Fine-Tuning as Quantum Phase Transition Point

Abstract

We discuss analogy between statistical mechanics and quantum field theory from the point of view of fine-tuning problem.

In the former, (first-order) phase transition (PT) point spans a finite parameter space in micro-canonical ensemble, while it is literally a point and looks like a fine-tuning of parameters in canonical ensemble.

In this talk, I would like to point out that similar picture holds in quantum field theory. As concrete examples, we discuss free scalar theory and \phi^4 theory and show that gapless point (m^2=0) is typically realized in micro-canonical ensemble. Then, as a phenomenological application, we show that the Higgs alignment in the two Higgs doublet  model can be realized in the micro-canonical picture without imposing any symmetries.

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