Invariance Breaking Research Articles

Fine-tuning with brane-localized flux in 6D supergravity

There are claims in the literature that the cosmological constant problem could be solved in a braneworld model with two large (micron-sized) supersymmetric extra dimensions. The mechanism relies on two basic ingredients: First, the cosmological constant only curves the compact bulk geometry into a rugby shape while the 4D curvature stays flat. Second, a brane-localized flux term is introduced in order to circumvent Weinberg's fine-tuning argument, which otherwise enters here through a backdoor via the flux quantization condition. In this paper, we show that the latter mechanism does not work in the way it was designed: The only localized flux coupling that guarantees a flat on-brane geometry is one which preserves the scale invariance of the bulk theory. Consequently, Weinberg's argument applies, making a fine-tuning necessary again. The only remaining window of opportunity lies within scale invariance breaking brane couplings, for which the tuning could be avoided. Whether the corresponding 4D curvature could be kept under control and in agreement with the observed value will be answered in our companion paper [arXiv:1512.03800].

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials

It is well known that a nonvanishing Hall conductivity requires broken time-reversal symmetry. However, in this work, we demonstrate that Hall-like currents can occur in second-order response to external electric fields in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the driving frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. The nonlinear Hall coefficient is a rank-two pseudotensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides, and Weyl semimetals.

Using gap symmetry and structure to reveal the pairing mechanism in Fe-based superconductors

I review theoretical ideas and implications of experiments for the gap structure and symmetry of the Fe-based superconductors. Unlike any other class of unconventional superconductors, one has in these systems the possibility to tune the interactions by small changes in pressure, doping or disorder. Thus, measurements of order parameter evolution with these parameters should enable a deeper understanding of the underlying interactions. I briefly review the "standard paradigm" for $s$-wave pairing in these systems, and then focus on developments in the past several years which have challenged this picture. I discuss the reasons for the apparent close competition between pairing in s- and d-wave channels, particularly in those systems where one type of Fermi surface pocket -- hole or electron -- is missing. Observation of a transition between $s$- and $d$-wave symmetry, possibly via a time reversal symmetry breaking "$s+id$" state, would provide an importantconfirmation of these ideas. Several proposals for detecting these novel phases are discussed, including the appearance of order parameter collective modes in Raman and optical conductivities. Transitions between two different types of $s$-wave states, involving various combinations of signs on Fermi surface pockets, can also proceed through a ${\cal T}$-breaking "$s+is$" state. I discuss recent work that suggests pairing may take place away from the Fermi level over a surprisingly large energy range, as well as the effect of glide plane symmetry of the Fe-based systems on the superconductivity, including various exotic, time and translational invariance breaking pair states that have been proposed. Finally, I address disorder issues, and the various ways systematic introduction of disorder can (and cannot) be used to extract information on gap symmetry and structure.

Quark Yukawa pattern from spontaneous breaking of flavour [formula omitted

A SU(3)Q×SU(3)u×SU(3)d invariant scalar potential breaking spontaneously the quark flavour symmetry can explain the Standard Model flavour puzzle. The approximate alignment in flavour space of the vacuum expectation values of the up and down ‘Yukawa fields’ results as a dynamical effect. The observed quark mixing angles, the weak CP violating phase, and hierarchical quark masses can be all reproduced at the cost of introducing additional (auxiliary) scalar multiplets, but without the need of introducing hierarchical parameters.

Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next-to-leading order

We present the first numerical solution to the next to leading order Balitsky-Kovchegov (BK) equation in coordinate space in the large-$N_\mathrm{c}$ limit. In addition to the dipole operator we also solve the evolution of the "conformal dipole" for which the conformal invariance breaking double logarithmic term is absent from the evolution equation. The NLO corrections are shown to slow down the evolution. We show that the solution depends strongly on the details of the initial condition, and that the solution to the equation is not positive definite with all initial conditions relevant for phenomenological applications.

Relic gravity waves and 7 keV dark matter from a GeV scale inflaton

We study the mechanism of generation of 7 keV sterile neutrino Dark Matter (DM) in the model with light inflaton χ, which serves as a messenger of scale invariance breaking. In this model the inflaton, in addition to providing reheating to the Standard Model (SM) particles, decays directly into sterile neutrinos. The latter are responsible for the active neutrino oscillations via seesaw type I mechanism. While the two sterile neutrinos may also produce the lepton asymmetry in the primordial plasma and hence explain the baryon asymmetry of the Universe, the third one being the lightest may be of 7 keV and serve as DM. For this mechanism to work, the mass of the inflaton is bound to be light (0.1–1 GeV) and uniquely determines its properties, which allows to test the model. For particle physics experiments these are: inflaton lifetime (10−5–10−12 s), branching ratio of B-meson to kaon and inflaton (10−6–10−4) and inflaton branching ratios into light SM particles like it would be for the SM Higgs boson of the same mass. For cosmological experiments these are: spectral index of scalar perturbations (ns≃0.957–0.967), and amount of tensor perturbations produced at inflation (tensor-to-scalar ratio r≃0.15–0.005).

