Global Symmetry Breaking Research Articles

On the origin of phase transitions in the absence of symmetry-breaking

In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimensions. Our model Hamiltonian is defined on the basis of a continuum version of a duality transformation of a three dimensional Ising model. The system so obtained undergoes a thermodynamic phase transition in the absence of a global symmetry-breaking and thus in the absence of an order parameter. It is found that the first order phase transition undergone by this model fits into a microcanonical version of an Ehrenfest-like classification of phase transitions applied to the configurational entropy. It is discussed why the seemingly divergent behaviour of the third derivative of configurational entropy is the effect of a deeper geometrical transition of the equipotential submanifolds of configuration space, which, in its turn, is likely to be the ”shadow” of an even deeper transition of topological kind.

Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions

Symmetry protected topological (SPT) states have boundary 't Hooft anomalies that obstruct an effective boundary theory realized in its own dimension with UV completion and an on-site $G$-symmetry. In this work, yet we show that a certain anomalous non-on-site $G$ symmetry along the boundary becomes on-site when viewed as an extended $H$ symmetry, via a suitable group extension $1\to K\to H\to G\to1$. Namely, a non-perturbative global (gauge/gravitational) anomaly in $G$ becomes anomaly-free in $H$. This guides us to construct exactly soluble lattice path integral and Hamiltonian of symmetric gapped boundaries, always existent for any SPT state in any spacetime dimension $d \geq 2$ of any finite symmetry group, including on-site unitary and anti-unitary time-reversal symmetries. The resulting symmetric gapped boundary can be described either by an $H$-symmetry extended boundary of bulk $d \geq 2$, or more naturally by a topological emergent $K$-gauge theory with a global symmetry $G$ on a 3+1D bulk or above. The excitations on such a symmetric topologically ordered boundary can carry fractional quantum numbers of the symmetry $G$, described by representations of $H$. (Apply our approach to a 1+1D boundary of 2+1D bulk, we find that a deconfined gauge boundary indeed has spontaneous symmetry breaking with long-range order. The deconfined symmetry-breaking phase crosses over smoothly to a confined phase without a phase transition.) In contrast to known gapped interfaces obtained via symmetry breaking (either global symmetry breaking or Anderson-Higgs mechanism for gauge theory), our approach is based on symmetry extension. More generally, applying our approach to SPT, topologically ordered gauge theories and symmetry enriched topologically ordered (SET) states, leads to generic boundaries/interfaces constructed with a mixture of symmetry breaking, symmetry extension, and dynamical gauging.

Kinetic effects of thermal ions and energetic particles on discrete kinetic BAE mode generation and symmetry breaking

The kinetic effects of both thermal ions and energetic particles (EPs) on global Alfvén mode generation and structure symmetry breaking are important for the understanding of resonant excitation and EP transport in tokamak plasmas. In this work, the formulation for the study of the beta induced Alfvén eigenmode (BAE) driven by EPs is derived for weakly coupled poloidal harmonics with finite Larmor radius (FLR) and finite orbit width (FOW). Agreement between the theoretical model and corresponding XHMGC simulations is demonstrated. It is shown that including FLR and FOW can lead to the global mode structure broadening. The non-perturbative effects of the energetic particles on global mode structure symmetry breaking is demonstrated. In particular, when the energetic particle drive shifts away from the mode rational surface, volume averaged parallel and radial wave numbers are generated in the plasma as a demonstration of EPs’ role on mode structure symmetry breaking. The connection of the mode structure symmetry breaking with experimental observations using ECEI and with particle/momentum transport are discussed.

