Search

Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without $U(1)$ symmetry, their spectra are usually given by inhomogeneous $T-Q$ relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic $XXZ$ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit., Comment: 19 pages, 8 figures

We propose a renormalizable U ( 1 ) B − L extension of the Standard model based on Σ ( 18 ) symmetry which accommodates the observed neutrino mass and mixing pattern. The smallness of the active neutrino masses and the normal neutrino mass ordering are induced by the type-I seesaw mechanism at the first order of perturbation theory. The effective neutrino mass governing the neutrinoless double beta decay is predicted to be 〈 m e e 〉 ∈ ( 2 . 40 , 3 . 60 ) meV , J C P ∈ ( − 0 . 034 , − 0 . 024 ) which are well consistent with the recent experimental data.

We explore the possibility of having a fermionic dark matter candidate within $U(1)'$ models for CE$\nu$NS experiments in light of the latest COHERENT data and the current and future dark matter direct detection experiments. A vector-like fermionic dark matter has been introduced which is charged under $U(1)'$ symmetry, naturally stable after spontaneous symmetry breaking. We perform a complementary investigation using CE$\nu$NS experiments and dark matter direct detection searches to explore dark matter as well as $Z^{\prime}$ boson parameter space. Depending on numerous other constraints arising from the beam dump, LHCb, BABAR, and the forthcoming reactor experiment proposed by the SBC collaboration, we explore the allowed region of $Z^{\prime}$ portal dark matter., Comment: Matches published version. 21 pages, 5 figures, 2 tables

We investigate the role of a local $U(1)'$ symmetry for the problem of CP violation in the effective theory for two Higgs doublet models and its microscopic counterparts. First, in two Higgs doublet models with $U(1)'$, we show that the higher-dimensional operators in the scalar potential violate the CP symmetry with an interplay with the mixing mass parameter, giving rise to small mixings between CP-even and CP-odd scalars. Motivated by the $B$-meson anomalies in recent years, we take the flavored $U(1)'$ to be a benchmark model for specifying the flavor structure. Then, we calculate the electric dipole moment of electron (eEDM) at two loops due to the CP-violating higher-dimensional operators and identify the correlation between the masses of heavy Higgs bosons and the cutoff scale from the bound on eEDM. We also comment on the possibility of making an independent test of the CP violation in the collider searches for heavy Higgs bosons. Finally, we show how the obtained eEDM results in the effective theory can be used to constrain microscopic models with an explicit CP violation in the partially decoupled or dark sectors., 37 pages, 5 figures, Journal version

We consider the Sasa–Satsuma (SS) and nonlinear Schrödinger (NLS) equations posed along the line, in 1 + 1 dimensions. Both equations are canonical integrable U(1) models, with solitons, multi-solitons and breather solutions Yang (2010 SIAM Mathematical Modeling and Computation). For these two equations, we recognize four distinct localized breather modes: the Sasa–Satsuma for SS, and for NLS the Satsuma–Yajima, Kuznetsov–Ma and Peregrine breathers. Very little is known about the stability of these solutions, mainly because of their complex structure, which does not fit into the classical soliton behavior Grillakis et al (1987 J. Funct. Anal. 74 160–97). In this paper we find the natural H 2 variational characterization for each of them. This seems to be the first known variational characterization for these solutions; in particular, the first one obtained for the famous Peregrine breather. We also prove that Sasa–Satsuma breathers are H 2 nonlinearly stable, improving the linear stability property previously proved by Pelinovsky and Yang (2005 Chaos 15 037115). Moreover, in the SS case, we provide an alternative understanding of the SS solution as a breather, and not only as an embedded soliton. The method of proof is based in the use of a H 2 based Lyapunov functional, in the spirit of Alejo and Muñoz (2013 Commun. Math. Phys. 324 233–62), extended this time to the vector-valued case. We also provide another rigorous justification of the instability of the remaining three nonlinear modes (Satsuma–Yajima, Peregrine and Kuznetsov–Ma), based in the study of their corresponding linear variational structure (as critical points of a suitable Lyapunov functional), and complementing the instability results recently proved e.g. in Muñoz (2017 Proyecciones (Antofagasta) 36 653–83).

