Showing papers on "Explicit symmetry breaking published in 2021"

The effective action of superrotation modes

Abstract: Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, we show that superrotation reparametrization modes are governed by an Alekseev-Shatashvili action on the celestial sphere. This two-dimensional conformal theory describes spontaneous symmetry breaking of Virasoro superrotations together with the explicit symmetry breaking of more general Diff( $$ {\mathcal{S}}^2 $$ ) superrotations. We arrive at this result by first reformulating the asymptotic field equations and symmetries of the radiative vacuum sector in terms of a Chern-Simons theory at null infinity, and subsequently performing a Hamiltonian reduction of this theory onto the celestial sphere.

Nonlocal symmetry constraints and exact interaction solutions of the (2+1) dimensional modified generalized long dispersive wave equation

Abstract: In this paper, nonlocal symmetry of the (2+1) dimensional modified generalized long dispersive wave system and its applications are investigated. The nonlocal symmetry related to the eigenfunctions in Lax pairs is derived, and infinitely many nonlocal symmetries are obtained. By introducing three potentials, the prolongation is found to localize the given nonlocal symmetry. Various finite-and infinite-dimensional integrable models are constructed by using the nonlocal symmetry constraint method. Moreover, applying the general Lie symmetry approach to the enlarged system, the finite symmetry transformation and similarity reductions are computed to give novel exact interaction solutions. In particular, the explicit soliton-cnoidal wave solution is obtained for the modified generalized long dispersive wave system, and it can be reduced to the two-dark-soliton solution in one special case.

Dark matter from a complex scalar singlet: the role of dark CP and other discrete symmetries

Abstract: We study the case of a pseudo-scalar dark matter candidate which emerges from a complex scalar singlet, charged under a global U(1) symmetry, which is broken both explicitly and spontaneously. The pseudo-scalar is naturally stabilized by the presence of a remnant discrete symmetry: dark CP. We study and compare the phenomenology of several simplified models with only one explicit symmetry breaking term. We find that several regions of the parameter space are able to reproduce the observed dark matter abundance while respecting direct detection and invisible Higgs decay limits: in the resonances of the two scalars, featuring the known as forbidden or secluded dark matter, and through non-resonant Higgs-mediated annihilations. In some cases, combining different measurements would allow one to distinguish the breaking pattern of the symmetry. Moreover, this setup admits a light DM candidate at the sub-GeV scale. We also discuss the situation where more than one symmetry breaking term is present. In that case, the dark CP symmetry may be spontaneously broken, thus spoiling the stability of the dark matter candidate. Requiring that this does not happen imposes a constraint on the allowed parameter space. Finally, we consider an effective field theory approach valid in the pseudo-Nambu-Goldstone boson limit and when the U(1) breaking scale is much larger than the electroweak scale.

Boundary criticality of the 3d O(N) model: from normal to extraordinary

Abstract: It was recently realized that the three dimensional O(N) model possesses an extraordinary boundary universality class for a finite range of $N \ge 2$. For a given $N$, the existence and universal properties of this class are predicted to be controlled by certain amplitudes of the normal universality class, where one applies an explicit symmetry breaking field to the boundary. In this paper, we study the normal universality class for $N = 2, 3$ using Monte Carlo simulations on an improved lattice model and extract these universal amplitudes. Our results are in good agreement with direct Monte Carlo studies of the extraordinary universality class serving as a non-trivial quantitative check of the connection between the normal and extraordinary classes.

Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration

Abstract: We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians In particular, we include the predictive function of a neural network, designed for phase classification, as a conjugate variable coupled to an external field within the Hamiltonian of a system Results in the two-dimensional Ising model evidence that the field can induce an order-disorder phase transition by breaking or restoring the symmetry, in contrast with the field of the conventional order parameter which can only cause explicit symmetry breaking The critical behaviour is then studied by proposing reweighting that is agnostic to the original Hamiltonian and forming a renormalization group mapping on quantities derived from the neural network Accurate estimates of the critical fixed point and the operators that govern the divergence of the correlation length are provided We conclude by discussing how the method provides an essential step towards bridging machine learning and physics

Symmetry breaking modelling for azimuthal combustion dynamics

Abstract: Annular combustors can exhibit azimuthal thermoacoustic instabilities, which can rotate as a spinning wave at the speed of sound in the azimuthal direction, oscillate as a standing wave with pressure nodes fixed in space, or be a linear combination of these. These oscillations happen if a positive feedback loop between acoustics and the response of the flames to the acoustics in the annulus occurs. This paper discusses how two different explicit symmetry breaking mechanisms affect the dynamics of these waves. We first show how small differences between the flame responses lead to one strong topological change in the dynamical system phase space, making the system prefer orientation angles at two azimuthal locations, one opposite of the other in the annulus, as found in the experiments. This symmetry breaking is modelled by directly perturbing the flame responses around the annulus with some scatter, to represent the effect of manufacturing tolerances of the burners. We then consider recent experimental evidence that the heat release rate of the flames depends on the spinning direction (clockwise or anticlockwise) when the system is spinning. In particular we model one experiment in which the flame response is found to be stronger when the wave rotates in the anticlockwise direction. We show that the statistics of the resulting model are qualitatively very similar to the experimental results showing a preference for spinning states in the anticlockwise direction.

Supersymmetry anomaly in the superconformal Wess-Zumino model

Abstract: We present a comprehensive analysis of supersymmetry anomalies in the free and massless Wess-Zumino (WZ) model in perturbation theory. At the classical level the model possesses $$ \mathcal{N} $$ = 1 superconformal symmetry, which is partially broken by quantum anomalies. The form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents used. It was previously shown that the R-symmetry anomaly of the conformal current multiplet induces an anomaly in Q-supersymmetry, which appears first in 4-point functions. Here we confirm this result by an explicit 1-loop computation using a supersymmetric Pauli-Villars regulator. The conformal current multiplet does not exist in the regulated theory because the regulator breaks conformal invariance, R-symmetry and S-supersymmetry explicitly. The minimal massive multiplet is the Ferrara-Zumino (FZ) one and the supersymmetry preserved by the regulator is a specific field dependent combination of Q- and S- supersymmetry of the conformal multiplet. While this supersymmetry is non anomalous, conformal invariance, R-symmetry and the original Q- and S-supersymmetries are explicitly broken by finite contact terms, both in the regulated and renormalized theories. A conformal current multiplet does exist for the renormalized theory and may be obtained from the FZ multiplet by a set of finite local counterterms that eliminate the explicit symmetry breaking, thus restoring superconformal invariance up to anomalies. However, this necessarily renders both Q- and S-supersymmetries anomalous, as is manifest starting at 4-point functions of conformal multiplet currents. The paper contains a detailed discussion of a number of issues and subtleties related to Ward identities that may be useful in a wider context.

Spontaneous chiral symmetry breaking in holographic soft wall models

Abstract: We investigate nonlinear extensions of the holographic soft wall model proposed by Karch, Katz, Son and Stephanov [1] including non-minimal couplings in the five-dimensional action. The non-minimal couplings bring a new parameter $a_0$ which controls the transition between spontaneous and explicit symmetry breaking near the limit of massless quarks (the chiral limit). In the physical region (positive quark mass), we show that above a critical value of the parameter $a_0$ the chiral condensate $\langle \bar{q} q \rangle$ is finite in the chiral limit, signifying spontaneous chiral symmetry breaking. This result is supported by the lightest states arising in the spectrum of the pseudoscalar mesons, which become massless in the chiral limit and are therefore intrepreted as Nambu-Goldstone bosons. Moreover, the decay constants of the pseudoscalar mesons also support this conclusion, as well as the Gell-Mann-Oakes-Renner (GOR) relation satisfied by the lightest states. We also calculate the spectrum of scalar, vector, and axial-vector mesons with their corresponding decay constants. We describe the evolution of masses and decay constants with the increasing of the quark mass and for the physical mass we compare our results against available experimental data. Finally, we do not find instabilities in our model for the physical region (positive quark mass)

