In the present paper, we consider a $\left(1 + 1\right)$-dimensional gauge model consisting of two complex scalar fields interacting with each other through an Abelian gauge field. When the model's gauge coupling constants are set equal to zero, the model possesses non-gauged Q-ball and kink solutions that do not interact with each other. It is shown that at nonzero gauge coupling constants, the model possesses the soliton solution describing the system consisting of interacting Q-ball and kink components. The kink and Q-ball components of the kink-Q-ball system have opposite electric charges, so the total electric charge of the kink-Q-ball system vanishes. Properties of the kink-Q-ball system are researched analytically and numerically. In particular, it was found that the kink-Q-ball system possesses a nonzero electric field and is unstable with respect to small perturbations of fields.
Radially excited $U(1)$ gauged $Q$-balls are studied using both analytical and numerical methods. Unlike the nongauged case, there exists only a finite number of radially excited gauged $Q$-balls at given values of the model's parameters. Similarly to the unexcited gauged $Q$-ball, the radially excited one cannot possess the Noether charge exceeding some limiting value. This limiting Noether charge decreases with an increase in the radial excitation of the gauged $Q$-ball. For $n$-th radial excitation, there is a maximum allowable value of the gauge coupling constant, and the existence of the …
In this paper, we present a detailed study of the problem of classical stability of U(1) gauged Q-balls. In particular, we show that the standard methods that are suitable for establishing the classical stability criterion for ordinary (nongauged) one-field and two-field Q-balls are not effective in the case of U(1) gauged Q-balls, although all the technical steps of calculations can be performed in the same way as those for ordinary Q-balls. We also present the results of numerical simulations in models with different scalar field potentials, explicitly demonstrating that, in general, the reg…
We discuss the $U(1)$ gauged Q-balls with $N$-power potential to examine their properties analytically. More numerical descriptions and some analytical consideration have been contributed to the models governed by four-power potential. We also demonstrate strictly some new limitations that the stable $U(1)$ gauged Q-balls should accept instead of estimating those with only some specific values of model variables numerically. Having derived the explicit expressions of radius, the Noether charge and energy of the gauged Q-balls, we find that these models under the potential of matter field with …
We study the canonical energy-momentum tensor of the spherically symmetric $U(1)$ gauged Q-ball configurations in the two-component Fridberg-Lee-Sirlin-Maxwell model, and in the one-component scalar model with a sixtic potential. We evaluate the distributions of the corresponding shear forces and pressure and study the stability criteria for these solutions. It is shown that the electrostatic repulsion may destabilize the $U(1)$ gauged Q-balls. However, in the limiting case of the Fridberg-Lee-Sirlin-Maxwell model with a long ranged real scalar component, the gauged Q-balls always remain stabl…
We consider the $U(1)$ gauged two-component Friedberg-Lee-Sirlin model in 3+1 dimensional Minkowski spacetime, which supports non-topological soliton configurations. Here we found families of axially-symmetric spinning gauged Q-balls, which possess both electric and magnetic fields. The coupling to the gauge sector gives rise to a new branch of solutions, which represent the soliton configuration coupled to a circular magnetic flux. Further, in superconducting phase this branch is linked to vorton type solutions which represent a vortex encircling the soliton. We discuss properties of these so…
We construct static axially symmetric multi-Q-ball configurations in the $U(1)$ gauged two-component Fridberg-Lee-Sirlin model a flat spacetime. The solutions represent electromagnetically bounded chains of stationary spinning charged Q-balls placed along the axis of symmetry. We discuss the properties of these configurations and exhibit their domain of existence.
