500908.

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