We investigate the evolution of population density vector, u = ( u 1 , ⋯ , u k ) , of k-species whose diffusion is controlled by its absolute value | u | . More precisely, we study the properties and asymptotic large time behaviour of solution u = ( u 1 , ⋯ , u k ) of degenerate parabolic system ( u i ) t = ∇ ⋅ ( | u | m − 1 ∇ u i ) for m > 1 and i = 1 , ⋯ , k . Under some regularity assumptions, we prove that the component u i which describes the population density of i-th species with population M i converges to M i | M | B | M | in space with two different approaches where B | M | is the Barenblatt solution of the standard porous medium equation with L 1 mass | M | = M 1 2 + ⋯ + M k 2 . As an application of the asymptotic behaviour, we establish a suitable Harnack type inequality which makes the spatial average of u i under control by the value of u i at one point. We also find 1-directional travelling wave type solutions and the properties of solutions which has travelling wave behaviour at infinity.

In Euclidean space R 3 , as a proper rigid motion, a rotation ρ about the origin can be described by a pair ( u , θ ) , where u = ( u 1 , u 2 , u 3 ) T ∈ R 3 is a unit vector denoting the axis of ρ...

This article examines nonnegative solutions of the two-component elliptic Gross-Pitaevskii system { ϵ 1 Δ u 1 = u 1 ( u 1 2 + λ u 2 2 − 1 ) in R n , ϵ 2 Δ u 2 = u 2 ( u 2 2 + λ u 1 2 − 1 ) in R n , for parameters 1 λ ∞ and ϵ 1 , ϵ 2 ∈ R + . We provide a natural counterpart of the De Giorgi's conjecture, regarding the Allen-Cahn equation, for the above system and we settle it for n ≤ 3 . We prove and apply a geometric Poincare inequality to show that ∇ u 1 ⋅ ∇ u 2 = − | ∇ u 1 | | ∇ u 2 | . We study symmetry of components when ϵ 1 = ϵ 2 and asymmetry of components when ϵ 1 ≠ ϵ 2 . In one dimension, we explore explicit profiles of solutions for specific parameters λ , ϵ 1 , ϵ 2 . In addition, we provide a gradient estimate, various energy estimates, Liouville theorems, monotonicity formulae and a formalization of surface tensions of the energy for solutions of the above system. Note that when λ = 0 , the above system becomes decoupled and recovers the Allen-Cahn equation. The De Giorgi conjecture (1978) for the Allen-Cahn equation states that bounded monotone solutions of the Allen-Cahn equation are one-dimensional when n ≤ 8 . This conjecture is already settled under certain assumptions. When 0 λ ≤ 1 , the system refers to the real-valued Ginzburg-Landau system and nonnegative solutions are trivial.

Supersymmetric models augmented by U(1)′ gauge symmetries resolve some of the outstanding problems in MSSM, such as the μ problem. Unfortunately collider phenomenology in such models is hindered by the stringent limits from the ATLAS and CMS collaborations on the Z′ boson mass. We explore possibilities of lowering the mass in either leptophobic models, by employing kinetic mixing, or in models with non-universal U(1)′ charges, where the Z′ boson does not couple either to the first two generation quarks, thus lowering its production cross-section, or to the first two generation leptons, thus lowering its di-lepton branching ratio. We verify consistency of these models with dark matter bounds and indicate the most promising signals at the collider.

This is the first of the two papers devoted to the study of global regularity of the 3 + 1 dimensional Einstein-Klein-Gordon system with a U(1) × ℝ isometry group. In this first part, the authors reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2 + 1 dimensional system. Then, the authors will give energy estimates and construct the null coordinate system, under which the authors finally show that the first possible singularity can only occur at the axis.

Monte Carlo simulation of gauge theories with a θ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which is a promising approach for its low computational cost. The drawback of this method, however, is the existence of a condition that has to be met in order for the results to be correct. As a first step, we apply the method to 2D U(1) gauge theory on a torus with a θ term, which can be solved analytically. We find that a naive implementation of the method fails because of the topological nature of the θ term. In order to circumvent this problem, we simulate the same theory on a punctured torus, which is equivalent to the original model in the infinite volume limit for |θ| < π. Rather surprisingly, we find that the CLM works and reproduces the exact results for a punctured torus even at large θ, where the link variables near the puncture become very far from being unitary.

Here, the existence of at least one positive radial solution of the Nonlinear nonhomogeneous Neumann problem − Δ H n u + R ( ξ ) u = a ( | ξ | H n ) | u | q − 2 u 1 + | u | q − p − b ( | ξ | H n ) ...

In this work, we find the terms of the complex of characteristic zero in the case of the skew-shape (8,6, 3)/(u,1), where u = 1 and 2. We also study this complex as a diagram by using the mapping Cone and other concepts.