The (1+1)-dimensional gauge model of two complex self-interacting scalar fields that interact with each other through an Abelian gauge field and a quartic scalar interaction is considered. It is shown that the model has nontopological soliton solutions describing soliton systems consisting of two Q-ball components possessing opposite electric charges. The two Q-ball components interact with each other through the Abelian gauge field and the quartic scalar interaction. The interplay between the attractive electromagnetic interaction and the repulsive quartic interaction leads to the existence o…
We analyze the axially-symmetric scalar perturbations of 6D chiral gauged supergravity compactified on the general warped geometries in the presence of two source branes. We find all of the conical geometries are marginally stable for normalizable perturbations (in disagreement with some recent calculations) and the nonconical for regular perturbations, even though none of them are supersymmetric (apart from the trivial Salam-Sezgin solution, for which there are no source branes). The marginal direction is the one whose presence is required by the classical scaling property of the field equati…
We study Q-balls associated with local U(1) symmetries. Such Q-balls are expected to become unstable for large values of their charge because of the repulsion mediated by the gauge force. We consider the possibility that the repulsion is eliminated through the presence in the interior of the Q-ball of fermions with charge opposite to that of the scalar condensate. Another possibility is that two scalar condensates of opposite charge form in the interior. We demonstrate that both these scenaria can lead to the existence of classically stable, large, gauged Q-balls. We present numerical solution…
In this paper we examine the properties of $U(1)$ gauged Q-balls in two models with different scalar field potentials. The obtained results demonstrate that in the general case $U(1)$ gauged Q-balls possess properties, which differ considerably from those of Q-balls in the nongauged case with the same forms of the scalar field potential. In particular, it is shown that in some cases the charge of $U(1)$ gauged Q-ball can be bounded from above, whereas it is not so for the corresponding nongauged Q-ball. Our conclusions are supported both by analytical considerations and numerical calculations.
We discuss finite regions of the deconfining phase of a confining gauge theory (plasma balls/kinks) as solitons of the large $N$, long wavelength, effective Lagrangian of the thermal gauge theory expressed in terms of suitable order parameters. We consider a class of confining gauge theories whose effective Lagrangian turns out to be a generic 1 dim. unitary matrix model. The dynamics of this matrix model can be studied by an exact mapping to a non-relativistic many fermion problem on a circle. We present an approximate solution to the equations of motion which corresponds to the motion (in Eu…
In this paper, the main properties of (3+1)-dimensional $U(1)$ gauged Q-balls are examined. In particular, it is shown that the relation $\frac{dE}{dQ}=ω$ holds for such gauged Q-balls in the general case. As a consequence, it is shown that the well-known estimate for the maximal charge of stable gauged Q-balls was derived by means of an inconsistent procedure and can not be considered as correct. A simple method for obtaining the main characteristics of gauged Q-balls using only the nongauged background solution for the scalar field in the case, when the back-reaction of the gauge field on th…
We examine the energetics of $Q$-balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged $Q$-balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the $Q$-ball. Similar to the case of gauged $Q$-balls, Maxwell-Chern-Simons $Q$-balls have a maximal charge. The properties of these solitons are studied as a function of the parameters of the model considered, using a numerical tec…
We examine the energetics of Q-balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged Q-balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the Q-ball. Similar to the case of gauged Q-balls, Maxwell-Chern-Simons Q-balls have a maximal charge. The properties of these solitons are studied as a function of the parameters of the model considered, using a numerical technique kno…
We consider gauged Q-balls in the gravity-mediation-type model in the Affleck-Dine mechanism, which is described by the potential $V_{\rm grav.}(ϕ):=(m_{\rm grav.}^2/2)ϕ^2\left[1+K\ln(ϕ/M)^2\right]$ with $K<0$. In many models of gauged Q-balls, which were studied in the literature, there are upper limits for charge and size of Q-balls due to repulsive Coulomb force. In the present model, by contrast, our numerical calculation strongly suggests that stable solutions with any amount of charge and size exist. As the electric charge $Q$ increases, the field configuration of the scalar field become…
Non-topological gauged soliton solutions called Q-balls arise in many scalar field theories that are invariant under a U(1) gauge symmetry. The related, but qualitatively distinct, Q-shell solitons have only been shown to exist for special potentials. We investigate gauged solitons in a generic sixth-order polynomial potential (that contains the leading effects of many effective field theories) and show that this potential generically allows for both Q-balls and Q-shells. We argue that Q-shell solutions occur in many, and perhaps all, potentials that have previously only been shown to contain …
We obtain first order equations that determine a supersymmetric kink solution in five-dimensional N=8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained be…
