Symmetry Breaking Pattern Research Articles

General prescription for globalU(1)’s in 6D SCFTs

We present a general prescription for determining the global U(1) symmetries of six-dimensional superconformal field theories (6D SCFTs). We use the quiver-like gauge theory description of the tensor branch to identify candidate U(1) symmetries which can act on generalized matter. The condition that these candidate U(1)'s are free of Adler-Bell-Jackiw (ABJ) anomalies provides bottom-up constraints for U(1)'s. This agrees with the answer obtained from symmetry breaking patterns induced by Higgs branch flows. We provide numerous examples illustrating the details of this proposal. In the F-theory realization of these theories, some of these symmetries originate from deformations of non-abelian flavor symmetries localized on a component of the discriminant, while others come from an additional generator of the Mordell-Weil group. We also provide evidence that some of these global U(1)'s do not arise from gauge symmetries, as would happen in taking a decoupling limit of a model coupled to six-dimensional supergravity.

SO(3) -invariant phase of the O(N)3 tensor model

We study classical and quantum (at large-$N$) field equations of bosonic tensor models with quartic interactions and $O(N)^3$ symmetry. Among various possible patterns of spontaneous symmetry breaking we highlight an $SO(3)$ invariant solution, with the tensor field expressed in terms of the Wigner $3jm$ symbol. We argue that such solution has a special role in the large-$N$ limit, as in particular its scaling in $N$ can provide an on-shell justification for the melonic large-$N$ limit of the two-particle irreducible effective action in a broken phase.

T -branes, string junctions, and 6D SCFTs

Recent work on 6D superconformal field theories (SCFTs) has established an intricate correspondence between certain Higgs branch deformations and nilpotent orbits of flavor symmetry algebras associated with T-branes. In this paper, we return to the stringy origin of these theories and show that many aspects of these deformations can be understood in terms of simple combinatorial data associated with multi-pronged strings stretched between stacks of intersecting 7-branes in F-theory. This data lets us determine the full structure of the nilpotent cone for each semi-simple flavor symmetry algebra, and it further allows us to characterize symmetry breaking patterns in quiver-like theories with classical gauge groups. An especially helpful feature of this analysis is that it extends to "short quivers" in which the breaking patterns from different flavor symmetry factors are correlated.

Applying Noether’s Theorem to Matter in the Milky Way: Evidence for External Perturbations and Non-steady-state Effects from Gaia Data Release 2

Abstract We apply Noether’s theorem to observations of main-sequence stars from the Gaia Data Release 2 archive to probe the matter distribution function of the Galaxy. That is, we examine the axial symmetry of stars at vertical heights z, , to probe the quality of the angular momentum L z as an integral of motion. The failure of this symmetry test would speak to a Milky Way, in both its visible and dark matter, that is not isolated and/or not in steady state. The left–right symmetry-breaking pattern we have observed, north and south, reveals both effects, with a measured deviation from symmetry of typically 0.5%. We show that a prolate form of the gravitational distortion of the Milky Way by the Large Magellanic Cloud, determined from fits to the Orphan stream by Erkal et al., is compatible with the size and sign of the axial-symmetry-breaking effects we have discovered in our sample of up to 14.4 million main-sequence stars, speaking to a distortion of an emergent, rather than static, nature.

Mixed gluinos and sgluons from a new SU(3) gauge group

I study supersymmetric models in which the QCD gauge group is the remnant diagonal subgroup from the spontaneous breaking of an $SU(3) \times SU(3)$ gauge group at a multi-TeV scale. In renormalizable models with soft supersymmetry breaking, the scalar potential is shown to have global minima with the required gauge symmetry breaking pattern. In addition to a massive color octet vector boson, this framework predicts 3 color octet spin-0 sgluons, and 4 color octet gluinos with both Dirac and Majorana mass terms. One of the gluino mass eigenstates typically has a coupling to quark-squark pairs that is at least as large as the prediction of minimal supersymmetry, but it need not be the lightest one.

Gravitational wave and collider searches for electroweak symmetry breaking patterns

We study the Electroweak symmetry breaking mechanism with extra Electroweak symmetry breaking contributions (eEWSB) that are bounded by the Fermi constant and limits from the related collider searches. The eEWSB is helpful to build a different zero temperature vacuum structure from the Standard Model (SM), and therefore leads to different Electroweak phase transition patterns at the early Universe. We investigate the collider search prospects and gravitational waves (GW) predictions from the strongly firstly order phase transition (SFOEWPT) in this scenario. The Higgs pair searches at lepton colliders are found to be complementary with the GW searches of the SFOEWPT parameter spaces.