Simplest little Higgs model revisited: Hidden mass relation, unitarity, and naturalness

We analyze the scalar potential of the Simplest Little Higgs (SLH) model in an approach consistent with the spirit of continuum effective field theory (CEFT). By requiring correct electroweak symmetry breaking (EWSB) with the $125\,\text{GeV}$ Higgs boson, we are able to derive a relation between the pseudo-axion mass $m_\eta$ and the heavy top mass $m_T$, which serves as a crucial test of the SLH mechanism. By requiring $m_\eta^2>0$ an upper bound on $m_T$ can be obtained for any fixed SLH global symmetry breaking scale $f$. We also point out that an absolute upper bound on $f$ can be obtained by imposing partial wave unitarity constraint, which in turn leads to absolute upper bounds of $m_T\lesssim 19\,\text{TeV}, m_\eta\lesssim 1.5\,\text{TeV}$ and $m_{Z'}\lesssim 48\,\text{TeV}$. We present the allowed region in the three-dimensional parameter space characterized by $f,t_\beta,m_T$, taking into account the requirement of valid EWSB and the constraint from perturbative unitarity. We also propose a strategy of analyzing the fine-tuning problem consistent with the spirit of CEFT and apply it to the SLH. We suggest that the scalar potential and fine-tuning analysis strategies adopted here should also be applicable to a wide class of Little Higgs and Twin Higgs models, which may reveal interesting relations as crucial tests of the related EWSB mechanism and provide a new perspective on assessing their degree of fine-tuning.

Lorentzian Goldstone modes shared among photons and gravitons

It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor-field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, A_{mu }^{2}=pm M_{A}^{2} and H_{mu nu }^{2}=pm M_{H}^{2} (M_{A} and M_{H} are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared by photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry SO(1, 3) of the electrogravity Lagrangian, the tensor-field constraint itself possesses much higher global symmetry SO(7, 3), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while the photon may only contain true Goldstone modes, the graviton appears at least partially to be composed of pseudo-Goldstone modes rather than of pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes considered in some detail. How this emergent electrogravity theory could be observationally different from conventional QED and GR theories is also briefly discussed.

Mode structure symmetry breaking of energetic particle driven beta-induced Alfvén eigenmode

The mode structure symmetry breaking of energetic particle driven Beta-induced Alfvén Eigenmode (BAE) is studied based on global theory and simulation. The weak coupling formula gives a reasonable estimate of the local eigenvalue compared with global hybrid simulation using XHMGC. The non-perturbative effect of energetic particles on global mode structure symmetry breaking in radial and parallel (along B) directions is demonstrated. With the contribution from energetic particles, two dimensional (radial and poloidal) BAE mode structures with symmetric/asymmetric tails are produced using an analytical model. It is demonstrated that the symmetry breaking in radial and parallel directions is intimately connected. The effects of mode structure symmetry breaking on nonlinear physics, energetic particle transport, and the possible insight for experimental studies are discussed.

Higgs compositeness in Sp(2N) gauge theories – Determining the low-energy constants with lattice calculations

As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) → Sp(4) global symmetry breaking pattern. We then consider an Sp(4) gauge theory with two Dirac fermion flavours in the fundamental representation on a lattice, which provides a concrete example of the microscopic realisation of the SU(4)/Sp(4) composite Higgs model. For this system, we outline a programme of numerical simulations aiming at the determination of the low-energy constants of the effective field theory and we test the method on the quenched theory. We also report early results from dynamical simulations, focussing on the phase structure of the lattice theory and a calculation of the lowest-lying meson spectrum at coarse lattice spacing.

Bifurcations from the orbit of solutions of the Neumann problem

The purpose of this paper is to study weak solutions of a nonlinear Neumann problem considered on a ball. Assuming that the potential is invariant, we consider an orbit of critical points, i.e. we do not assume that critical points are isolated. We apply techniques of equivariant analysis to examine bifurcations from the orbits of trivial solutions. We formulate sufficient conditions for local and global bifurcations, in terms of the right-hand side of the system and eigenvalues of the Laplace operator. Moreover, we characterise orbits at which global symmetry breaking phenomena occur.