We propose a model of an electrically charged fermion as a regular localized solution of electromagnetic and spinor fields interacting with a physical vacuum, which is phenomenologically described as a logarithmic superfluid. We analytically study the asymptotic behavior of the solution, while obtaining its form by numerical methods. The solution has physically plausible properties, such as finite size, self-energy, total charge and mass. In the case of spherical symmetry, its electric field obeys the Coulomb asymptotics at large distances from its core. It is shown that the observable rest ma…
We consider a scalar field model with a self-interaction potential that possesses a discrete vacuum manifold. We point out that this model allows for both topological as well as non-topological solitons. In (1+1) dimensions both type of solutions have finite energy, while in (3+1) dimensions, the topological solitons have finite energy per unit area only and correspond to domain walls. Non-topological solitons with finite energy do exist in (3+1) dimensions due to a non-trivial phase of the scalar field and an associated U(1) symmetry of the model, though. We construct these so-called Q-ball s…
Non-topological solitons such as Q-balls and Q-shells have been studied for scalar fields invariant under global and gauged U(1) symmetries. We generalize this framework to include a Proca mass for the gauge boson, which can arise either from spontaneous symmetry breaking or via the Stückelberg mechanism. A heavy (light) gauge boson leads to solitons reminiscent of the global (gauged) case, but for intermediate values these Proca solitons exhibit completely novel features such as disconnected regions of viable parameter space and Q-shells with unbounded radius. We provide numerical solutions a…
By studying various, known extrema of 1) SU(3) sectors, 2) SO(5) sectors and 3) SO(3)xSO(3) sectors of gauged N =8 supergravity in four-dimensions, one finds that the deformation of seven sphere §^7 gives rise to non-trivial renormalization group(RG) flow in three-dimensional boundary conformal field theory from UV fixed point to IR fixed point. For SU(3) sectors, this leads to four-parameter subspace of the supergravity scalar-gravity action and we identify one of the eigenvalues of A_1 tensor of the theory with a superpotential of scalar potential that governs RG flows on this subspace. We a…
Article for the forthcoming Encyclopedia of Mathematical Physics, to be published by Elsevier. Covers kinks & breathers, sigma-models & Skyrmions, abelian-Higgs vortices, monopoles, Yang-Mills instantons, and Q-balls.
We provide a review of non-topological solitonic solutions arising in theories with a complex scalar field and global or gauge $U(1)$-symmetry. It covers Q-balls, homogeneous charged scalar condensates, and nonlinear localized holes and bulges in a classically stable condensate. A historical overview is followed by the discussion of properties of solutions, including their stability, from different perspectives. Solitons in models with additional massive degrees of freedom are also revisited, and their relation to one-field Q-balls is showed. We also discuss theories with a gauge field giving …
Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for $SO(N)$ vector 4-point functions in general dimension $D$. In the large $N$ limit, upper bounds on the scaling dimensions of the lowest $SO(N)$ singlet and traceless symmetric scalars interpolate between two solutions at $Δ=D/2-1$ and $Δ=D-1$ via generalized free field th…
In this paper, we study gauged solutions associated to a massive vector field representing a spin-one condensate, namely the Proca field. We focus on regular spherically-symmetric solutions which we construct either using a self-interaction potential or general relativity in order to glue the solutions together. We start generating non-gravitating solutions, so-called, Proca Q-balls and charged Proca Q-balls. Then, we turn-on backreaction on the metric, allowing gravity to hold together the Proca condensate, to study the so-called Proca stars, charged Proca stars, Proca Q-stars and charged Pro…
We present rigid supersymmetric backgrounds for three-dimensional N=2 supersymmetric gauge theories, comprising a two-parameter U(1)xU(1)-invariant deformed three-sphere, and their gravity duals. These are described by supersymmetric solutions of four-dimensional N=2 gauged supergravity with a self-dual metric on the ball and different instantons for the graviphoton field. We find two types of solutions, distinguished by their holographic free energies. In one type the holographic free energy is constant, whereas in another type it depends in a simple way on the parameters and is generically c…
We present a toy model that exhibits clash-of-symmetries style Higgs field kink configurations in a Randall-Sundrum-like spacetime. The model has two complex scalar fields Phi_{1,2}, with a sextic potential obeying global U(1)xU(1) and discrete Phi_1 <--> Phi_2 interchange symmetries. The scalar fields are coupled to 4+1 dimensional gravity endowed with a bulk cosmological constant. We show that the coupled Einstein-Higgs field equations have an interesting analytic solution provided the sextic potential adopts a particular form. The 4+1 metric is shown to be that of a smoothed-out Randall-Sun…
We review the current status of the problem of constructing classical field theory solutions describing stationary vortex rings in Minkowski space in 3+1 dimensions. We describe the known up to date solutions of this type, such as the static knot solitons stabilized by the topological Hopf charge, the attempts to gauge them, the anomalous solitons stabilized by the Chern-Simons number, as well as the non-Abelian monopole and sphaleron rings. Passing to the rotating solutions, we first discuss the conditions insuring that they do not radiate, and then describe the spinning $Q$-balls, their twis…