Pattern selection in core-shell spheres

Curvature-induced symmetry-breaking pattern formation and transition are widely observed in curved film/substrate systems across different length scales such as embryogenesis, heterogeneous micro-particles, dehydrated fruits, growing tumors and planetary surfaces. Here, we find, both experimentally and theoretically, that morphological pattern selection of core-shell spheres, upon shrinkage of core or expansion of surface layer, is primarily determined by a single dimensionless parameter Cs which characterizes the stiffness ratio of core/shell and geometric curvature of the system. When the core remains relatively soft (Cs < 1.3), the core-shell sphere usually experiences subcritical buckling behavior with local dimples at the critical threshold. With a stiffer substrate (1.3 < Cs < 15), the system morphs into periodic buckyball patterns. With the continuous increase of the core stiffness (Cs > 15), symmetry-breaking disordered patterns involving polygon and labyrinth modes appear to be energetically favorable. With extremely large Cs ~ 1000, the core-shell sphere approximates to a planar film/substrate system and thus checkerboard patterns with grain boundaries are observed. Moreover, we find that the transition from subcritical to supercritical bifurcations can be quantitatively characterized by this parameter. Pattern selection based on this single key factor remarkably agrees with our experimental observations on oxidized polydimethylsiloxane (PDMS) microspheres in the entire validity range. Our results not only provide fundamental understanding of pattern selection in spherical film/substrate systems, but also pave a promising way to facilitate the design of morphology-related functional surfaces by quantitatively harnessing such curvature-modulus co-determined pattern formation.

General composite non-Abelian strings and flag manifold sigma models

We fully investigate the symmetry breaking patterns occurring upon creation of composite non-Abelian strings: vortex strings in non-Abelian theories where different sets of colours have different amounts of flux. After spontaneous symmetry breaking, there remains some internal colour degrees of freedom attached to these objects, which we argue must exist in a Flag manifold, a more general kind of projective space than both $\mathbb{CP}(N)$ and the Grassmannian manifold. These strings are expected to be BPS, since its constituents are. We demonstrate that this is true and construct a low-energy effective action for the fluctuations of the internal Flag moduli, which we then re-write it in two different ways for the dynamics of these degrees of freedom: a gauged linear sigma model with auxiliary fields and a non-linear sigma model with an explicit target space metric for the Flag Manifolds, both of which $\mathcal{N}=(2,2)$ supersymmetric. We finish by performing some groundwork analysis of the resulting theory.

Patterns of flavor symmetry breaking in hadron matrix elements involving u , d , and s quarks

By considering a flavour expansion about the SU(3)-flavour symmetric point, we investigate how flavour-blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference between quarks. Similarly to hadron masses we find the expansions to be constrained along a mass trajectory where the singlet quark mass is held constant, which provides invaluable insight into the mechanism of flavour symmetry breaking and proves beneficial for extrapolations to the physical point. Expansions are given up to third order in the expansion parameters. Considering higher orders would give no further constraints on the expansion parameters. The relation of the expansion coefficients to the quark-line-connected and quark-line disconnected terms in the 3-point correlation functions is also given. As we consider Wilson clover-like fermions, the addition of improvement coefficients is also discussed and shown to be included in the formalism developed here. As an example of the method we investigate this numerically via a lattice calculation of the flavour-conserving matrix elements of the vector first class form factors.

Self-gravitating SU(5) Higgs domain walls as a braneworld

Five-dimensional domain walls in gauged $SU(5)$ generate a position-dependent symmetry breaking pattern along the additional dimension. We analyze the perturbative stability and the four-dimensional (4D) spectrum of these walls in the self-gravitating case, in terms of diffeomorphism-invariant and Lie algebra gauge-invariant field fluctuations. We show that tachyonic modes are absent, ensuring perturbative stability. As expected, gravitational tensor and vector fluctuations behave like their counterparts in the standard ${Z}_{2}$ domain walls. All the Lie algebra valued fluctuations exhibit towers of 4D massive modes, which propagate in the bulk, with a continuous spectrum starting from zero. All the would-be 4D Nambu-Goldstone fields, which are gravitationally trapped in the case of a global symmetry, are nontrivially absent. However, we find no localizable 4D gauge bosons, either massless or massive. Instead, quasilocalizable discrete 4D massive modes for the gauge field fluctuations are found, along the spontaneously broken directions.

