String Solutions Research Articles

Presence of Exotic Matter in Levia-Civita and Cosmic String Solutions

Presence of Exotic Matter in Levia-Civita and Cosmic String Solutions

Rotating AdS3× S3 and dyonic strings from 3-dimensions

We make a general Killing spinor analysis of a particular D = 3, N = 4 gauged supergravity that comes from a consistent S3 reduction of D = 6, N = (1, 0) supergravity coupled to a single chiral tensor multiplet. We then focus on its supersymmetric solutions with a null Killing vector and find three new ones. Two of these, namely the null warped AdS3 (also known as the Schrödinger spacetime) and the charged domain wall solutions, admit non-trivial gauge fields which give rise to rotating solutions in 6-dimensions. The uplift of the first one produces an interesting AdS3 × S3 background with a non-trivial rotation in the U(1) fiber direction of the S3 which retains the Schrödinger scale invariance that the seed solution has. The second one leads to the well-known rotating dyonic string solution. Finally, the uplift of the third one, which is a domain wall solution with no gauge fields, results in a distribution of dyonic strings.

A perturbative approach to the non-relativistic string spectrum

In this letter we use a perturbative approach to find the spectrum of non-relativistic strings in the String Newton-Cartan (SNC) AdS5×S5 spacetime. We perturb the bosonic sector of the action around a BMN-like folded string solution in light-cone gauge. We find strong evidence that the theory is described by a combination of massive and massless free fields in an anti-de Sitter background by showing that interaction terms up to six scalars vanish after field redefinitions.

An existence theorem for generalized Abelian Higgs equations and its application

In this note, we construct self-dual vortices and cosmic strings from the generalized Abelian Higgs theory in which the Higgs potential is a polynomial whose degree depends on the number m . When | m | > 0 , we obtain sharp existence theorems for vortices and strings corresponding to the absence and presence of gravity, respectively, over the whole plane. In the absence of gravity, we prove the existence of vortices by using a monotone iteration method. When gravity is taken into account, a regularization method and a fixed-point theorem are used to show that multiple string solutions exist under a sufficient condition imposed only on the total number of strings. In addition, a series of properties with respect to vortices and strings have also been established.

Electroweak strings in the standard model

We argue that the existence of the electroweak monopole predicts the existence of the electroweak string in the standard model made of monopole–antimonopole pair separated infinitely apart, which carry the quantized magnetic flux 4πn/e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4 \\pi n/e$$\\end{document}. We show how to construct such quantized magnetic flux string solution. Our result strongly indicates that genuine fundamental electromagnetic string could exist in nature which could actually be detected. We discuss the physical implications of our result in cosmology.

Cosmic Strings from Thermal Inflation

Thermal inflation was proposed as a mechanism to dilute the density of cosmological moduli. Thermal inflation is driven by a complex scalar field possessing a large vacuum expectation value and a very flat potential, called a “flaton”. Such a model admits cosmic string solutions, and a network of such strings will inevitably form in the symmetry breaking phase transition at the end of the period of thermal inflation. We discuss the differences of these strings compared to the strings which form in the Abelian Higgs model. Specifically, we find that the upper bound on the symmetry breaking scale is parametrically lower than in the case of Abelian Higgs strings, and that the lower cutoff on the string loop distribution is determined by cusp annihilation rather than by gravitational radiation (for the value of the transition temperature proposed in the original work on thermal inflation).

Dynamical simulations of colliding superconducting strings

We study the collisions of elastic superconducting strings, also referred to as current-carrying strings, formed in a U local(1) × U global(1) field-theory model, using three-dimensional numerical field-theoretic simulations. The breaking of U local (1) leads to string formation via the Higgs mechanism, while the scalar field of the second U global(1) carries the current, which condenses onto the string. We construct straight and static superconducting string solutions numerically and identify the regions in which they exist in the model parameter space. We then perform dynamical simulations for colliding superconducting strings with various collision angles and collision velocities. We explore the kinematic parameter space for six sets of model parameters characterising the coupling between the two scalar fields and the current on the string. The final states of the strings (after the collision) are reported diagrammatically. We classify them into four categories: (i) regular intercommutation, (ii) double intercommutation, (iii) bound state, and (iv) expanding string solution. We find that the outcome of the collision process is the regular intercommutation of the colliding strings in most of the kinematic parameter space while they form bound states for small velocities and small angles. We also find that the strings undergo two successive intercommutations and, therefore, pass through one other in a small region corresponding to relatively small angles and velocities of order c/2. The string structure breaks down when there is a relatively large coupling between the two scalar fields, even if each string is stable before the occurrence of the collision.

