The two-loop ϕ4 kink mass

Evslin, Jarah

doi:10.1016/j.physletb.2021.136628

“…In refs. [21,22], the calculation of γ1 was reviewed and it played an essential role in the elimination of IR divergences in the calculation of the two-loop kink mass. The shifted counterterm and all successive terms are finite at Λ → ∞, with the first few given in eq.…”

Section: Jhep01(2023)073mentioning

confidence: 99%

Cut-off kinks

Evslin

¹

,

Royston

²

,

Zhang

³

2023

J. High Energ. Phys.

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We answer the question: If a vacuum sector Hamiltonian is regularized by an energy cutoff, how is the one-kink sector Hamiltonian regularized? We find that it is not regularized by an energy cutoff, indeed normal modes of all energies are present in the kink Hamiltonian, but rather the decomposition of the field into normal mode operators yields coefficients which lie on a constrained surface that forces them to become small for energies above the cutoff. This explains the old observation that an energy cutoff of the kink Hamiltonian leads to an incorrect one-loop kink mass. To arrive at our conclusion, we impose that the regularized kink sector Hamiltonian is unitarily equivalent to the regularized vacuum sector Hamiltonian. This condition implies that the two regularized Hamiltonians have the same spectrum and so guarantees that the kink Hamiltonian yields the correct kink mass.

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“…Quantising the parameter describing the kink separation would be the 1D equivalent of studying vibrational quantisation for skyrmions [27]. We could also study one-(or two- [22])loop corrections of the 2kink. The only attempted loop calculation for non-integrable solitons was done in [44], where it was shown that the 2-baby-skyrmion is unstable when the corrections were included.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Stable Kink-Kink and Metastable Kink-Antikink Solutions

Halcrow¹,

Babaev²

2023

SIGMA

4

0

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We construct and study two kink theories. One contains a static 2-kink configuration with controllable binding energy. The other contains a locally stable non-topological solution, which we call a lavion. The new models are 1D analogs of non-integrable systems in higher dimensions such as the Skyrme model and realistic vortex systems. To help construct the theories, we derive a simple expression for the interaction energy between two kinks.

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“…In Refs. [20,21], the calculation of γ1 was reviewed and it played an essential role in the elimination of IR divergences in the calculation of the two-loop kink mass. The shifted counterterm and all successive terms are finite at Λ → ∞, with the first few given in Eq.…”

Section: The Relation To Normal Orderingmentioning

confidence: 99%

Cut-Off Kinks

Evslin¹,

Royston²,

Zhang³

2022

Preprint

0

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We answer the question: If a vacuum sector Hamiltonian is regularized by an energy cutoff, how is the one-kink sector Hamiltonian regularized? We find that it is not regularized by an energy cutoff, indeed normal modes of all energies are present in the kink Hamiltonian, but rather the decomposition of the field into normal mode operators yields coefficients which lie on a constrained surface that forces them to become small for energies above the cutoff. This explains the old observation that an energy cutoff of the kink Hamiltonian leads to an incorrect one-loop kink mass. To arrive at our conclusion, we impose that the regularized kink sector Hamiltonian is unitarily equivalent to the regularized vacuum sector Hamiltonian. This condition implies that the two regularized Hamiltonians have the same spectrum and so guarantees that the kink Hamiltonian yields the correct kink mass.

show abstract

The two-loop ϕ4 kink mass

Cited by 11 publications

References 21 publications

Cut-off kinks

Cut-off kinks

Stable Kink-Kink and Metastable Kink-Antikink Solutions

Cut-Off Kinks

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