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Consider a classical (1+1)-dimensional oscillon of small amplitude $\epsilon$. To all orders in $\epsilon$, the oscillon solution is exactly periodic. We study small perturbations of such periodic configurations. These perturbations are themselves periodic up to a monodromy matrix. We explicitly find the eigenvectors of the monodromy matrix, which are the analogues of normal modes for oscillons. Dashen, Hasslacher and Neveu used such eigenvectors to quantize the sine-Gordon breather, and we suspect that they will be necessary to quantize the oscillon. Our results, regardless of the chosen model, suggest that low amplitude oscillons do not reflect small amplitude radiation., Comment: 31 pages, 4 PDF figures

Bosonic stars represent a hypothetical exotic type of compact stellar objects that could be observed from the gravitational signal of coalescing binaries in current and future gravitational wave detectors. There are two main families of bosonic stars, which depend on the nature that governs the particles that build them: Einstein-Klein-Gordon and Proca Stars. We study the multipolar structure for both families of rotating objects, using realistic potentials with the aim of finding possible universal relations and, thus, a method that allows us to distinguish between these and other compact objects in the gravitational wave paradigm. We also show how certain relevant observables can be obtained for these hypothetical but well-motivated astrophysical objects., Comment: 23 pages, 22 figures. We made some corrections

We show that coupling the $\textrm{SU}(2)$-valued Skyrme field to the $\rho$-meson solves the long-standing issue of (in)compressibility in the solitonic Skyrme model. Even by including only one $\rho\pi$ interaction term, motivated by a holographic-like reduction of Yang-Mills action by Sutcliffe, reduces the compression modulus from $K_0 \simeq 1080$ MeV, in the massive Skyrme model, to $K_0\simeq 351$ MeV., Comment: 20 pages, 5 figures

We show that any nonlinear field theory giving rise to static solutions with finite energy like, e.g., topological solitons, allows us to derive a continuous infinity of integral identities which any such solution has to obey. These integral identities can always be understood as being generated by field transformations and their related Noether currents. We also explain why all integral identities generated by coordinate transformations become trivial for Bogomolnyi-Prasad-Sommerfield (BPS) solitons, i.e., topological solitons which saturate a topological energy bound. Finally, we consider applications of these identities to a broad class of nonlinear scalar theories, including the Skyrme model. More concretely, we find nontrivial integral identities that can be seen as model-independent relations between certain physical properties of the solitons in such theories, and we comment on the possible connection between these new relations and those already found in the context of astrophysical compact objects. We also demonstrate the usefulness of said identities to estimate the precision of the numerical calculation of soliton observables., Comment: 29 pages, LaTex, v3: improvements in the discussion of the BPS case and the conclusions

In this article we study properties of isospin asymmetric nuclear matter in the generalized Skyrme model. This is achieved by canonically quantizing the isospin collective degrees of freedom of the recently found multi-wall skyrmion crystal. We obtain, for the first time, an equation of state from the Skyrme model which interpolates between infinite isospin asymmetric nuclear matter and finite isospin symmetric atomic nuclei. This enables us to describe neutron stars with crusts within the Skyrme framework. Furthermore, we observe that the symmetry energy tends to a constant value at zero density, which can be identified with the asymmetry coefficient in the semi-empirical mass formula for atomic nuclei. The symmetry energy also reveals a cusp in its structure below the nuclear saturation point $n_0$ at $n_*\sim 3n_0/4$. This cusp density point $n_*$ can be interpreted as the nuclear density whereby the infinite crystalline multi-wall configuration undergoes a phase transition to a finite isolated multi-wall configuration. Both of these observations are observed to be generic features of skyrmion crystals that tend asymptotically to somewhat isolated skyrmion configurations in the zero density limit. We find that the resulting neutron stars from our study agree quite well with recent NICER/LIGO observational data., Comment: 23 pages, 7 figures

Hertzberg has constructed a quantum oscillon that decays into pairs of relativistic mesons with a power much greater than the radiation from classical oscillon decay. This result is often construed as a proof that quantum oscillons decay quickly, and so are inconsequential. We apply a construction similar to Hertzberg's to the quantum kink. Again it leads to a rapid decay via the emission of relativistic mesons. However, we find that this is the decay of a squeezed kink state to a stable kink state, and so it does not imply that the quantum kink is unstable. We then consider a time-dependent solution, which may be an oscillon, and we see that the argument proceeds identically., Comment: 19 pages, no figures

A general review of the crystalline solutions of the generalized Skyrme model and their application to the study of cold nuclear matter at finite density and the Equation of State (EOS) of neutron stars is presented. For the relevant range of densities, the ground state of the Skyrme model in the three torus is shown to correspond to configurations with different symmetries, with a sequence of phase transitions between such configurations. The effects of nonzero finite isospin asymmetry are taken into account by the canonical quantization of isospin collective coordinates, and some thermodynamical and nuclear observables (such as the symmetry energy) are computed as a function of the density. We also explore the extension of the model to accommodate strange degrees of freedom, and find a first order transition for the condensation of kaons in the Skyrme crystal background in a thermodynamically consistent, non-perturbative way. Finally, an approximate EOS of dense matter is constructed by fitting the free parameters of the model to some nuclear observables close to saturation density, which are particularly relevant for the description of nuclear matter. The resulting neutron star mass-radius curves already reasonably satisfy current astrophysical constraints., Comment: 54 pages, 28 figures, review

