高温对紧凑型结构的影响
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Eur. Phys. J. C (2016) 76:418
DOI 10.1140/epjc/s10052-016-4272-9
Regular Article - Theoretical Physics
High temperature effects on compact-like structures
D. Bazeia
a
, E. E. M. Lima, L. Losano
Departamento de Física, Universidade Federal da Paraíba, João Pessoa, PB 58051-900, Brazil
Received: 24 May 2016 / Accepted: 18 July 2016 / Published online: 27 July 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract In this work we investigate the transition from
kinks to compactons at high temperatures. We deal with a
family of models, described by a real scalar field with stan-
dard kinematics, controlled by a single parameter, real and
positive. The family of models supports kink-like solutions,
and the solutions tend to become compact when the param-
eter increases to larger and larger values. We study the one-
loop corrections at finite temperature, to see how the thermal
effects add to the effective potential. The results suggest that
the symmetry is restored at very high temperatures.
1 Introduction
Topological defects are of current interest and have attracted
a great deal of attention in high energy physics [1–3] and
in other areas of nonlinear science; see, e.g., Refs. [4–12].
Among them, the simplest topological structures are kinks,
which appear in models described by real scalar fields in
(1, 1) spacetime dimensions. They can be embedded in (3, 1)
spacetime dimensions as domain walls, and usually they
evolve under standard kinematics, subject to a potential that
develops spontaneous symmetry breaking.
Under specific conditions, another kind of kink-like
defect, called compacton, appears in models with general-
ized kinematics that include a nonlinear dispersion [13–20].
These structures are nontrivial configurations with compact
support, and have been studied in distinct contexts in [21–35].
In particular, in Ref. [35] one shows how a kink-like solu-
tion can be transformed into a compact structure, driven by a
single parameter, even though the model engenders standard
kinematics.
Motivated by this fact, in the current work we are inter-
ested to study how the compact structure is impacted by the
presence of quantum corrections. The idea was advanced in
[36], where the one-loop shift of the energy of a compacton
a
e-mail: bazeia@fisica.ufpb.br
was calculated in a model with modified kinematics. Here,
however, we study a model first introduced in [35], with stan-
dard kinematics. Due to the standard kinematics, we could
calculate the one-loop correction to get to the effective poten-
tial following the usual route. In this sense, the present inves-
tigation is indirect, since we will study the effective potential
instead of the effective action. However, if the thermal effects
are suitable to restore the symmetry at some critical tempera-
ture T
c
, the system cannot support defect structure anymore,
when the temperature is higher than or equal to the critical
one.
As one knows, in the standard scenario [37,38], the high
temperature effects allows the symmetry restoration, lead-
ing to a phase transition where topological structures appear
below the critical temperature. Although this is the gen-
eral wisdom, there are models where the symmetry is never
restored [39,40], implying the absence of phase transition at
high temperatures. So, it is of current interest to study how
the thermal effects act to control the smooth transition that
changes the kink into a compact structure.
To ease the investigation, we organize the work as follows.
In the next section, we briefly review models of a single real
scalar field and in Sect. 3 we describe the connection between
kinks and compactons. In Sect. 4 we develop the procedure
to obtain the effective potential in the high temperature limit,
and we study how it behaves in the compact limit. As far as
we can see, the present calculations provide the first results
to suggest how compact kinks behave at finite temperature.
We end the work including our comments and conclusions
in Sect. 5.
2 Generalities
We start our investigation from the general Lagrange density
describing a relativistic system driven by a single real scalar
field defined as
L =
1
2
∂
μ
φ∂
μ
φ − V (φ), (1)
123
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