Relaxation of the composite Higgs little hierarchy

We describe a composite Higgs scenario in which a cosmological relaxation mechanism naturally gives rise to a hierarchy between the weak scale and the scale of spontaneous global symmetry breaking. This is achieved through the scanning of sources of explicit global symmetry breaking by a relaxion field during an exponentially long period of inflation in the early universe. We explore this mechanism in detail in a specific composite Higgs scenario with QCD-like dynamics, based on an ultraviolet SU(N )TC ‘technicolor’ confining gauge theory with three Dirac technifermion flavors. We find that we can successfully generate a hierarchy of scales ξ≡〈h〉2/Fπ2 ≳ 1.2 × 10− 4 (i.e., compositeness scales Fπ ∼ 20 TeV) without tuning. This evades all current electroweak precision bounds on our (custodial violating) model. While directly observing the heavy composite states in this model will be challenging, a future electroweak precision measurement program can probe most of the natural parameter space for the model. We also highlight signatures of more general composite Higgs models in the cosmological relaxation framework, including some implications for flavor and dark matter.

Emergent exotic superconductivity in artificially engineered tricolor Kondo superlattices

In the quest for exotic superconducting pairing states, the Rashba effect, which lifts the electron-spin degeneracy as a consequence of strong spin-orbit interaction (SOI) under broken inversion symmetry, has attracted considerable interest. Here, to introduce the Rashba effect into two-dimensional (2D) strongly correlated electron systems, we fabricate non-centrosymmetric (tricolor) superlattices composed of three kinds of $f$-electron compounds with atomic thickness; $d$-wave heavy fermion superconductor CeCoIn$_5$ sandwiched by two different nonmagnetic metals, YbCoIn$_5$ and YbRhIn$_5$. We find that the Rashba SOI induced global inversion symmetry breaking in these tricolor Kondo superlattices leads to profound changes in the superconducting properties of CeCoIn$_5$, which are revealed by unusual temperature and angular dependences of upper critical fields that are in marked contrast with the bulk CeCoIn$_5$ single crystals. We demonstrate that the Rashba effect incorporated into 2D CeCoIn$_5$ block layers is largely tunable by changing the layer thickness. Moreover, the temperature dependence of in-plane upper critical field exhibits an anomalous upturn at low temperatures, which is attributed to a possible emergence of a helical or stripe superconducting phase. Our results demonstrate that the tricolor Kondo superlattices provide a new playground for exploring exotic superconducting states in the strongly correlated 2D electron systems with the Rashba effect.

Heavy neutral pseudoscalar decays into gauge bosons in the Littlest Higgs model

We study two-body decays of a new neutral pseudoscalar into standard model gauge bosons within the context of the Littlest Higgs model. The processes induced at the one-loop level, with , are considered. Since the branching ratios of the decays result were very suppressed, only the processes are thoroughly studied. The branching ratios for the and decays are of the order of 10−5 and 10−7, respectively, for f around 3 TeV, which represents the global symmetry breaking scale of the theory. The production cross section of the boson via gluon fusion at the LHC is estimated.

LHC phenomenology of composite 2-Higgs doublet models

We investigate the phenomenology of Composite 2-Higgs doublet models (C2HDMs) of various Yukawa types based on the global symmetry breaking SO(6)rightarrow SO(4)times SO(2). The kinetic part and the Yukawa Lagrangian are constructed in terms of the pseudo Nambu–Goldstone Boson (pNGB) matrix and a 6-plet of fermions under SO(6). The scalar potential is assumed to be the same as that of the Elementary 2-Higgs doublet model (E2HDM) with a softly broken discrete Z_2 symmetry. We then discuss the phenomenological differences between the E2HDM and C2HDM by focusing on the deviations from standard model (SM) couplings of the discovered Higgs state (h) as well as on the production cross sections and branching ratios (BRs) at the large Hadron collider (LHC) of extra Higgs bosons. We find that, even if the same deviation in the hVV (V=W,Z) coupling is assumed in the two scenarios, there appear significant differences between the E2HDM and C2HDM from the structure of the Yukawa couplings, so that production and decay features of extra Higgs bosons can be used to distinguish between the two scenarios.

