Tunneling decay of false vortices with gravitation

We consider the Skyrme model modified by the addition of mass terms which explicitly break chiral symmetry and pick out a specific point on the model's target space as the unique true vacuum. However, they also allow the possibility of false vacua, local minima of the potential energy. These false vacuum configurations admit metastable skyrmions, which we call false skyrmions. False skyrmions can decay due to quantum tunnelling, consequently causing the decay of the false vacuum. We compute the rate of decay of the false vacuum due to the existence of false skyrmions.

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“…This result is not exclusive to false skyrmions. It was also observed for vortices [34]. This can be understood in the following way.…”

Section: Vacuum Decay Ratesmentioning

confidence: 59%

“…where we maintain the thin-wall approximation for which r ≈ R on the wall. To compute this term, it is useful to introduce the Gaussian normal coordinate system (see [34] for an example of the application in the vortex system)…”

Section: Tunnelling Decaymentioning

confidence: 99%

Vacuum decay induced by false Skyrmions

et al. 2019

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“…They obtained an analytical expression for the black hole mass 𝑀 in terms of the scalar charge 𝑐 and the winding number 𝑛. Later, how vortices affect the tunneling decay of a symmetry-breaking false vacuum in 2 + 1 dimensional Einstein gravity was studied in [3]. There have also been recent studies of gravitating magnetic monopoles [4].…”

Section: Introductionmentioning

confidence: 99%

Gravitating Nielsen-Olesen vortices in an AdS$_3$ and Minkowski background

Edery¹

2022

Proceedings of the European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2021)

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We consider Nielsen-Olesen vortices under Einstein gravity in an AdS 3 background. We find numerically non-singular solutions characterized by three parameters: the cosmological constant Λ, the winding number 𝑛 and the vacuum expectation value (VEV) labeled by 𝑣. The mass (ADM mass) of the vortex is expressed in two ways: one involves subtracting the value of two metrics asymptotically and the other is expressed as an integral over matter fields. The latter shows that the mass has an approximately 𝑛 2 𝑣 2 dependence and our numerical results corroborate this. We also observe that as the magnitude of the cosmological constant increases the core of the vortex becomes slightly smaller and the mass increases. We then embed the vortex under gravity in a Minkowski background and obtain numerical solutions for different values of Newton 's constant. There is a smooth transition from the non-singular origin to an asymptotic conical spacetime with angular deficit that increases as Newton's constant increases. We end by stating that the well-known logarithmic divergence in the energy of the vortex in the absence of gauge fields can be seen in a new light with gravity: it shows up in the metric as a 2 + 1 Newtonian logarithmic potential leading to a divergent ADM mass.

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“…In particular, they obtain a compact analytical expression for the black hole mass M in terms of the scalar charge c and the winding number n: M = λ 2 c 2 /4+n 2 where λ 2 is a parameter appearing in the potential. More recently, the effect of vortices on the tunneling decay of a symmetry-breaking false vacuum in 2 + 1 dimensional Einstein gravity was studied [6]. They found that the tunneling exponent for vortices, the dominant factor in the decay rate, is half that of Coleman-de Luccia bubbles [7].…”

Section: Introductionmentioning

confidence: 99%

Non-singular vortices with positive mass in 2+1-dimensional Einstein gravity with AdS3 and Minkowski background

Edery

2021

J. High Energ. Phys.

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In previous work, black hole vortex solutions in Einstein gravity with AdS3 background were found where the scalar matter profile had a singularity at the origin r = 0. In this paper, we find numerically static vortex solutions where the scalar and gauge fields have a non-singular profile under Einstein gravity in an AdS3 background. Vortices with different winding numbers n, VEV v and cosmological constant Λ are obtained. These vortices have positive mass and are not BTZ black holes as they have no event horizon. The mass is determined in two ways: by subtracting the numerical values of two separate asymptotic metrics and via an integral that is purely over the matter fields. The mass of the vortex increases as the cosmological constant becomes more negative and this coincides with the core of the vortex becoming smaller (compressed). We then consider the vortex with gravity in asymptotically flat spacetime for different values of the coupling α = 1/(16πG). At the origin, the spacetime has its highest curvature and there is no singularity. It transitions to an asymptotic conical spacetime with angular deficit that increases significantly as α decreases. For comparison, we also consider the vortex without gravity in flat spacetime. For this case, one cannot obtain the mass by the first method (subtracting two metrics) but remarkably, via a limiting procedure, one can obtain an integral mass formula. In the absence of gauge fields, there is a well-known logarithmic divergence in the energy of the vortex. With gravity, we present this divergence in a new light. We show that the metric acquires a logarithmic term which is the 2 + 1 dimensional realization of the Newtonian gravitational potential when General Relativity is supplemented with a scalar field. This opens up novel possibilities which we discuss in the conclusion.

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Tunneling decay of false vortices with gravitation

Cited by 5 publications

References 44 publications

Vacuum decay induced by false Skyrmions

Vacuum decay induced by false Skyrmions

Gravitating Nielsen-Olesen vortices in an AdS$_3$ and Minkowski background

Non-singular vortices with positive mass in 2+1-dimensional Einstein gravity with AdS3 and Minkowski background

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