String Solutions Research Articles

On the Longest Common Cartesian Substring Problem

AbstractA Cartesian tree is associated with a string of numbers and is structured as a heap from which the original string can be recovered. Although Cartesian trees have been introduced 40 years ago, the Cartesian tree matching problem appeared very recently. It consists in finding all substrings of given text, which have the same Cartesian tree as that of a given pattern. In this paper, we address the problem of computing the longest common Cartesian substrings of two strings and present three methods for such problem. Our first method is based on a classical suffix tree construction and solves the problem in randomized linear time and linear space, although the space overhead is quite prohibitive in the case of large strings. Our second solution is based on classical dynamic programming, and our third solution is based on a constructive approach. Both of them run in quadratic worst case time but are more space economical in practice. From our experimental results, it turns out that our second solution runs faster than the standard suffix tree solution for short strings, whereas our third solution is more suitable for large strings, when storing a full suffix tree becomes prohibitive.

\u03b1\u2032-corrections to near extremal dyonic strings and weak gravity conjecture

We construct non-extremal dyonic string solutions in 6D minimal supergravity where the leading higher derivative corrections arise from either the type IIA string theory compactified on K3 or the heterotic string theory compactified on 4-torus. The thermodynamical quantities and Euclidean actions of the strings are computed. In the near extremal regime, we calculate the force felt by a probe fundamental string in the background of the macroscopic dyonic string with leading α′ corrections. We find that in both the IIA and heterotic setups, away from extremality, the attractive force overwhelms the repulsive force. However, close to extremality, the α′ corrections can reduce the attractive force in the isoentropic process, where the charges are fixed. This feature may be used as a new constraint for supergravity models with consistent quantum gravity embedding, in cases where the extremal limit coincides with the BPS limit and the higher derivative corrections do not affect the mass-to-charge ratio. By contrast, the α′ corrections can enhance the attractive force in the isothermal or isoenergetic processes.

N-spike string in AdS3\xd7 S1 with mixed flux

Sigma model in AdS3× S3 background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for N-spike strings moving in AdS3× S1 with angular momentum J in S1 ⊂ S5 in the presence of mixed flux. We observe that the addition of angular momentum J or winding number m results in the spikes getting rounded off and not end in cusp. The presence of flux shows no alteration to the rounding-off nature of the spikes. We also consider the large N-limit of N-spike string in AdS3× S1 in the presence of flux and show that the so-called Energy-Spin dispersion relation is analogous to the solution we get for the periodic-spike in AdS3− pp-wave ×S1 background with flux.

Comments on axions, domain walls, and cosmic strings

Axions have for some time been considered a plausible candidate for dark matter. They can be produced through misalignment, but it has been argued that when inflation occurs before a Peccei-Quinn transition, appreciable production can result from cosmic strings. This has been the subject of extensive simulations. But there are reasons to be skeptical about the possible role of axion strings. We review and elaborate on these questions, and argue that parametrically strings are already accounted for by the assumption of random misalignment angles. We review and elaborate on these questions, and provide several qualitative arguments that parametrically strings are already accounted for by the assumption of random misalignment angles. The arguments are base on considerations of the collective modes of the string solutions, on computations of axion radiation in particular models, and reviews of simulations.

Scaling solutions of wiggly cosmic strings

Cosmic strings may have formed in the early universe due to the Kibble mechanism. While string networks are usually modeled as being of Nambu-Goto type, this description is understood to be a convenient approximation, which neglects the typically expected presence of additional degrees of freedom on the string worldsheet. Previous simulations of cosmic strings in expanding universes have established beyond doubt the existence of a significant amount of short-wavelength propagation modes (commonly called wiggles) on the strings, and a wiggly string extension of the canonical velocity-dependent one-scale model has been recently developed. Here we improve the physical interpretation of this model, by studying the possible asymptotic scaling solutions of this model, and in particular how they are affected by the expansion of the universe and the available energy loss or transfer mechanisms -- e.g., the production of loops and wiggles. In addition to the Nambu-Goto solution, to which the wiggly model reduces in the appropriate limit, we find that there are also solutions where the amount of wiggliness can grow as the network evolves or, for specific expansion rates, become a constant. Our results show that full scaling of the network, including the wiggliness, is much more likely in the matter era than in the radiation era, which is in agreement with numerical simulation results.

Joint optimal mission aborting and replacement and maintenance scheduling in dual-unit standby systems

This paper models a dual-unit standby system with non-identical, reusable units that perform the mission task alternatively according to a pre-specified replacement and maintenance schedule (RMS). When one unit is online operating, the other unit undergoes maintenance of a particular type determined by the RMS. In the case of one unit failing and the amount of work completed before the unit failure not exceeding a threshold value, the system aborts the primary mission and immediately activates a rescue procedure to avert or alleviate the risk of system failure and thus any associated damages. Both the RMS and the mission abort threshold parameter adopted can affect the mission success probability (MSP) significantly. This paper makes contributions by formulating and solving a constrained optimization problem that determines the joint RMS and mission abort policy, maximizing the MSP while meeting a constraint on the damage avoidance probability (DAP). A probabilistic method is suggested to evaluate the MSP and DAP of the considered system. Based on the string solution representation designed in this work, the genetic algorithm is then implemented to solve the optimization problem. A case study on a dual-pump liquid transfer system used in the chemical reactor is conducted to demonstrate the proposed model, and optimization solutions balancing MSP and DAP.