Gauge invariance and spontaneous symmetry breaking in two-gap superconductors

The gauge symmetry of the Ginzburg-Landau theory for two-gap superconductors is analyzed in this letter. We argue that the existence of two different phases, associated with the two independent scalar Higgs fields, explicitly breaks the gauge symmetry of the Ginzburg-Landau hamiltonian, unless a new additional vector field is included. Furthermore, the interference term, or Josephson coupling, holding a direct dependence with the phase difference, also explicitly breaks down the gauge symmetry. We show that a solution for the problem is achieved by adding an additional kinetic coupling term between the two vector fields, which generates the desired terms through a spontaneous symmetry breaking mechanism. Finally, the electrodynamics of the system is also presented in terms of the supercurrents inside the superconducting region.

Optical conductivity of curved graphene

We compute the optical conductivity for an out-of-plane deformation in graphene using an approach based on solutions of the Dirac equation in curved space. Different examples of periodic deformations along one direction translates into an enhancement of the optical conductivity peaks in the region of the far- and mid-infrared frequencies for periodicities ∼100 nm. The width and position of the peaks can be changed by dialling the parameters of the deformation profiles. The enhancement of the optical conductivity is due to intraband transitions and the translational invariance breaking in the geometrically deformed background. Furthermore, we derive an analytical solution of the Dirac equation in a curved space for a general deformation along one spatial direction. For this class of geometries, it is shown that curvature induces an extra phase in the electron wave function, which can also be explored to produce interference devices of the Aharonov–Bohm type.

Quark masses, mixings, andCPviolation from spontaneous breaking of flavorSU(3)3

A ${\cal G}_{\cal F}=SU(3)_{Q}\times SU(3)_{u}\times SU(3)_{d}$ invariant scalar potential breaking spontaneously the quark flavor symmetry can explain the standard model flavor puzzle. The approximate alignment in flavor space of the vacuum expectation values of the up and down ``Yukawa fields'' is explained as a dynamical effect, and the observed quark mixing angles, the weak CP violating phase, and hierarchical quark masses can be reproduced without introducing hierarchical parameters.

Effective dynamics of a classical point charge

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out.

Persistence of Spin Edge Currents in Disordered Quantum Spin Hall Systems

For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance breaking term (such as the Rashba coupling), it is proved that the spin edge currents persist provided there is a spectral gap and the spin Chern numbers are well-defined and non-trivial. These conditions on being in the quantum spin Hall phase do not require time-reversal symmetry. The result materializes the general philosophy that topological insulators are non-trivial bulk systems with edge currents that are topologically protected against Anderson localization.

Inducing Time-Reversal-Invariant Topological Superconductivity and Fermion Parity Pumping in Quantum Wires

We propose a setup to realize time-reversal-invariant topological superconductors in quantum wires, proximity coupled to conventional superconductors. We consider a model of quantum wire with strong spin-orbit coupling and proximity coupling to two s-wave superconductors. When the relative phase between the two superconductors is ϕ=π a Kramers pair of Majorana zero modes appears at each edge of the wire. We study the robustness of the phase in the presence of both time-reversal-invariant and time-reversal-breaking perturbations. In addition, we show that the system forms a natural realization of a fermion parity pump, switching the local fermion parity of both edges when the relative phase between the superconductors is changed adiabatically by 2π.

Search for CPT and Lorentz invariance violation with neutral kaons at KLOE

The neutral kaon system offers a unique possibility to perform fundamental tests of fundamental symmetry such CP and CPT invariance. In this contribution the KLOE search for CPT symmetry and Lorentz Invariance breaking in the Standard Model Extension framework is reported. Preliminary results are:

Free boundary ballooning mode representation

A new type of ballooning mode invariance is found in this paper. Application of this invariance is shown to be able to reduce the two-dimensional problem of free boundary high n modes, such as the peeling-ballooning modes, to a one-dimensional problem. Here, n is toroidal mode number. In contrast to the conventional ballooning representation, which requires the translational invariance of the Fourier components of the perturbations, the new invariance reflects that the independent solutions of the high n mode equations are translationally invariant from one radial interval surrounding a single singular surface to the other intervals. The conventional ballooning mode invariance breaks down at the vicinity of plasma edge, since the Fourier components with rational surfaces in vacuum region are completely different from those with rational surfaces in plasma region. But, the new type of invariance remains valid. This overcomes the limitation of the conventional ballooning mode representation for studying free boundary modes.