Boson Stars are, at present, hypothetical compact stellar objects whose existence, however, could resolve several enigmas of current astrophysics. If they exist, either as independent astrophysical entities or as a matter admixture of more standard compact stars, then their imprints can probably be observed in the not-too-distant future from the gravitational signal of coalescing binaries in current and future GW detectors. Here we show that the multipole moments of rotating boson stars obey certain universal relations, valid for a broad set of models and various states in terms of the \textit{harmonic indices}. These universal relations are equivalent to a kind of no-hair theorem for this exotic matter, allowing to map these universal (i.e. model independent) multipoles to an equally universal gravitational field around the stellar object. Further, the multipole moments can be related to observable astrophysical quantities., Comment: 17 pages, 21 figures. We have added some references

We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the mutual distance and the position of the center of mass) is of a wormhole type, whose throat shrinks to a point for symmetric kinks. In this case, a singularity is formed. For non-zero momentum, it prohibits solutions where the solitons pass through each other. We show that this unphysical feature can be cured by enlarging the dimension of the moduli space, e.g., by the inclusion of internal modes.

We address the possibility of the appearance of a charged kaon condensate in neutron star cores described within a generalized Skyrme model. Our treatment of strange degrees of freedom is based on the Bound State Approach by Callan and Klebanov, which allows to obtain an in-medium effective potential for the $s$-wave kaon condensate. We predict the onset of kaon condensation at a certain threshold density - whose value depends on the parameters of the model, and ranges between 1.5 and 2.5 times saturation density -, and obtain both the particle fractions and equation of state for dense matter in the kaon condensed phase. Finally, we discuss the effect of such condensates on the mass-radius curves and other observable properties of neutron stars with kaon condensed cores., Comment: 17 pages, 8 figures

We show that a spectral wall, i.e., an obstacle in the dynamics of a bosonic soliton, which arises due to the transition of a normal mode into the continuum spectrum, exists after coupling the original bosonic model to fermions. This spectral wall can be experienced if the boson or fermion field is in an excited state. Furthermore, while passing through a spectral wall, an incoming kink-fermion bound state can be separated into purely bosonic kink, which continues to move to spatial infinity and a fermionic cloud that spreads in the region before the wall.

Boson stars represent a hypothetical exotic type of compact stellar object that may be observed from the gravitational signal of coalescing binaries in current and future GW detectors. In this work we show that the moment of inertia $I$, the (dimensionless) angular momentum $\chi$ and the quadrupole moment $Q$ of rotating boson stars obey a universal relation, valid for a wide set of boson star models. Further, the obtained $I-\chi-Q~$ relation clearly differs from its famous neutron star counterpart, providing us with an unequivocal diagnostic tool to distinguish boson stars from ordinary compact stars or other celestial bodies in GW observations. Such universal (i.e. model-independent) relations also provide a useful tool to probe the strong gravity regime of general relativity and to constrain the equation of state of matter inside compact stars., Comment: 12 pages, 20 figures. In this current version, we have changed the format and the Appendix

A spectral wall is a surface in a moduli space of classically BPS solitons where an internal excitation crosses the continuum mass threshold. It has recently been shown that spectral walls in classical field theory repel solitons whose corresponding internal excitations are excited. We investigate, for the first time, the fate of spectral walls in a quantum theory, calculating the instantaneous acceleration of a wave packet of classically BPS antikinks in the presence of an impurity. We find that, in the quantum theory, the antikinks are repelled even when the bound mode is not excited. Perhaps due to this repulsive force, the dramatic classical effects of the spectral wall are not seen in our quantum calculation., Comment: 34 pages, 9 figures

The canonical quantization method for collective coordinates in crystalline configurations of the generalized Skyrme model is applied in order to find the quantum ground state of Skyrmion crystals and study the quantum corrections to the binding energy resulting from the isospin degrees of freedom. This leads to a consistent description of asymmetric nuclear matter within the Skyrme framework and allows us to compute the symmetry energy of the Skyrmionic crystal as a function of the baryon density, and to compare with recent observational constraints., Comment: V3: 16 pages, 4 figures. Some typos corrected. Minor changes in figures 1, 3 and 4. References added

Skyrmion crystals are the field configurations which minimize the energy per baryon in the infinitely large topological charge sector of the Skyrme model, at least for sufficiently high density. They are, therefore, an important tool to describe the ground state of cold, symmetric nuclear matter at high density regimes. In this work, we analyze different crystalline phases and the existence of phase transitions between them within the generalized Skyrme model, with the ultimate goal of describing symmetric nuclear matter in a wide regime of densities. Furthermore, we propose a new energy-minimizing phase for densities lower than the nuclear saturation point ($n_0$) which also presents a good qualitative behavior in the zero density limit, thereby improving the description of strongly interacting matter in the region $n