Decoding the Spin-Matrix limit of strings on AdS5 × S5

In this Letter, we explore nonrelativistic string solutions in various subsectors of the SU(1,2|3) SMT strings that correspond to different spin groups and satisfy the respective BPS bounds. In particular, we carry out an explicit analysis on rotating string solutions in the light of recently proposed SMT limits. We explore newly constructed SMT limits of type IIB (super) strings on AdS5×S5 and estimate the corresponding leading order stringy corrections near the respective BPS bounds.

Electroweak axion string and superconductivity

We study the axion strings with the electroweak gauge flux in the DFSZ axion model and show that these strings, called the electroweak axion strings, can exhibit superconductivity without fermionic zeromodes. We construct three types of electroweak axion string solutions. Among them, the string with W-flux can be lightest in some parameter space, which leads to a stable superconducting cosmic string. We also show that a large electric current can flow along the string due to the Peccei-Quinn scale much higher than the electroweak scale. This large current induces a net attractive force between the axion strings with the same topological charge, which opens a novel possibility that the axion strings form Y-junctions in the early universe.

Multispin magnons from Spin-Matrix strings on AdS5 × S5

The present Letter derives multispin nonrelativistic magnon spectrum considering various near BPS corners within SU(1,2|3) Spin-Matrix theory (SMT) limit of strings on AdS5×S5. In particular, we focus on some typical rotating string solutions those correspond to two spin as well as three spin configurations in the bulk and identify the associated nonrelativistic magnon like excitations in these models.

Black string in massive gravity

We will analyze a black string in dRGT massive theory of gravity. Considering different approaches, we will study the critical behavior, phase transition and thermal stability for such a black string solution. We will analyze the Van der Waals behavior for this system, and observe that the Van der Waals behavior depends on mass of graviton. We will also analyze the geometrical thermodynamics of black strings using different thermodynamic metrics. It will be observed that the thermal fluctuations can modify the behavior of this system. We will explicitly analyze the effects of such fluctuations on the stability of this black string solutions. This will be done using the Hessian matrix for this system.

Strong Bound on Canonical Ultralight Axion Dark Matter from the Lyman-Alpha Forest.

We present a new bound on the ultralight axion (ULA) dark matter mass m_{a}, using the Lyman-alpha forest to look for suppressed cosmic structure growth: a 95% lower limit m_{a}>2×10^{-20} eV. This strongly disfavors (>99.7% credibility) the canonical ULA with 10^{-22} eV<m_{a}<10^{-21} eV, motivated by the string axiverse and solutions to possible tensions in the cold dark matter model. We strengthen previous equivalent bounds by about an order of magnitude. We demonstrate the robustness of our results using an optimized emulator of improved hydrodynamical simulations.

Attractor mechanism and nonrenormalization theorem in 6D (1, 0) supergravity

We compute the macroscopic entropy of the supersymmetric rotating dyonic strings carrying linear momentum in 6D (1, 0) supergravity with curvature squared corrections. Our calculation is based on Sen's entropy function formalism applied to the near-horizon geometry of the string solution taking the form of an extremal Ban\ifmmode \tilde{}\else \~{}\fi{}ados-Teitelboim-Zanelli $\ifmmode\times\else\texttimes\fi{}{S}^{3}$. The final entropy formula states that the two independent supersymmetric completions of Riemann tensor squared contribute equally to the entropy. A further ${S}^{3}$ compactification of the 6D theory results in a matter coupled 3D supergravity model in which the quantization condition of the ${\mathrm{SU}(2)}_{R}$ Chern-Simons level implies the horizon value of the dilaton is not modified by higher derivative interactions beyond supersymmetric curvature squared terms.

Pulsating strings in Schr5 × T 1,1 background

The quest for extension of holographic correspondence to non-relativistic sectors naturally includes Schrödinger backgrounds and their field theory duals. In this paper we study the holography by probing the correspondence with pulsating strings. The case we consider is pulsating strings in five-dimensional Schrödinger space times five-torus T 1,1, which has as field theory dual a dipole CFT. First we find particular pulsating string solutions and then semi-classically quantize the theory. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT.

On the BTZ black hole and the spinning cosmic string

We review the Baňados–Teitelboim–Zanelli (BTZ) black hole solution in connection with the spinning string solution. We find a new exact solution, which can be related to the (2 + 1)-dimensional spinning point particle solution. There is no need for a cosmological constant, and so the solution can be up-lifted to (3 + 1) dimensions. The exact solution in a conformally invariant gravity model, where the space–time is written as $$g_{\mu \nu }=\omega ^2 {\tilde{g}}_{\mu \nu }$$ , is horizon free and has an ergo-circle, while $${\tilde{g}}_{\mu \nu }$$ is the BTZ solution. The dilaton $$\omega $$ determines the scale of the model. It is conjectured that the conformally invariant non-vacuum BTZ solution will solve the boundary and causality problems which one encounters in spinning cosmic string solutions.