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 rise to gauged Q-balls and theories with dynamical gravity giving rise to boson stars., 19 pages, 11 figures; this version: minor corrections, references added

In this paper, we find the critical exponent for the existence of global small data solutions to: u t t + ( − Δ ) σ u + ( − Δ ) θ 2 u t = f ( u , u t ) , t ≥ 0 , x ∈ R n , ( u , u t ) ( 0 , x ) = ( 0 , u 1 ( x ) ) , in the case of so-called non-effective damping, θ ∈ ( σ , 2 σ ] , where σ ≠ 1 and f = | u | α or f = | u t | α , in low space dimension. By critical exponent we mean that global small data solution exists for supercritical powers α > α and do not exist, in general, for subcritical powers 1 α α . Assuming initial data to be small in L 1 or in some other L p space, p ∈ ( 1 , 2 ) , in addition to the energy space, the critical exponent only depends on the ratio n / ( σ p ) . We also prove the global existence of small data solutions in high space dimension for α > α , but we leave open to determine if a counterpart nonexistence result for α α holds or not.

The latest measurements of the anomalous muon magnetic moment show a discrepancy between the theoretical prediction of the Standard Model and the experimental observations. To account for such a discrepancy, we consider a possible extension of the type-(I+II) seesaw model for neutrino mass generation with a gauged symmetry. By explicitly constructing an economical model with only one extra scalar singlet, we demonstrate that the gauge symmetry and its spontaneous breaking are crucial not only for explaining the muon result but also for generating the neutrino masses and leptonic flavor mixing. Various phenomenological implications and experimental constraints on the model parameters are also discussed.

Let ( V , D ) be a covering approximation space and let f : U ⟶ V be a surjective map, where U is a nonempty set. We can achieve a covering C of U by defining C = { f − 1 ( D ) : D ∈ D } . This is a natural way to construct a covering for U and this motivates the research of covering rough sets from the mapping point of view. In this paper, we have shown that the inverse image of a neighborhood under f is a neighborhood and the inverse image of the closure of a point under f is again the closure of the corresponding point. Thus some approximation operators on the two covering approximation spaces must be related to each other. Some theorems and propositions with respect to the relationships between the approximation operators defined on U and the corresponding ones defined on V have been obtained. The purpose is to emphasize the importance of mappings between two covering approximation spaces. Finally, given two covering approximation spaces ( U 1 , A ) and ( U 2 , B ) , we define the product covering for U 1 × U 2 as { A × B | A ∈ A , B ∈ B } . This is a method to construct a new covering approximation space out of existing ones. Then we research the connections between the neighborhoods and closures of U 1 × U 2 and the corresponding ones of factor spaces. In the last part of this paper, we explore the connections between the approximation operators defined on U 1 × U 2 and the corresponding ones defined on factor spaces.

We explore muon anomalous magnetic moment (muon g−2) in a scotogenic neutrino model with a gauged lepton number symmetry U(1)μ−τ. In this model, a dominant muon g−2 contribution comes not from an additional gauge sector but from a Yukawa sector. In our numerical Δχ2 analysis, we show that our model is in favor of normal hierarchy with some features. We demonstrate one benchmark point, satisfying muon g−2 at the best fit value 25.1×10−10.

In this paper we study a new class of holographic heat engines via charged AdS black hole solutions of Einstein gravity coupled with logarithmic nonlinear $U(1)$ gauge theory. So, Logarithmic $U(1)$ AdS black holes with a horizon of positive, zero and negative constant curvatures are considered as a working substance of a holographic heat engine and the corrections to the usual Maxwell field are controlled by non-linearity parameter $\beta$. The efficiency of an ideal cycle ($\eta$), consisting of a sequence of isobaric $\to$ isochoric $\to$ isobaric $\to$ isochoric processes, is computed using the exact efficiency formula. It is shown that $\eta/\eta_{C}$, with $\eta_{C}$ the Carnot efficiency (the maximum efficiency available between two fixed temperatures), decreases as we move from the strong coupling regime ($\beta \to 0$) to the weak coupling domain ($\beta \to \infty$). We also obtain analytic relations for the efficiency in the weak and strong coupling regimes in both low and high temperature limits. The efficiency for planar and hyperbolic logarithmic $U(1)$ AdS black holes is computed and it is observed that efficiency versus $\beta$ behaves in the same qualitative manner as the spherical black holes., Comment: 23 pages, 20 figures, accepted version