A UV complete compositeness scenario: LHC constraints meet the lattice

We investigate a recently proposed UV-complete composite Higgs scenario in the light of the first LHC runs. The model is based on a SU(4) gauge group with global flavour symmetry breaking SU(5) → SO(5), giving rise to pseudo Nambu-Goldstone bosons in addition to the Higgs doublet. This includes a real and a complex electroweak triplet with exotic electric charges. Including these, as well as constraints on other exotic states, we show that LHC measurements are not yet sensitive enough to significantly constrain the model’s low energy constants. The Higgs potential is described by two parameters which are on the one hand constrained by the LHC measurement of the Higgs mass and Higgs decay channels and on the other hand can be computed from correlation functions in the UV-complete theory. Hence to exclude the model at least one constant needs to be determined and to validate the Higgs potential both constants need to be reproduced by the UV-theory. Due to its UV-formulation, a certain number of low energy constants can be computed from first principle numerical simulations of the theory formulated on a lattice, which can help in establishing the validity of this model. We assess the potential impact of lattice calculations for phenomenological studies, as a preliminary step towards Monte Carlo simulations.

Heavy neutral scalar decays into electroweak gauge bosons in the littlest Higgs model

We study the heavy neutral scalar decays into standard model electroweak gauge bosons in the context of the littlest Higgs model. We focus our attention on the processes induced at the one-loop level, with . Since the branching ratios of the decays are very suppressed, only the process is analyzed in the framework of possible experimental scenarios by using heavy scalar masses between 1.6 TeV and 3.3 TeV. The branching ratio for the decay is of the order of 10−3 throughout the interval , which represents the global symmetry breaking scale of the theory. Thus, the associated production cross section for is estimated, finding around ten events for at best.

Probing composite models at the LHC with exotic quarks production

After the Higgs boson hunt, the LHC could be a powerful tool to unravel the mystery of which physics lies beyond the realm of the Standard Model. Different new sectors have been postulated to address naturalness: SUSY, extra dimensions and strong dynamics theories. Composite models extend EWSB to a global symmetry breaking whose pseudo-Goldstone boson is the SM Higgs boson. The resulting mass spectrum originates from a partial mixing between fundamental fermions and composite fields which creates massive states including new heavy quarks coupled preferentially to the top quark. Searches for these top partners have been carried out by the ATLAS and CMS collaborations, constraining the models. Other composite contributions are expected to enhance the 4-top production, which should be observable in the next years at the LHC.

Minimal ingredients for orbital-texture switches at Dirac points in strong spin–orbit coupled materials

AbstractRecent angle-resolved photoemission spectroscopy measurements on strong spin–orbit coupled materials have shown an in-plane orbital-texture switch at their respective Dirac points, regardless of whether they are topological insulators or ‘trivial’ Rashba materials. This feature has also been demonstrated in a few materials (Bi2Se3, Bi2Te3 and BiTeI) though DFT calculations. Here we present a minimal orbital-derived tight binding model to calculate the electron wavefunction in a two-dimensional crystal lattice. We show that the orbital components of the wavefunction demonstrate an orbital-texture switch in addition to the usual spin switch seen in spin polarised bands. This orbital-texture switch is determined by the existence of three main properties: local or global inversion symmetry breaking, strong spin–orbit coupling and non-local physics (the electrons are on a lattice). Using our model, we demonstrate that the orbital-texture switch is ubiquitous and to be expected in many real systems. The orbital hybridisation of the bands is the key aspect for understanding the unique wavefunction properties of these materials, and this minimal model helps to establish the quantum perturbations that drive these hybridisations.