Spontaneous Symmetry Breaking, Spectral Statistics, and the Ramp

Abstract: Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and approximate global symmetries of a system have clear signatures in these spectral statistics, enhancing the spectral form factor or correspondingly weakening level repulsion. This paper extends those results to the case of spontaneous symmetry breaking, and shows that, surprisingly, spontaneously breaking a symmetry further enhances the spectral form factor. For both RMT-inspired toy models and models where the symmetry breaking has a description in terms of fluctuating hydrodynamics, we obtain formulas for this enhancement for arbitrary symmetry breaking patterns, including $Z_n$, $U(1)$, and partially or fully broken non-Abelian symmetries.

Extended Lipkin-Meshkov-Glick Hamiltonian

Abstract: The Lipkin-Meshkov-Glick (LMG) model was devised to test the validity of different approximate formalisms to treat many-particle systems. The model was constructed to be exactly solvable and yet non-trivial, in order to capture some of the main features of real physical systems. In the present contribution, we explicitly review the fact that different many-body approximations commonly used in different fields in physics clearly fail to describe the exact LMG solution. With similar assumptions as those adopted for the LMG model, we propose a new Hamiltonian based on a general two-body interaction. The new model (Extended LMG) is not only more general than the original LMG model and, therefore, with a potentially larger spectrum of applicability, but also the physics behind its exact solution can be much better captured by common many-body approximations. At the basis of this improvement lies a new term in the Hamiltonian that depends on the number of constituents of the system and polarizes it, producing an explicit symmetry breaking.

Helical Symmetry Breaking and Quantum Anomaly in Massive Dirac Fermions

Abstract: Helical symmetry of massive Dirac fermions is broken explicitly in the presence of electric and magnetic fields. Here we present two equations for the divergence of helical and axial-vector currents following the Jackiw-Johnson approach to the anomaly of the neutral axial vector current. We discover the contribution from the helical symmetry breaking is attributed to the occupancy of the two states at the top of the valence band and the bottom of the conduction band. The explicit symmetry breaking fully cancels the anomalous correction from the quantum fluctuation in the band gap. The chiral anomaly can be derived from the helical symmetry breaking. It provides an alternative route to understand the chiral anomaly from the point of view of the helical symmetry breaking. The pertinent physical consequences in condensed matter are the helical magnetic effect which means a charge current circulating at the direction of the magnetic field, and the mass-dependent positive longitudinal magnetoconductivity as a transport signature. The discovery not only reflects anomalous magneto-transport properties of massive Dirac materials but also reveals the close relation between the helical symmetry breaking and the physics of chiral anomaly in quantum field theory and high energy physics.

Mass–action equivalence with respect to Explicit Symmetry Breaking

Abstract: The mass–action equivalence emerges naturally as the consequence of Relativistic Heisenberg Uncertainty (RHU) It changes the structure of relativistic energy–momentum equation that has been underpinning the chosen Lagrangian of the Standard Model, ie, the Lagrangian which the Higgs mechanism works The transition from the mass–energy to the mass–action equivalence zone occurs at a certain value of the particle’s wave group velocity $$v_{{\text{g}}}$$ indicating the crossing curve between relativistic energy and action Due to this transition, particles in the Standard Model are not going to gain inertial mass coming from the Higgs mechanism and related Higgs field, but from another mechanism which can break the Lagrangian symmetry of the Standard Model This mechanism corresponds to Explicit Symmetry Breaking by generating the new type of field, ie, the X-Higgs-like field and works based on the mass–action equivalence This field provides the mass for the X Matter as well as Higgs field for Ordinary Matter The gaining mass of particles due to this mechanism is not related to the form of ordinary relativistic energy, but to the form of relativistic action It leads us to the new dynamical equation instead of the ordinary Klein–Gordon and Dirac equation There are two phenomena due to the increasing and decreasing of particle’s velocity in this mechanism From the lower to the higher velocity, particle gains additional inertial mass from the X Matter, while conversely particle loses its inertial mass It is reasonable for us to view that the missing inertial mass of particles in the Standard Model is compensated as the Dark Matter The X-Higgs-like field breaking to be the Dark-Higgs-like and recognized Higgs field can be considered to explain the origin of the Dark and Ordinary Matter from the X Matter