Hiçyılmaz, Yasar (Balikesir Author), We attribute deviations of the muon and electron magnetic moments from the theoretical predictions to the presence of an additional U(1)' supersymmetric model. We interpret the discrepancies between the muon and electron anomalous magnetic moments to be due to the presence of non-universal U(1)' charges. In a minimally extended model, we show that requiring both deviations to be satisfied imposes constraints on the spectrum of the model, in particular on dark matter candidates and slepton masses and ordering. Choosing three benchmarks with distinct dark matter features, we study implications of the model at colliders, concentrating on variables that can distinguish our non-universal scenario from other U(1)' implementations., Natural Sciences and Engineering Research Council of Canada (NSERC) SAP105354

We study a class of gauge groups that can automatically yield a perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the axion quality problem is solved at all operator dimensions. Gauge groups belonging to this class can also enforce and protect accidental symmetries of the clockwork type, and we present a toy model where an `invisible' axion arises from a single breaking of the gauge and global symmetries., Comment: 6 pages

Multi-component dark matter scenarios are studied in the model with U(1)X dark gauge symmetry that is broken into its product subgroup Z2 × Z3 á la Krauss-Wilczek mechanism. In this setup, there exist two types of dark matter fields, X and Y, distinguished by different Z2 × Z3 charges. The real and imaginary parts of the Z2-charged field, XR and XI, get different masses from the U(1)X symmetry breaking. The field Y, which is another dark matter candidate due to the unbroken Z3 symmetry, belongs to the Strongly Interacting Massive Particle (SIMP)-type dark matter. Both XI and XR may contribute to Y’s 3 → 2 annihilation processes, opening a new class of SIMP models with a local dark gauge symmetry. Depending on the mass difference between XI and XR, we have either two-component or three-component dark matter scenarios. In particular two- or three-component SIMP scenarios can be realised not only for small mass difference between X and Y, but also for large mass hierarchy between them, which is a new and unique feature of the present model. We consider both theoretical and experimental constraints, and present four case studies of the multi-component dark matter scenarios.

In this paper, we explore possibilities of resolving the Hubble tension and $(g-2)_{\mu}$ anomaly simultaneously in a U(1)$_{L_\mu - L_\tau}$ model with Majoron. We only focus on a case where the Majoron $\phi$ does not exist at the beginning of the universe and is created by neutrino inverse decay $\nu\nu\to \phi$ after electron-positron annihilation. In this case, contributions of the new gauge boson $Z'$ and Majoron $\phi$ to the effective number of neutrino species $N_{\rm eff}$ can be calculated in separate periods. These contribution are labelled $N'_{\rm eff}$ for the U(1)$_{L_\mu - L_\tau}$ gauge boson and $\Delta N_{\rm eff}^\prime$ for the Majoron. The effective number $N_{\rm eff} = N'_{\rm eff} + \Delta N_{\rm eff}^\prime$ is evaluated by the evolution equations of the temperatures and the chemical potentials of light particles in each period. As a result, we found that the heavier $Z'$ mass $m_{Z^\prime}$ results in the smaller $N_{\mathrm{eff}}^\prime$ and requires the larger $\Delta N_{\mathrm{eff}}^\prime$ to resolve the Hubble tension. Therefore, compared to previous studies, the parameter region where the Hubble tension can be resolved is slightly shifted toward the larger value of $m_{Z^\prime}$., Comment: 19 pages, 7 figures, published in PTEP

We study circuit complexity for a free vector field of a $U(1)$ gauge theory in Coulomb gauge, and Gaussian states. We introduce a quantum circuit model with Gaussian states, including reference and target states. Using the Nielsen's geometric approach, the complexity then can be found as the shortest geodesic in the space of states. This geodesic is based on the notion of geodesic distance on the Lie group of Bogoliubov transformations equipped with a right-invariant metric. We use the framework of the covariance matrix to compute circuit complexity between Gaussian states. We apply this framework to the free vector field in general dimensions where we compute the circuit complexity of the ground state of the Hamiltonian., 11 pages, submitted to MPLA