Nonrelativistic spinning strings

We construct nonrelativistic spinning string solutions corresponding to SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5× S5. Considering various nonrelativistic spinning string configurations both in AdS5 as well as S5 we obtain corresponding dispersion relations in the strong coupling regime of SMT where the strong coupling ( sim sqrt{mathfrak{g}} ) corrections near the BPS bound have been estimated in the slow spinning limit of strings in AdS5. We generalize our results explicitly by constructing three spin folded string configurations that has two of its spins along AdS5 and one along S5. Our analysis reveals that the correction to the spectrum depends non trivially on the length of the NR string in AdS5. The rest of the paper essentially unfolds the underlying connection between SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5× S5 and the nonrelativistic Neumann-Rosochatius like integrable models in 1D. Taking two specific examples of NR spinning strings in R × S3 as well as in certain sub-sector of AdS5 we show that similar reduction is indeed possible where one can estimate the spectrum of the theory using 1D model.

Cosmic string in Abelian-Higgs model with enhanced symmetry \u2014 Implication to the axion domain-wall problem

In our previous work, we found new types of the cosmic string solutions in the Abelian-Higgs model with an enhanced U(1) global symmetry. We dubbed those solutions as the compensated/uncompensated strings. The compensated string is similar to the conventional cosmic string in the Abrikosov-Nielsen-Olesen (ANO) string, around which only the would-be Nambu-Goldstone (NG) boson winds. Around the uncompensated string, on the other hand, the physical NG boson also winds, where the physical NG boson is associated with the spontaneous breaking of the enhanced symmetry. Our previous simulation in the 2+1 dimensional spacetime confirmed that both the compensated/uncompensated strings are formed at the phase transition of the symmetry breaking. Non-trivial winding of the physical NG boson around the strings potentially causes the so-called axion domain- wall problem when the model is applied to the axion model. In this paper, we perform simulation in the 3+1 dimensional spacetime to discuss the fate of the uncompensated strings. We observe that the evolution of the string-network is highly complicated in the 3+1 dimensional simulation compared with that seen in the previous simulation. Despite such complications, we find that the number of the uncompensated strings which could cause can be highly suppressed at late times. Our observation suggests that the present setup can be applied to the axion model without suffering from the axion domain-wall problem.

More on Schr\xf6dinger holography

We find explicit solutions for giant magnons and spiky strings living on the Schrödinger space Schr5 × T1,1 and compute dispersion relations. The holographic dual field theory is conjectured to be a non-local dipole-deformed CFT at strong coupling. We find that the dependence between conserved charges in the dispersion relations is transcen- dental, which is quite different from the most symmetric case of spherical internal space. Keeping the squashing parameter b general allows us to take some limits and to compare our results to known cases.

Finite size effects in classical string solutions of the Schr\xf6dinger geometry

We study finite size corrections to the semiclassical string solutions of the Schrödinger spacetime. We compute the leading order exponential corrections to the infinite size dispersion relation of the single spin giant magnon and of the single spin single spike solutions. The solutions live in a S3 subspace of the five-sphere and extent in the Schrödinger part of the metric. In the limit of zero deformation the finite size dispersion relations flow to the undeformed AdS5 × S5 counterparts and in the infinite size limit the correction term vanishes and the known infinite size dispersion relations are obtained.

Mimetic black strings

We present two new classes of black string solutions in the context of mimetic gravity. The horizon topology of these solutions can be either a flat T2 torus with topology S1× S1, or a standard cylindrical model with topology R × S1. The first class describes uncharged rotating black string which its asymptotic behavior is a quotient of anti-de Sitter (AdS) space, while the second class represents asymptotically AdS charged rotating black string. We study the casual structure and physical properties of these spacetimes and calculate, the entropy, electric charge, mass and angular momentum per unit length of rotating black strings.

TsT, mathrm{T}overline{mathrm{T}} and black strings

We study the relationship between TsT transformations, marginal deformations of string theory on AdS3 backgrounds, and irrelevant deformations of 2d CFTs. We show that TsT transformations of NS-NS backgrounds correspond to instantaneous deformations of the worldsheet action by the antisymmetric product of two Noether currents, holographically mirroring the definition of the Toverline{T},Joverline{T},Toverline{J} , and Joverline{J} deformations of 2d CFTs. Applying a TsT transformation to string theory on BTZ ×S3 × M4 we obtain a general class of rotating black string solutions, including the Horne-Horowitz and the Giveon-Itzhaki-Kutasov ones as special cases, which we show are holographically dual to thermal states in single-trace Toverline{T} -deformed CFTs. We also find a smooth solution interpolating between global AdS3 in the IR and a linear dilaton background in the UV that is interpreted as the NS-NS ground state in the dual Toverline{T} -deformed CFT. This background suggests the existence of an upper bound on the deformation parameter above which the solution becomes complex. We find that the worldsheet spectrum, the thermodynamics of the black strings (in particular their Bekenstein-Hawking entropy), and the critical value of the deformation parameter match the corresponding quantities obtained from single-trace Toverline{T} deformations.