Boosted rotating dyonic strings in Salam-Sezgin model

We show that the bosonic sector of the N = (1, 0), 6D Salam-Sezgin gauged supergravity model possesses a T-duality symmetry upon a circle reduction to D = 5. We then construct a simple magnetic rotating string solution with two equal angular momenta. Applying the T-duality transformation to this solution, we obtain the general boosted rotating dyonic black string solutions whose global structures and thermodynamic quantities are also analyzed. Owing to the fact that the solutions are not asymptotically flat, we find that there are two distinct globally-different non-extremal solutions with two different sets of thermal dynamic variables, with both satisfying the thermodynamic first law and the corresponding Small relations. However, their BPS limit becomes the same and we show that it preserves one quarter of supersymmetry by directly solving the corresponding Killing spinor equations.

Behaviors of black holes and black strings in M-theory on Calabi–Yau manifolds

In this work, we reconsider the study of black holes and black strings in the compactification of M-theory on a Calabi–Yau three-fold, considered as a complete intersection of hypersurfaces in a product of weighted projective spaces given by [Formula: see text]. Using the [Formula: see text] supergravity formalism in five dimensions, we examine the BPS and non-BPS solutions by wrapping M-branes on appropriate cycles in such a Calabi–Yau geometry. For the black hole case, we compute certain thermodynamical quantities. In particular, we calculate the entropy taking a maximal value corresponding to the ordinary projective space [Formula: see text] with [Formula: see text]. Using extended black hole entropies, we evaluate the temperature involving a minimal value for [Formula: see text]. Then, we approach the stability of the non-BPS black holes via the recombination factor. In the allowed electric charge regions, we show that such states are unstable. For the black string solutions, we calculate the tension taking a minimal value corresponding to [Formula: see text]. Computing the recombination factor, we show that the associated non-BPS black string states are stable in the allowed magnetic charge regions of the moduli space.

Cosmic strings arising in a self-dual Abelian Higgs model

In this note we construct self-dual cosmic strings from an Abelian Higgs model in two-dimension with a polynomial formation of the potential energy density. By integrating the Einstein equations, we obtain an equivalent form to the sources, which is a nonlinear elliptic equation with singularities and complicated exponential terms. We prove the existence of a solution governing strings in the broken symmetry category on the whole plane, and the multiple string solutions are valid under a sufficient condition imposed only on the total number of strings. The technique of upper–lower solutions and the method of regularization are employed to show the existence of a solution when there are at least two distant string centers. When all the string centers are identical, a fixed-point theorem is used to study the properties of the nonlinear elliptic equation. Finally, we establish the sharp asymptotic estimate for the solutions at infinity and derive the dependence of the total gravitational curvature on the string number.

Gauged global strings

We investigate the string solutions and cosmological implications of the gauge U(1)Z × global U(1)PQ model. With two hierarchical symmetry-breaking scales, the model exhibits three distinct string solutions: a conventional global string, a global string with a heavy core, and a gauge string as a bound state of the two global strings. This model reveals rich phenomenological implications in cosmology. During the evolution of the universe, these three types of strings can form a Y-junction configuration. Intriguingly, when incorporating this model with the QCD axion framework, the heavy-core global strings emit more axion particles compared to conventional axion cosmic strings due to their higher tension. This radiation significantly enhances the QCD axion dark matter abundance, thereby opening up the QCD axion mass window. Consequently, axions with masses exceeding ~ 10−5 eV have the potential to constitute the whole dark matter abundance. Furthermore, in contrast to conventional gauge strings, the gauge strings in this model exhibit a distinctive behavior by radiating axions.