The ${U}_{1}$ leptoquark is known to be a suitable candidate for explaining the semileptonic $B$-decay anomalies. We derive precise limits on its parameter space relevant for the anomalies from the current LHC high-${p}_{\mathrm{T}}$ dilepton data. We consider an exhaustive list of possible $B$-anomalies-motivated simple scenarios with one or two new couplings that can also be used as templates for obtaining bounds on more complicated scenarios. To obtain precise limits, we systematically consider all possible ${U}_{1}$ production processes that can contribute to the dilepton searches, including the resonant pair and single productions, nonresonant $t$-channel ${U}_{1}$ exchange, as well as its large interference with the Standard Model background. We demonstrate how the inclusion of resonant production contributions in the dilepton signal can lead to appreciably improved exclusion limits. We point out new search channels of ${U}_{1}$ that can act as unique tests of the flavor-motivated models. The template scenarios can also be used for future ${U}_{1}$ searches at the LHC. We compare the LHC limits with other relevant flavor bounds and find that a TeV-scale ${U}_{1}$ can accommodate both ${R}_{{D}^{(*)}}$ and ${R}_{{K}^{(*)}}$ anomalies while satisfying all the bounds.

Here, the authors report the discovery of novel types of U(1) and \ensuremath{\mathbb{Z}}${}_{2}$ quantum spin liquids on the pyrochlore lattice through a projective symmetry group classification. The classification highlights a special type of U(1) spin liquid, possessing an unusual symmetry-protected gapless multi-nodal-line structure in the spinon bands. The effect of gauge fluctuations for such a nodal structure is discussed. The leading contributions to the low-temperature specific heat are calculated, providing a clear experimental diagnostic of this U(1) spin liquid.

The singlet pseudoscalar sector of light mesons is investigated in the soft-wall model, a bottom-up approach to the AdS/QCD correspondence. The ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass results from the mixing among the fields dual to the axial current, pseudoscalar current and the $G\stackrel{\texttildelow{}}{G}$ operator. The topological susceptibility is computed for any quark mass, and the Witten-Veneziano relation is obtained in the large ${N}_{c}$ limit.

R.P. was supported by the EPSRC Scottish Doctoral Training Centre in Condensed Matter Physics (CM-CDT), Grant No. EP/L015110/1. We consider a generalized Dicke model with U(1) symmetry, which can undergo a transition to a superradiant state that spontaneously breaks this symmetry. By exploiting the difference in timescale between atomic and cavity dynamics, one may eliminate the cavity dynamics, providing an atom-only theory. We show that the standard Redfield theory cannot describe the transition to the superradiant state, but including higher-order corrections does recover the transition. Our work reveals how the forms of effective theories must vary for models with continuous symmetry, and provides a template to develop effective theories of more complex models. Publisher PDF

Generative models are a promising technology for the enhancement of quantum simulators. These machine learning methods are capable of reconstructing a quantum state from experimental measurements, and can aid in the calculation of physical observables. In this paper, we employ a recurrent neural network (RNN) to reconstruct the ground state of the spin-1/2 XY model, a prototypical Hamiltonian explored in trapped ion simulators. We explore its performance after enforcing a U(1) symmetry, which was recently shown by Hibat-Allah et al. [Phys. Rev. Research 2, 023358 (2020)] to preserve the autoregressive nature of the RNN. By studying the reconstruction of the XY model ground state from projective measurement data, we show that imposing U(1) symmetry on the RNN significantly increases the efficiency of learning, particularly in the early epoch regime. We argue that this performance increase may result from the tendency of the enforced symmetry to alleviate vanishing and exploding gradients, which helps stabilize the training process. Thus, symmetry-enforced RNNs may be particularly useful for applications of quantum simulators where a rapid feedback between optimization and circuit preparation is necessary, such as in hybrid classical-quantum algorithms., Comment: 10 pages, 8 figures

We consider the Cauchy problem for the higher-order nonlinear Schrodinger equation (0.1) i ∂ t u + 1 2 ∂ x 2 u − 1 4 ∂ x 4 u = i 3 λ 1 u 3 + λ 2 u 2 u , t > 1 , x ∈ R , u 1 , x = u 0 x , x ∈ R , where the coefficients 0 λ 1 λ 2 . The aim of the present paper is to prove the global existence of solutions to (??). Also we find the large time decay estimates for the solutions.

This note is devoted to investigating blow-up criteria for the three dimensional nematic liquid crystal flows. More precisely, we mainly proved that the strong solution ( u , d ) can be extended beyond T , provided that the horizontal velocity components u h = ( u 1 , u 2 ) satisfy u h ∈ L s ( 0 , T ; L q ( R 3 ) ) , 2 s + 3 q ≤ 1 2 , 6 ≤ q ≤ ∞ .