Continuum Goldstone spectrum of two-color QCD at finite density with staggered quarks

We carry out lattice simulations of two-color QCD and spectroscopy at finite density with two flavors of rooted-staggered quarks and a diquark source term. As in a previous four-flavor study, for small values of the inverse gauge coupling we observe a Goldstone spectrum which reflects the symmetry-breaking pattern of a Gaussian symplectic chiral random-matrix ensemble (GSE) with Dyson index $\beta_D=4$, which corresponds to any-color QCD with adjoint quarks in the continuum instead of QC$_2$D wih fundamental quarks. We show that this unphysical behavior occurs only inside of the bulk phase of $SU(2)$ gauge theory, where the density of $Z_2$ monopoles is high. Using an improved gauge action and a somewhat larger inverse coupling to suppress these monopoles, we demonstrate that the continuum Goldstone spectrum of two-color QCD, corresponding to a Gaussian orthogonal ensemble (GOE) with Dyson index $\beta_D=1$, is recovered also with rooted-staggered quarks once simulations are performed away from the bulk phase. We further demonstrate how this change of random-matrix ensemble is reflected in the distribution of eigenvalues of the Dirac operator. By computing the unfolded level spacings inside and outside of the bulk phase, we demonstrate that, starting with the low-lying eigenmodes which determine the infrared physics, the distribution of eigenmodes continuously changes from the GSE to the GOE one as monopoles are suppressed.

The minimal simple composite Higgs model

Most of the analysis of composite Higgs have focussed on the Minimal Composite Higgs Model, based on the coset SO(5) × U(1)X/ SO(4) × U(1)X. We consider a model based on the coset of simple groups SO(7)/ SO(6), with SO(4) × U(1)X embedded into SO(6). This extension of the minimal model leads to a new complex pNGB that has hypercharge and is a singlet of SU(2)L, with properties mostly determined by the pattern of symmetry breaking and a mass of order TeV. Composite electroweak unification also leads to new bosonic and fermion resonances with exotic charges, not present in the minimal model, the lightest of these resonances being stable. A new rich phenomenology is expected at LHC.

Roberge-Weiss transitions at different center symmetry breaking patterns in a Z3 -QCD model

We study how the Roberge-Weiss (RW) transition depends on the pattern of center symmetry breaking using a $\mathbb{Z}_{3}$-QCD model. We adopt flavor-dependent quark imaginary chemical potentials, namely $(\mu_{u},\mu_{d},\mu_{s})/iT=(\theta-2\pi{C}/3,\,\theta,\,\theta+2\pi{C}/3)$ with $C\in[0,1]$. The RW periodicity is guaranteed and the center symmetry of $\mathbb{Z}_{3}$-QCD is explicitly broken when $C\neq{1}$ or/and quark masses are non-degenerate. For $N_{f}=3$ and $C\neq{1}$, the RW transition occurs at $\theta=\theta_{RW}=(2k+1)\pi/3\,(k\in\mathbb{Z})$, which becomes stronger with decrease of $C$. When $C={1}$, the $\theta_{RW}$ turns into $2k\pi/3$ for $N_{f}=2+1$, but keeps $(2k+1)\pi/3$ for $N_{f}=1+2$; in both cases, the RW transitions get stronger with the mass mismatch. For other $C\neq{0}$ cases, the $\theta_{RW}$'s are not integral multiples of $\pi/3$. We find that the RW transition is more sensitive to the deviation of $C$ from one compared to the mass non-degeneracy and thus the strength of the traditional RW transition with $C=0$ is the strongest. The nature of RW endpoints and its implications to deconfinement transition are investigated.

Electroweak breaking and Higgs boson profile in the simplest linear seesaw model

We examine the simplest realization of the linear seesaw mechanism within the Standard Model gauge structure. Besides the standard scalar doublet, there are two lepton-number-carrying scalars, a nearly inert SU(2)L doublet and a singlet. Neutrino masses result from the spontaneous violation of lepton number, implying the existence of a Nambu-Goldstone boson. Such “majoron” would be copiously produced in stars, leading to stringent astrophysical constraints. We study the profile of the Higgs bosons in this model, including their effective couplings to the vector bosons and their invisible decay branching ratios. A consistent electroweak symmetry breaking pattern emerges with a compressed spectrum of scalars in which the “Standard Model” Higgs boson can have a sizeable invisible decay into the invisible majorons.