Lorentz completion of effective string (and p-brane) action

The formation of a confining string (or a p-brane) in a Poincare' invariant theory breaks spontaneously this symmetry which is thereby realized non-linearly in the effective action of these extended objects. As a consequence the form of the action is strongly constrained. A new general method is described to obtain in a systematic way higher order Lorentz invariant contributions to this action. We find a simple recipe to promote a term invariant under the stability subgroup to an expression invariant under the whole Lorentz group. It is based on the following three steps: in the saturation of worldsheet (or worldvolume) indices replace the Minkowski metric with the inverse of the induced metric; in the saturation of indices of the transverse coordinates describing the position of the extended object replace the Euclidean metric with a certain new metric; finally replace the field derivatives of order higher than two with a certain covariant derivative. Lorentz invariance of the expression modified this way immediately follows. We find in particular that the leading bulk deviation of the Nambu Goto action in any space-time dimensions is proportional to the square of scalar curvature.

3-loop 3PI effective action for 3D SU(3) QCD

The 3PI method is a technique to resum an infinite class of diagrams, which may be useful in studying nonperturbative thermodynamics and dynamics in quantum field theory. But it has never been successfully applied to gauge theories, where there are serious questions about gauge invariance breaking. We show how to perform the 3PI resummation of QCD in 3 Euclidean spacetime dimensions, a warmup problem to the 4 or 3+1 dimensional case. We present the complete details of the technical problems and how they are overcome. We postpone a comparison of gauge invariant correlation functions with their lattice-determined counterparts to a future publication.

Gauge theory andSIM(2)superspace

In this paper the SIM(2) superspace formulation of the supersymmetric Yang-Mills gauge theory minimally coupled to chiral superfields is discussed. The super-Poincare invariant supersymmetric Yang-Mills theory is rewritten to SIM(2) superspace formalism and the effects of SIM(2) invariant but Lorentz breaking terms are discussed. Two approaches are investigated. The first is based on the gauge chiral representation of the supersymmetric gauge theory and the second is based on the covariant representation of the supersymmetric gauge theory.

Primordial magnetic fields and dynamos from parity violated torsion

It is well known that torsion induced magnetic fields may seed galactic dynamos, but the price one pays for that is the conformal and gauge invariance breaks and a tiny photon mass. More recently I have shown [L.C. Garcia de Andrade, Phys. Lett. B 468 (2011) 28] that magnetic fields decay in a gauge invariant non-minimal coupling theory of torsion is slow down, which would allow for dynamo action to take place. In this Letter, by adding a parity violation term of the type Rμνρσϵμνρσ to the non-coupling term, a magnetic dynamo equation is obtained. From dynamo equation it is shown that torsion terms only appear in the dynamo equation when diffusion in the cosmic plasma is present. Torsion breaks the homogeneity of the magnetic field in the universe. Since Zeldovich anti-dynamo theorem assumes that the spacetime should be totally flat, torsion is responsible for violation of anti-dynamo theorem in 2D spatial dimensions. Contrary to previous results torsion induced primordial magnetic fields cannot seed galactic dynamos since from torsion and diffusion coefficient the decaying time of the magnetic field is 106yrs, which is much shorter than the galaxy age.

Search for Lorentz Invariance breaking with a likelihood fit of the PKS 2155-304 flare data taken on MJD 53944

Several models of Quantum Gravity predict Lorentz Symmetry breaking at energy scales approaching the Planck scale (∼10 19 GeV). With present photon data from the observations of distant astrophysical sources, it is possible to constrain the Lorentz Symmetry breaking linear term in the standard photon dispersion relations. Gamma Ray Bursts (GRB) and flaring Active Galactic Nuclei (AGN) are complementary to each other for this purpose, since they are observed at different distances in different energy ranges and with different levels of variability. Following a previous publication of the High Energy Stereoscopic System (H.E.S.S.) collaboration [1], a more sensitive event-by-event method consisting of a likelihood fit is applied to PKS 2155-304 flare data of MJD 53944 (July 28, 2006) as used in the previous publication. The previous limit on the linear term is improved by a factor of ∼3 up to M QG l > 2.1 × 10 18 GeV and is currently the best result obtained with blazars. The sensitivity to the quadratic term is lower and provides a limit of M QG q > 6.4 × 10 10 GeV, which is the best value obtained so far with an AGN and similar to the best limits obtained with GRB.

Spontaneous breaking of superconformal invariance in [formula omitted] supersymmetric Chern–Simons-matter theories in the large N limit

In this work we study the spontaneous breaking of superconformal and gauge invariances in the Abelian N = 1 , 2 three-dimensional supersymmetric Chern–Simons-matter (SCSM) theories in a large N flavor limit. We compute the Kählerian effective superpotential at subleading order in 1 / N and show that the Coleman–Weinberg mechanism is responsible for the dynamical generation of a mass scale in the N = 1 model. This effect appears due to two-loop diagrams that are logarithmic divergent. We also show that the Coleman–Weinberg mechanism fails when we lift from the N = 1 to the N = 2 SCSM model.