We prove the global well-posedness of weak solutions for nonlinear wave equations with supercritical source and damping terms on a three-dimensional torus T 3 of the prototype u t t − Δ u + | u t | m − 1 u t = | u | p − 1 u , ( x , t ) ∈ T 3 × R + ; u ( 0 ) = u 0 ∈ H 1 ( T 3 ) ∩ L m + 1 ( T 3 ) , u t ( 0 ) = u 1 ∈ L 2 ( T 3 ) , where 1 ≤ p ≤ min ⁡ { 2 3 m + 5 3 , m } . Notably, p is allowed to be larger than 6.

In this paper, we consider the following complex-valued semilinear heat equation ∂ t u = Δ u + u p , u ∈ C , in the whole space R n , where p ∈ N , p ≥ 2 . We aim at constructing for this equation a complex solution u = u 1 + i u 2 , which blows up in finite time T and only at one blowup point a, with the following estimates for the final profile u ( x , T ) ∼ [ ( p − 1 ) 2 | x − a | 2 8 p | ln ⁡ | x − a | | ] − 1 p − 1 , u 2 ( x , T ) ∼ 2 p ( p − 1 ) 2 [ ( p − 1 ) 2 | x − a | 2 8 p | ln ⁡ | x − a | | ] − 1 p − 1 × 1 | ln ⁡ | x − a | | , as x → a . Note that the imaginary part is non-zero and that it blows up also at point a. Our method relies on two main arguments: the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to get the conclusion. Up to our knowledge, this is the first time where the blowup behavior of the imaginary part is derived in multi-dimension.

Let H be a commutative and cancellative monoid. The elasticity ρ ( a ) of a non-unit a ∈ H is the supremum of m / n over all m , n for which there are factorizations of the form a = u 1 ⋅ … ⋅ u m = v 1 ⋅ … ⋅ v n , where all u i and v j are irreducibles. The elasticity ρ ( H ) of H is the supremum over all ρ ( a ) . We establish a characterization, valid for finitely generated monoids, when every rational number q with 1 q ρ ( H ) can be realized as the elasticity of some element a ∈ H . Furthermore, we derive results of a similar flavor for locally finitely generated monoids (they include all Krull domains and orders in Dedekind domains satisfying certain algebraic finiteness conditions) and for weakly Krull domains.

Additional Abelian gauge interactions are generic to string compactifications. In heterotic string models, gauge coupling unification of such forces and other gauge interactions is natural due to their common origin. In this letter we study systematically the 1-loop running of the coupling constants in effective vacua emerging from Z8 heterotic orbifold compactifications that provide the matter spectrum of the MSSM plus some vectorlike exotics, restricting to vacua that yield a non-anomalous U(1)' symmetry, gauge coupling unification and the observed values of known gauge couplings. We determine the low-energy value of the U(1)' coupling constant for different scales of supersymmetry breakdown. We find that the U(1)' coupling constant is quite restricted in string models to lie in the range 0.46-0.7 for low-scale supersymmetry or 0.44-0.6 in other cases. We argue that the phenomenology of these string vacua should be further explored to solve some extant issues, such as the stability of the Higgs vacuum., 19 pages, 4 figures, 4 tables; v2: matches version published in PLB

We study the following Cauchy problems for semi-linear structurally damped σ-evolution models: u t t + ( − Δ ) σ u + μ ( − Δ ) δ u t = f ( u , u t ) , u ( 0 , x ) = u 0 ( x ) , u t ( 0 , x ) = u 1 ( x ) with σ ≥ 1 , μ > 0 and δ ∈ ( 0 , σ 2 ) . Here the function f ( u , u t ) stands for the power nonlinearities | u | p and | u t | p with a given number p > 1 . We are interested in investigating L 1 estimates for oscillating integrals in the presentation of the solutions to the corresponding linear models with vanishing right-hand sides by applying the theory of modified Bessel functions and Faa di Bruno's formula. By assuming additional L m regularity on the initial data, we use ( L m ∩ L q ) − L q and L q − L q estimates with q ∈ ( 1 , ∞ ) and m ∈ [ 1 , q ) , to prove the global (in time) existence of small data Sobolev solutions to the above semi-linear models from suitable function spaces basing on L q spaces.