Dynamics of azimuthal thermoacoustic modes in imperfectly symmetric annular geometries

Abstract: Using a nominally symmetric annular combustor, we present experimental evidence of a predicted spontaneous symmetry breaking and an unexpected explicit symmetry breaking in the neighborhood of the Hopf bifurcation, which separates linearly-stable azimuthal thermoacoustic modes from self-oscillating modes. We derive and solve a multidimensional Fokker-Planck equation to unravel a unified picture of the phase space topology. We demonstrate that symmetric probability density functions of the thermoacoustic state vector are elusive, because the effect of asymmetries, even imperceptible ones, is magnified close to the bifurcation.

Dark matter from a complex scalar singlet: The role of dark CP and other discrete symmetries.

Abstract: We study the case of a pseudo-scalar dark matter candidate which emerges from a complex scalar singlet, charged under a global U(1) symmetry, which is broken both explicit and spontaneously. The pseudo-scalar is naturally stabilized by the presence of a remnant discrete symmetry: dark CP. We study and compare the phenomenology of several simplified models with only one explicit symmetry breaking term. We find that several regions of the parameter space are able to reproduce the observed dark matter abundance while respecting direct detection and invisible Higgs decay limits: in the resonances of the two scalars, featuring the known as forbidden or secluded dark matter, and through non-resonant Higgs-mediated annihilations. In some cases, combining different measurements would allow one to distinguish the breaking pattern of the symmetry. We also discuss the situation where more than one symmetry breaking term is present. In that case, the dark CP symmetry may be spontaneously broken and spoil the stability of the dark matter candidate. Requiring that this does not happen imposes a constraint on the allowed parameter space. Finally, we consider an effective field theory approach valid in the pseudo-Nambu-Goldstone boson limit and when the U(1) breaking scale is much larger than the electroweak scale.

Quark and Gluon Condensates in Strongly Magnetized Nuclear Matter

Abstract: Medium modification of the quark and gluon condensates in the strongly magnetized symmetric nuclear medium has been calculated using chiral SU(3) model. The explicit symmetry breaking term and the broken scale invariance part of Lagrangian density of the model are exploited to express the quark and gluon condensates in terms of \(\sigma \), \(\zeta \), \(\delta \), and \(\chi \) fields. The density and temperature dependence of these scalar fields, for different magnetic field strength, are evaluated first and subsequently used as input in the expressions of quark and gluon condensates. Our present study on medium modification of quark and gluon condensates can be used further as input in different QCD sum rules. Consequently, this may help to understand the experimental observables arising from various heavy-ion collision experiments whose one of the aim is to explore the in-medium properties of hadrons.

Noether's Learning Dynamics: Role of Symmetry Breaking in Neural Networks.

Abstract: In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle to efficiently capture regularities in the world, but the role of symmetry breaking is not well understood. Here, we develop a theoretical framework to study the "geometry of learning dynamics" in neural networks, and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. To build this understanding, we model the discrete learning dynamics of gradient descent using a continuous-time Lagrangian formulation, in which the learning rule corresponds to the kinetic energy and the loss function corresponds to the potential energy. Then, we identify "kinetic symmetry breaking" (KSB), the condition when the kinetic energy explicitly breaks the symmetry of the potential function. We generalize Noether's theorem known in physics to take into account KSB and derive the resulting motion of the Noether charge: "Noether's Learning Dynamics" (NLD). Finally, we apply NLD to neural networks with normalization layers and reveal how KSB introduces a mechanism of "implicit adaptive optimization", establishing an analogy between learning dynamics induced by normalization layers and RMSProp. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.