Black strings in asymptotically safe gravity

In this paper, we study black strings in asymptotic safety gravity (ASG) scenario. The ASG approach is introduced by implementing gravitational and cosmological running coupling constants directly in the black string metric. We calculate the Hawking temperature, entropy, and heat capacity of the improved black string metric in two cases: considering the cosmological constant fixed in some fixed point and the general case where both Newton’s constant and cosmological constant are improved. For the identification of the scale moment we used an general inverse law setting k(r) ∼ 1/r n . We show that improving only the Newton’s constant the problem of singularity is solved for the identifications with n > 1. However, if the cosmological constant is also running the singularity persists in the solution. Also, we show that the ASG effects predicts the presence of a remnant mass in the final evaporation process. Besides that, a logarithmic correction is observed in the entropy. However, a running cosmological constant introduces new correction terms to the entropy beyond that. We show that the improved black string solution remains stable, as in the usual case. Phase transitions are not observed in both cases studied here.

Self–dual solutions of a field theory model of two linked rings

In this work the connection established in [7,8] between a model of two linked polymers rings with fixed Gaussian linking number forming a 4-plat and the statistical mechanics of non-relativistic anyon particles is explored. The excluded volume interactions have been switched off and only the interactions of entropic origin arising from the topological constraints are considered. An interpretation from the polymer point of view of the field equations that minimize the energy of the model in the limit in which one of the spatial dimensions of the 4-plat becomes very large is provided. It is shown that the self-dual contributions are responsible for the long-range interactions that are necessary for preserving the global topological properties of the system during the thermal fluctuations. The non self-dual part is also related to the topological constraints, and takes into account the local interactions acting on the monomers in order to prevent the breaking of the polymer lines. It turns out that the energy landscape of the two linked rings is quite complex. Assuming as a rough approximation that the monomer densities of half of the 4-plat are constant, at least two points of energy minimum are found. Classes of non-trivial self-dual solutions of the self-dual field equations are derived. One of these classes is characterized by densities of monomers that are the squared modulus of holomorphic functions. The second class is obtained under some assumptions that allow to reduce the self-dual equations to an analog of the Gouy-Chapman equation for the charge distribution of ions in a double layer capacitor. In the present case, the spatial distribution of the electric potential of the ions is replaced by the spatial distribution of the fictitious magnetic fields associated with the presence of the topological constraints. In the limit in which two of the spatial dimensions are large in comparison with the third one, we provide exact formulas for the conformations of the monomer densities of the 4-plat by using the elliptic, hyperbolic and trigonometric solutions of the sinh-Gordon and cosh-Gordon equations which have been used for instance in the construction of classical string solutions in AdS3 and dS3 [9].

Dyonic black strings and the charge lattice in Salam-Sezgin model

We obtain a class of dyonic black string solutions in 6D Salam-Sezgin model. We then calculate various thermodynamic quantities associated with this solution. Interestingly, for the thermodynamic quantities to be well defined, the temperature is bounded from above. However, the mass and entropy can still grow without any upper bound, reaching infinity at the maximal temperature. The quantization condition obeyed by various charges is also analyzed. In particular, we find that the Dirac quantization condition selects one particular sign choice for the magnetic string charges.

Stable non-BPS black holes and black strings in five dimensions

In this paper we study black hole and black string solutions in five dimensional N=2 supergravity theories arising from the compactification of M-theory on Calabi-Yau manifolds. In particular, we consider explicit examples of three parameter Calabi-Yau manifolds which are obtained as hypersurfaces in toric varieties. Using the attractor mechanism, we obtain Bogomol’nyi-Prasad-Sommerfield (BPS) as well as non-BPS black holes in these compactified supergravity theories. We also consider the black string solutions in these models. We analyze the stability of these extremal black brane configurations by computing the recombination factor. We find multiple stable non-BPS attractor solutions in some of these models. Published by the American Physical Society 2024

Small black string thermodynamics

We consider a cylindrically symmetric solution for the field equations of Einstein-Hilbert action with a negative cosmological constant in four dimensions. The small statistical fluctuation in the equilibrium thermodynamics of the black string solution is investigated. The small black string under the influence of small statistical fluctuation also follows the first law of thermodynamics. The behaviour of equation of states for black string changes significantly due to the fluctuation. The fluctuation causes instability to the small-sized black string only. Assuming the black string is fluid, the compressibility of the black string is inversely proportional to the fluctuation parameter.