We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N=1 toy supermembrane model, and an N=4 model with a U(1) gauge multiplet and a charged chiral multiplet., Comment: 26 pages, 15 figures; typos corrected

Given a finite non-empty set A , let A + denote the free semigroup generated by A consisting of all finite words u 1 u 2 ⋯ u n with u i ∈ A . A word u ∈ A + is said to be closed if either u ∈ A or if u is a complete first return to some factor v ∈ A + , meaning u contains precisely two occurrences of v, one as a prefix and one as a suffix. We study the function f x c : N → N which counts the number of closed factors of each length in an infinite word x. We derive an explicit formula for f x c in case x is an Arnoux-Rauzy word. As a consequence we prove that lim inf n → ∞ f x c ( n ) = + ∞ .

Consider the nonlinear Schrodinger system − Δ u 1 + V 1 ( x ) u 1 = μ 1 ( x ) u 1 3 + β ( x ) u 1 u 2 2 in R N , − Δ u 2 + V 2 ( x ) u 2 = β ( x ) u 1 2 u 2 + μ 2 ( x ) u 2 3 in R N , u j ∈ H 1 ( R N ) , j = 1 , 2 , where N = 1 , 2 , 3 , and the potentials V j , μ j , β are periodic or V j are well-shaped and μ j , β are anti-well-shaped. When the coupling coefficient β is either small or large in terms of V j and μ j , existence of a positive ground state solution was proved in Liu and Liu (2015). In this paper, we describe the asymptotic behavior of ground state solutions when | β | L ∞ ( R N ) tends to zero or min R N β tends to + ∞ .

This paper is concerned with the existence of wavefront solutions to a system of degenerate quasilinear reaction–diffusion equations of mixed quasi-monotone properties in the form ∂ u i ∕ ∂ t = ∇ ⋅ D i u i ∇ u i + f i u − ∞ x ∞ , t > 0 for i = 1 , … , n . The important features of this system are that some of the diffusion coefficients D i u i are density dependent and may vanish at certain value of u i , and that each function f i is quasi-monotone increasing for some components of u = u 1 , … , u n and decreasing for other components of u . Such systems model reaction–diffusion processes with density driven diffusion mechanism. Under certain general conditions we prove the existence of a traveling wave solution that is between a pair of coupled upper and lower solutions. A predator–prey model with nonlinear diffusion is used as an illustration of application. The presence of wavefront solutions flowing toward the coexistence states is established by constructing appropriate upper and lower solutions.

We propose a neutrino model in which neutrino masses are generated at one loop level and three right-handed fermions have non-trivial charges under U(1)B−L gauge symmetry in no conflict with anomaly cancellation. After the spontaneously symmetry breaking, a remnant Z2 symmetry is induced and plays an role in assuring the stability of dark matter candidate.

The photon-added coherent states of Barut-Girardello and Perelomov types are constructed using Holstein-Primakoff realization of the su(1, 1) Lie algebra. Basic properties of the constructed states have been discussed. In addition, their non-classical features have been analyzed by computing photon detection probability distribution, Mandel Q-parameter and quadrature squeezing. It is shown that SU(1, 1) photon-added coherent states may exhibit sub-Poissonian statistics and quadrature squeezing for a chosen set of parameters. Moreover, it has been observed that their non-classical behavior increases as the number of added-photons increases.

We revisit the physical effects of discrete $\mathbb{Z}_p$ gauge charge on black hole thermodynamics, building on the seminal work of Coleman, Preskill, and Wilczek. Realising the discrete theory from the spontaneous breaking of an Abelian gauge theory, we consider the two limiting cases of interest, depending on whether the Compton wavelength of the massive vector is much smaller or much larger than the size of the black hole -- the so-called thin- and thick-string limits respectively. We find that the qualitative effect of discrete hair on the mass-temperature relationship is the same in both regimes, and similar to that of unbroken $U(1)$ charge: namely, a black hole carrying discrete gauge charge is always colder than its uncharged counterpart. In the thick-string limit, our conclusions bring into question some of the results of Coleman et al., as we discuss. Further, by considering the system to be enclosed within a finite cavity, we argue how the unbroken limit may be smoothly defined, and the unscreened electric field of the standard Reissner-Nordstrom solution recovered., Comment: 19 pages, 5 figures; references added, matches published version

UBe13 was the second discovered heavy fermion superconductor, and numerous pieces of evidence exist that imply that it is an unconventional (non-BCS, non-s wave pairing symmetry) superconductor. Exhibiting even more signs of unconventional superconductivity, Th-doped UBe13 is perhaps the most puzzling of any of the unconventional superconductors. This review considers both the parent, undoped compound as well as the more interesting Th-doped UBe13. After summarizing the rather thorough characterization, which because of the interest in these compounds has continued from their discovery in 1983 and 1984 to date, these properties are compared with a recent template for determining whether a superconductor is unconventional. Finally, further experiments are suggested., accepted review to appear in Journal of Low Temperature Physics