Local and global symmetry breaking in itemset mining

The concept of symmetry has been extensively studied in the field of constraint programming and in the propositional satisfiability. Several methods for detection and removal of these symmetries have been developed, and their use in known solvers of these domains improved dramatically their effectiveness on a big variety of problems considered difficult to solve. The concept of symmetry may be exported to other areas where some structures can be exploited effectively. Particularly, in the area of data mining where some tasks can be expressed as constraints or logical formulas. We are interested here, by the detection and elimination of local and global symmetries in the item-set mining problem. Recent works have provided effective encodings as Boolean constraints for these data mining tasks and some idea on symmetry elimination in this area begin to appear, but still few and the techniques presented are often on global symmetry that is detected and eliminated statically in a preprocessing phase. In this work we study the notion of local symmetry and compare it to global symmetry for the itemset mining problem. We show how local symmetries of the boolean encoding can be detected dynamically and give some properties that allow to eliminate theses symmetries in SAT-based itemset mining solvers in order to enhance their efficiency.

The excitation of the global symmetry-breaking vacuum in composite Higgs models

We consider scenarios of Higgs compositeness where the Higgs doublet arises as a pseudo-Nambu Goldstone boson. Our focus is the physical scalar ("radial") excitation associated with the global symmetry breaking vacuum, which we call the "global Higgs". For the minimal case of a $SO(5)/SO(4)$ coset, the couplings of the global Higgs to Standard Model (SM) particles are fully determined by group theoretical factors and two decay constants. The global Higgs also couples to the composite resonances of the theory, inducing an interaction with the SM gauge bosons at one-loop. We thoroughly analyze representative fermionic sectors, considering a global Higgs both in the $\bf 5$ and $\bf 14$ representations of $SO(5)$ and taking into account the renormalization group evolution of couplings in the composite sector. We derive the one-loop effective couplings and all decays of the global Higgs, showing that its decay width over mass can range from $ O (10^{-3})$ to $ O(1)$. Because of the multiplicity of the resonances, the coupling of the global Higgs to gluons is sizeable, potentially opening a new window into composite models at the LHC.

Macroscopic response and directional disorder dynamics in chemically substituted ferroelectrics

Using temperature-resolved dielectric spectroscopy in the range 25--320 K we investigate the macroscopic response, phase symmetry, and order/disorder states in bulk ferroelectric ${\text{K}}_{1\ensuremath{-}y}{\text{Li}}_{y}{\text{Ta}}_{1\ensuremath{-}x}{\text{Nb}}_{x}$ (KLTN). Four long-range symmetry phases are identified with their relative transitions. Directional analysis of the order/disorder states using Fr\ohlich entropy indicates global symmetry breaking along the growth axis and an anisotropic dipolar effective thermodynamic behavior, which ranges from disordered to ordered at the same temperature for different directions in the sample. Results indicate that the macroscopic polarization, driven by nanosized polar regions, follows a microscopic perovskite eight-sites lattice model.

Long-lived, colour-triplet scalars from unnaturalness

Long-lived, colour-triplet scalars are a generic prediction of unnatural, or split, composite Higgs models where the spontaneous global-symmetry breaking scale $f \gtrsim 10$ TeV and an unbroken $SU(5)$ symmetry is preserved. Since the triplet scalars are pseudo Nambu-Goldstone bosons they are split from the much heavier composite-sector resonances and are the lightest exotic, coloured states. This makes them ideal to search for at colliders. Due to discrete symmetries the triplet scalar decays via a dimension-six term and given the large suppression scale $f$ is often metastable. We show that existing searches for collider-stable R-hadrons from Run-I at the LHC forbid a triplet scalar mass below 845 GeV, whereas with $300\,\mathrm{fb}^{-1}$ at 13 TeV triplet scalar masses up to 1.4 TeV can be discovered. For shorter lifetimes displaced-vertex searches provide a discovery reach of up to 1.8 TeV. In addition we present exclusion and discovery reaches of future hadron colliders as well as indirect limits that arise from modifications of the Higgs couplings.