λϕ 4 theory — Part II. the broken phase beyond NNNN(NNNN)LO
| Autor: | Giovanni Villadoro, Gabriele Spada, Marco Serone |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics Instanton Field Theories in Lower Dimensions Nonperturbative Effects Physics - Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Phenomenology Duality (optimization) 01 natural sciences symbols.namesake Theoretical physics Vacuum energy 0103 physical sciences lcsh:Nuclear and particle physics. Atomic energy. Radioactivity 010306 general physics Physics 010308 nuclear & particles physics Analytic continuation Settore FIS/02 - Fisica Teorica Modelli e Metodi Matematici symbols lcsh:QC770-798 Perturbation theory (quantum mechanics) Hamiltonian (quantum mechanics) Mass gap Vacuum expectation value |
| Zdroj: | Journal of High Energy Physics, Vol 2019, Iss 5, Pp 1-36 (2019) Journal of High Energy Physics |
| ISSN: | 1029-8479 |
| DOI: | 10.1007/JHEP05(2019)047 |
| Popis: | We extend the study of the two-dimensional euclidean ϕ 4 theory initiated in ref. [1] to the ℤ2 broken phase. In particular, we compute in perturbation theory up to N4LO in the quartic coupling the vacuum energy, the vacuum expectation value of ϕ and the mass gap of the theory. We determine the large order behavior of the perturbative series by finding the leading order finite action complex instanton configuration in the ℤ2 broken phase. Using an appropriate conformal mapping, we then Borel resum the perturbative series. Interestingly enough, the truncated perturbative series for the vacuum energy and the vacuum expectation value of the field is reliable up to the critical coupling where a second order phase transition occurs, and breaks down around the transition for the mass gap. We compute the vacuum energy using also an alternative perturbative series, dubbed exact perturbation theory, that allows us to effectively reach N8LO in the quartic coupling. In this way we can access the strong coupling region of the ℤ2 broken phase and test Chang duality by comparing the vacuum energies computed in three different descriptions of the same physical system. This result can also be considered as a confirmation of the Borel summability of the theory. Our results are in very good agreement (and with comparable or better precision) with those obtained by Hamiltonian truncation methods. We also discuss some subtleties related to the physical interpretation of the mass gap and provide evidence that the kink mass can be obtained by analytic continuation from the unbroken to the broken phase. |
| Databáze: | OpenAIRE |
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