Perturbation theory of a large class of scalar field theories in d < 4 can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the λϕ4 theory in two dimensions in the Z2 symmetric phase. We extend the results for the perturbative expansion of several quantities up to N8LO and show how the behavior of the theory at strong coupling can be recovered successfully using known resummation techniques. In particular, we compute the vacuum energy and the mass gap for values of the coupling up to the critical point, where the theory becomes gapless and lies in the same universality class of the 2d Ising model. Several properties of the critical point are determined and agree with known exact expressions. The results are in very good agreement (and with comparable precision) with those obtained by other non-perturbative approaches, such as lattice simulations and Hamiltonian truncation methods.

lambda phi(4) theory - Part I. The symmetric phase beyond NNNNNNNNLO / Serone, Marco; Spada, Gabriele; Villadoro, Giovanni. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2018:8(2018), pp. 1-34. [10.1007/JHEP08(2018)148]

lambda phi(4) theory - Part I. The symmetric phase beyond NNNNNNNNLO

Serone, Marco;Spada, Gabriele;Villadoro, Giovanni
2018

Abstract

Perturbation theory of a large class of scalar field theories in d < 4 can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the λϕ4 theory in two dimensions in the Z2 symmetric phase. We extend the results for the perturbative expansion of several quantities up to N8LO and show how the behavior of the theory at strong coupling can be recovered successfully using known resummation techniques. In particular, we compute the vacuum energy and the mass gap for values of the coupling up to the critical point, where the theory becomes gapless and lies in the same universality class of the 2d Ising model. Several properties of the critical point are determined and agree with known exact expressions. The results are in very good agreement (and with comparable precision) with those obtained by other non-perturbative approaches, such as lattice simulations and Hamiltonian truncation methods.
2018
8
1
34
148
10.1007/JHEP08(2018)148
https://arxiv.org/abs/1805.05882
Serone, Marco; Spada, Gabriele; Villadoro, Giovanni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/85597
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