Comprehensive study of cylindrical Levi-Civita and cosmic string solutions in Rastall theory of gravity

In this manuscript, the main aim is to investigate the cylindrically symmetric solutions in a well known Rastall theory of gravity. For this purpose, we consider the cylindrically symmetric space–time to discuss the cylindrical solutions in some realistic regions. First, we investigate four distinct cases of exact solutions using the field equations of Rastall theory of gravity. Furthermore, we set some suitable values of the Rastall coupling constant (λ) for the investigation of well-known Levi-Civita and cosmic string solutions. The Energy conditions are also investigated for all different cases and observed that null energy conditions are violated, which is the indication of the existence of cylindrical wormholes.

Black String Solutions in Rainbow Gravity

In this paper, we studied black string solutions under the consideration of rainbow gravity. We analytically obtained the solution for four-dimensional black strings in terms of the functions f(E/Ep) and g(E/Ep) that sets the energy scale where the rainbow gravity becomes relevant. We also obtained the Hawking temperature for the black string, from which we can see that the rainbow functions play the role of increasing or decreasing the Hawking temperature for a given horizon radius depending on the choice of such rainbow functions. We computed the entropy, specific heat and free energy for the black string. The entropy and specific heat exhibit a rainbow dependence, whereas the free energy is not modified by the rainbow functions. Finally, we studied the effects of rainbow gravity in the orbits of massive and massless particles around a black string. We could verify that neither massive nor massless particles exhibit stable orbits around a black string in the scenario of rainbow gravity for any configuration of rainbow functions.

Fluid model of a black hole-string transition

A fluid model of self-gravitating strings is proposed. It is expected that black holes turn into strings around the end of black hole evaporation. The transition will occur near the Hagedorn temperature. After the transition, strings would form a bound state by the self-gravitation. Horowitz and Polchinski formulated a model of self-gravitating strings by using winding strings wrapping on the Euclidean time circle [arXiv:hep-th/9707170]. In this paper, we first show that winding strings in the Horowitz-Polchinski model approximately behave as a perfect fluid. Then, we solve the Einstein equation for the fluid of winding strings. Our solution reproduces behaviors of the self-gravitating string solution in the Horowitz-Polchinski model near the Hagedorn temperature, while it approaches the Schwarzschild black hole at low temperatures. Thus, our fluid model of self-gravitating strings gives a description of the transition between black holes and strings.

New supersymmetric AdS_5 black strings from 5D N=4 gauged supergravity

We find a large class of new supersymmetric AdS_5 black strings from five-dimensional N=4 gauged supergravity coupled to five vector multiplets with SO(2)_Dtimes SO(3)times SO(3) gauge group. These solutions have near horizon geometries of the form AdS_3times Sigma ^2 for Sigma ^2 being a two-sphere (S^2) or a hyperbolic space (H^2). There are four supersymmetric AdS_5 vacua with N=4 and N=2 supersymmetries. By performing topological twists along Sigma ^2 with SO(2)times SO(2)_{text {diag}} and SO(2)_{text {diag}} gauge fields, we find a number of AdS_3times Sigma ^2 fixed points describing near horizon geometries of black strings in asymptotically AdS_5 spaces. Most of the solutions take the form of AdS_3times H^2 with only one being AdS_3times S^2 preserving SO(2)_{text {diag}} symmetry. We also give the corresponding black string solutions interpolating between asymptotically locally AdS_5 vacua and the near horizon AdS_3times Sigma ^2 geometries. There are a number of solutions flowing from one, two or three AdS_5 vacua to an AdS_3times Sigma ^2 fixed point. These solutions can also be considered as holographic RG flows across dimensions from N=2 and N=1 SCFTs in four dimensions to two-dimensional SCFTs with N=(2,0) or N=(0,2) supersymmetry.