We linearize nonlinear supersymmetry in the Volkov-Akulov (VA) theory for extended SUSY in two dimensional spacetime ($d = 2$) based on the commutator algebra. Linear SUSY transformations of basic component fields for general vector supermultiplets are uniquely determined from variations of functionals (composites) of Nambu-Goldstone (NG) fermions, which are represented as simple products of powers of the NG fermions and a fundamental determinant in the VA theory. The structure of basic component fields with general auxiliary fields in the vector supermultiplets and transitions to $U(1)$ gauge supermultiplets through recombinations of the functionals of the NG fermions are explicitly shown both in $N = 2$ and $N = 3$ theories as the simplest and general examples for extended SUSY theories in $d = 2$., Comment: 26 pages

We study $$ \frac{1}{2} $$ 1 2 -BPS vortex-strings in four dimensional $$ \mathcal{N} $$ N = 2 supersymmetric quiver theories with gauge group SU(N) n × U(1). The matter content of the quiver can be represented by what we call a tetris diagram, which simplifies the analysis of the Higgs vacua and the corresponding strings. We classify the vacua of these theories in the presence of a Fayet-Iliopoulos term, and study strings above fully-Higgsed vacua. The strings are studied using classical zero modes analysis, supersymmetric localization and, in some cases, also S-duality. We analyze the conditions for bulk-string decoupling at low energies. When the conditions are satisfied, the low energy theory living on the string’s worldsheet is some 2d $$ \mathcal{N} $$ N = (2, 2) supersymmetric non-linear sigma model. We analyze the conditions for weak→weak 2d-4d map of parameters, and identify the worldsheet theory in all the cases where the map is weak→weak. For some SU(2) quivers, S-duality can be used to map weakly coupled worldsheet theories to strongly coupled ones. In these cases, we are able to identify the worldsheet theories also when the 2d-4d map of parameters is weak→strong.

The $U(1)$ global symmetry to solve the strong $CP$ problem could be the remnant of multi-$U(1)$ symmetries from QCD and hidden strong dynamics. Both Peccei-Quinn $U(1)$ and dynamical $U(1)$ are described uniformly, based on which we classify various mixed two-$U(1)$ models to solve both strong $CP$ and quality problems. We propose a moose diagram method with different fermion assignments to directly read relations between $CP$ phases, which illustrate how strong $CP$ problem is solved in terms of cancellation between $CP$ phases. In two axion models, we find the lightest axion is still same as QCD axion at infrared region, while one axion model with $Z_2$ symmetry enhances the axion mass spectrum. Our discussions can be extended to multi-axion cases., 25 pages, 3 figures

We study $Z'$ phenomenology at hadron colliders in an $U(1)'$ extended MSSM. We choose a $U(1)'$ model with a secluded sector, where the tension between the electroweak scale and developing a large enough mass for $Z'$ is resolved by incorporating three additional singlet superfields into the model. We perform a detailed analysis of the production, followed by decays, including into supersymmetric particles, of a $Z'$ boson with mass between 4 and 5.2 TeV, with particular emphasis on its possible discovery. We select three different scenarios consistent with the latest available experimental data and relic density constraints, and concentrate on final signals with two leptons, four leptons and six leptons. Including the SM background from processes with two, three or four vector bosons, we show the likelihood of observing a $Z^\prime$ boson is not promising for the HL-LHC at 14 TeV. While at 27 and 100 TeV, the situation is more optimistic, and we devise specific benchmark scenarios which could be observed., 21 pages, 9 figures, 9 tables, published version; title changed, more references and a new table added

Building on quantum Monte Carlo simulations, we study the phase diagram of a one-parameter Hamiltonian interpolating between trivial and topological Ising paramagnets in two dimensions, which are dual to the toric code and the double semion. We discover an intermediate phase with stripe order which spontaneously breaks the protecting Ising symmetry. Remarkably, we find evidence that this intervening phase is gapless due to the incommensurability of the stripe pattern and that it is dual to a $U(1)$ gauge theory exhibiting Cantor deconfinement., Comment: 7 pages, 4 figures, supplemental material included (7 pages, 10 figures)