Monopoles, strings, and necklaces in SO(10) and E6

We employ a variety of symmetry breaking patterns in SO(10) and E6 Grand Unified Theories to demonstrate the appearance of topological defects including magnetic monopoles, strings, and necklaces. We show that independent of the symmetry breaking pattern, a topologically stable superheavy monopole carrying a single unit of Dirac charge as well as color magnetic charge is always present. Lighter intermediate mass topologically stable monopoles carrying two or three quanta of Dirac charge can appear in SO(10) and E6 models respectively. These lighter monopoles as well as topologically stable intermediate scale strings can survive an inflationary epoch. We also show the ap­ pearance of a novel necklace configuration in SO(10) broken to the Standard Model via SU(4)c × SU(2)L × SU(2)R. It consists of SU(4)c and SU(2)R monopoles connected by flux tubes. Necklaces consisting of monopoles and antimonopoles joined together by flux tubes are also identified. Even in the absence of topologically stable strings, a monopole-string system can temporarily appear. This system decays by emitting gravity waves and we provide an example in which the spectrum of these waves is strongly peaked around 10−4 Hz with Ωqwh2 ≃10−12. This spectrum should be within the detection capability of LISA.

Spontaneous symmetry breaking and the flat phase of crystalline membranes

Crystalline membranes are one of the rare examples of bidimensional systems in which long-range order can stabilise an ordered phase in the thermodynamic limit. By a careful analysis of the Goldstone modes counting, we propose a symmetry breaking mechanism associated with the generation of the flat phase and show how it highlights the crucial role played by the crystalline lattice in the establishment of long-range order in these objects. Comparison with other symmetry breaking mechanisms in membrane physics is also used to unveil the links between symmetry breaking patterns and the physical properties of the flat phase.

Shift-symmetric spin-1 theories

We study interacting massive spin-1 theories in de Sitter (dS) and anti-de Sitter (AdS) space that possess shift symmetries parametrized by (A)dS Killing vectors. We show how they emerge from the massless limit of massive spin-2 theories on (A)dS space. In the case of massive gravity, the corresponding spin-1 theory realizes a symmetry breaking pattern that takes two copies of the (A)dS isometry group down to a diagonal subgroup. By taking the flat space limit of this theory, we find a new symmetry of the decoupling limit of massive gravity in flat space. This symmetry acts on the vector modes, is parametrize by an antisymmetric tensor, and fixes the nonlinear structure of the scalar-vector sector of the decoupling limit.

Lessons from topological superfluids: Safe and dangerous routes to antispacetime

All realistic second order phase transitions are undergone at finite transition rate and are therefore non-adiabatic. In symmetry-breaking phase transitions the non-adiabatic processes, as predicted by Kibble and Zurek [1, 2], lead to the formation of topological defects (the so-called Kibble-Zurek mechanism). The exact nature of the resultingdefects depends on the detailed symmetry-breaking pattern.

Spontaneous Symmetry Breaking Induced by Quantum Monitoring.

Spontaneous symmetry breaking (SSB) is responsible for structure formation in scenarios ranging from condensed matter to cosmology. SSB is broadly understood in terms of perturbations to the Hamiltonian governing the dynamics or to the state of the system. We study SSB due to quantum monitoring of a system via continuous quantum measurements. The acquisition of information during the measurement process induces a measurement backaction that seeds SSB. In this setting, by monitoring different observables, an observer can tailor the topology of the vacuum manifold, the pattern of symmetry breaking, and the nature of the resulting domains and topological defects.

A new approach to fuzzy sets: Application to the design of nonlinear time series, symmetry-breaking patterns, and non-sinusoidal limit-cycle oscillations

Abstract It is shown that characteristic functions of sets can be made fuzzy by means of the B κ -function, recently introduced by the author, where the fuzziness parameter κ ∈ R controls how much a fuzzy set deviates from the crisp set obtained in the limit κ → 0. As applications, we present first a general expression for a switching function that may be of interest in electrical engineering and in the design of nonlinear time series. We then introduce another general expression that allows wallpaper and frieze patterns for every possible planar symmetry group (besides patterns typical of quasicrystals) to be designed. We show how the fuzziness parameter κ plays an analogous role to temperature in physical applications and may be used to break the symmetry of spatial patterns. As a further, important application, we establish a theorem on the shaping of limit cycle oscillations far from bifurcations in smooth deterministic nonlinear dynamical systems governed by differential equations. Following this application, we briefly discuss a generalization of the Stuart-Landau equation to non-sinusoidal oscillators.