First proposed in 2013 by Yagi and Yunes, the quasi-universal \emph{I-Love-Q relations} consist of a set of relations between the moment of inertia, the spin-induced quadrupole moment and the electric quadrupolar tidal deformability of neutron stars which are independent of the Equation of State (EoS) within an accuracy of $\sim1\%$. In this work, we show that these relations hold for different Skyrme-based nuclear matter EoS and also for the star-like solutions of different Einstein-BPS-Skyrme-models, some of which do not even present a barotropic equation of state. Further, other quasi-universal relations are analyzed, and together with recent GW observations, we use them to select the generalized Skyrme model that better reproduces observations. Our results reaffirm both the universality of the \emph{I-Love-Q} relations and the suitability of generalized Skyrme models to describe nuclear matter inside neutron stars., Comment: 23 pages, 11 figures

We propose a new equation of state for nuclear matter based on a generalized Skyrme model which is consistent with all current constraints on the observed properties of neutron stars. This generalized model depends only on two free parameters related to the ranges of pressure values at which different submodels are dominant, and which can be adjusted so that mass-radius and deformability constraints from astrophysical and gravitational wave measurements can be met. Our results support the Skyrme model and its generalizations as good candidates for a low energy effective field-theoretic description of nuclear matter even at extreme conditions such as those inside neutron stars., Comment: 8 pages, 3 figures. Minor typos fixed. Version accepted for publication in Phys. Lett. B

We investigate the role of pressure in a class of generalised Skyrme models. We introduce pressure as the trace of the spatial part of the energy-momentum tensor and show that it obeys the usual thermodynamical relation. Then, we compute analytically the mean-field equation of state in the high and medium pressure regimes by applying topological bounds on compact domains. The equation of state is further investigated numerically for the charge one skyrmions. We identify which term in a generalised Skyrme model is responsible for which part in the equation of state. Further, we compare our findings with the corresponding results in the Walecka model., Comment: 29 pages, 8 figures; updated to match published version in Phys. Rev. C

We argue that the conventional method to calculate the OPE coefficients in the strong coupling limit for heavy-heavy-light operators in the N=4 Super-Yang-Mills theory has to be modified by integrating the light vertex operator not only over a single string worldsheet but also over the moduli space of classical solutions corresponding to the heavy states. This reflects the fact that we are primarily interested in energy eigenstates and not coherent states. We tested our prescription for the BMN vacuum correlator, for folded strings on $S^5$ and for two-particle states. Our prescription for two-particle states with the dilaton leads to a volume dependence which matches exactly to the structure of finite volume diagonal formfactors. As the volume depence does not rely on the particular light operator we conjecture that symmetric OPE coefficients can be described for any coupling by finite volume diagonal form factors., Comment: 32 pages, 1 figure; v2: small corrections including signs, references added

We consider operators in N=4 SYM theory which are dual, at strong coupling, to classical strings rotating in S^5. Three point correlation functions of such operators factorize into a universal contribution coming from the AdS part of the string sigma model and a state-dependent S^5 contribution. Consequently a similar factorization arises for the OPE coefficients. In this paper we evaluate the AdS universal factor of the OPE coefficients which is explicitly expressed just in terms of the anomalous dimensions of the three operators., Comment: 49 pages, 3 figures; v.2 references corrected; v3: corrected discussion in section 5, results unchanged

Recently it has been pointed out that the "Faddeev-Niemi" equations that correspond to the Yang-Mills equations of motion for a decomposed gauge field, can have solutions that obey the standard Yang-Mills equations with a source term. Here we present a general class of such gauge field configurations., Comment: 4 pages; v2 typos corrected

We explore how to compute, classically at strong coupling, correlation functions of local operators corresponding to classical spinning string states. The picture we obtain is of `fattened' Witten diagrams, the evaluation of which turns out to be surprisingly subtle and requires a modification of the naive classical action due to a necessary projection onto appropriate wave functions. We examine string solutions which compute the simplest case of a two-point function and reproduce the right scaling with the anomalous dimensions corresponding to the energies of the associated spinning string solutions. We also describe, under some simplifying assumptions, how the spacetime dependence of a conformal three-point correlation function arises in this setup., Comment: 27 pages, 3 figures; v2: references and comments added.

We briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions, it turns out that these conservation laws are, in fact, generated by a class of geometric target space transformations, namely the volume-preserving diffeomorphisms. We classify the possible conservation laws of field theories for the case of a three-dimensional target space. Further, we discuss some explicit examples., Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

QCD motivated effective models coupled with the cosmological dilaton field are analyzed. It is shown that all models possess confining solutions with the linear potential of confinement even thought such solutions are not observed in the original effective theory. In case of the Pagels-Tomboulis model analytical solutions are explicit found., Comment: 10 pages