non-Abelian Dynamics Research Articles

Floquet non-Abelian topological insulator and multifold bulk-edge correspondence

Topological phases characterized by non-Abelian charges are beyond the scope of the paradigmatic tenfold way and have gained increasing attention recently. Here we investigate topological insulators with multiple tangled gaps in Floquet settings and identify uncharted Floquet non-Abelian topological insulators without any static or Abelian analog. We demonstrate that the bulk-edge correspondence is multifold and follows the multiplication rule of the quaternion group Q8. The same quaternion charge corresponds to several distinct edge-state configurations that are fully determined by phase-band singularities of the time evolution. In the anomalous non-Abelian phase, edge states appear in all bandgaps despite trivial quaternion charge. Furthermore, we uncover an exotic swap effect—the emergence of interface modes with swapped driving, which is a signature of the non-Abelian dynamics and absent in Floquet Abelian systems. Our work, for the first time, presents Floquet topological insulators characterized by non-Abelian charges and opens up exciting possibilities for exploring the rich and uncharted territory of non-equilibrium topological phases.

Non-Abelian effects in dissipative photonic topological lattices

Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to a plethora of intriguing effects such as topological lasing, exceptional surfaces, as well as non-Hermitian bulk-boundary correspondence. Here, we show that Bloch eigenstates associated with lattices with dissipatively coupled elements exhibit geometric properties that cannot be described via scalar Berry phases, in sharp contrast to conservative Hamiltonians with non-degenerate energy levels. This unusual behavior can be attributed to the significant population exchanges among the corresponding dissipation bands of such lattices. Using a one-dimensional example, we show both theoretically and experimentally that such population exchanges can manifest themselves via matrix-valued operators in the corresponding Bloch dynamics. In two-dimensional lattices, such matrix-valued operators can form non-commuting pairs and lead to non-Abelian dynamics, as confirmed by our numerical simulations. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena.

Super-soft CP violation

Solutions of the Strong CP Problem based on the spontaneous breaking of CP must feature a non-generic structure and simultaneously explain a coincidence between a priori unrelated CP-even and CP-odd mass scales. We show that these properties can emerge from gauge invariance and a CP-conserving, but otherwise generic, physics at the Planck scale. In our scenarios no fundamental scalar is introduced beyond the Standard Model Higgs doublet, and CP is broken at naturally small scales by a confining non-abelian dynamics. This approach is remarkably predictive: robustness against uncontrollable UV corrections to the QCD topological angle requires one or more families of vector-like quarks below a few 10’s of TeV, hence potentially accessible at colliders. Because CP violation is communicated to the SM at these super-soft scales, our solution of the Strong CP Problem is not spoiled by the presence of heavy new states motivated by other puzzles in physics beyond the Standard Model. In addition, these models generically predict a dark sector that may lead to interesting cosmological signatures.

Non-Abelian Shortcuts to Adiabaticity Simulated by Classical Resonant Oscillators

Quantum degenerate systems can be simulated by the classical resonant oscillators in the means of quantum-classical mapping theory. In this work, we show the classical version of shortcuts to adiabaticity-transitionless quantum driving (TQD) for the non-Abelian quantum systems by averaging the quantum version. The non-Abelian geometric angle corresponding to the quantum Wilczek-Zee phase is given and the non-Abelian angle gauge potential is just the opposite of the third term of TQD Hamiltonian or the averaging of Wilczek-Zee gauge potential. An example of Hamiltonian with two degenerate subspaces is employed to illustrate the classical non-Abelian dynamics, geometric angle and shortcuts to adiabaticity. This provides a promising platform to simulate the quantum shortcut or for quantum computation and quantum information processing.

Non-Abelian quantum adiabatic dynamics and phase simulation with classical resonant oscillators

It is known that the dynamics and geometric phase of a quantum system could be mapped mathematically into a classical system of coupled oscillators without loss of physics. In this work, we show that this quantum-classical mapping can also be used to simulate non-Abelian dynamics and phase of the quantum system with energy degeneracy by interpreting the quantum degeneracy as the resonance between the eigenfrequencies of the classical oscillators. The quantum evolution and Wilczek-Zee phase in the degenerate subspace can also be described by the classical non-Abelian evolution and a non-Abelian geometric angle in the resonant subspace. By studying the adiabatic evolution in this classical non-Abelian case, our results can also be used to generalize the concept of averaging principle and Hannay's angle into the classical system with resonant eigenfrequencies. The quantum-classical mapping of a tripod-scheme Hamiltonian with two degenerate dark states is employed to illustrate the classical non-Abelian dynamics and geometric angles.

Quantum evolution of quarkonia with correlated and uncorrelated noise

In the quark-gluon plasma (QGP), it is well known that the evolution of quarkonia is affected by the screening of the interaction between the quark and the anti-quark. In addition, exchange of energy and color with the surrounding medium can be included via the incorporation of noise terms in the evolution Hamiltonian. For noise correlated locally in time, these dynamics have been studied in a simple setting by Kajimoto et al.[PHYS. REV. D 97, 014003(2018)]. We extend this calculation by considering non-Abelian dynamics for a three-dimensional wavefunction. We also propose a modification of the noise correlation, allowing it to have a finite correlation in time with the motivation to include long-lived gluonic correlations. We find that in both cases the results differ significantly from solutions of rate equations.

Derivation of the gap and Bethe-Salpeter equations at large Nc limit and symmetry preserving truncations

We develop a framework for deriving Dyson-Schwinger Equations (DSEs) and Bethe-Salpeter Equation (BSE) in QCD at large $N_c$ limit. The starting point is a modified form (with auxiliary fields) of QCD generating functional. This framework provides a natural order-by-order truncation scheme for DSEs and BSE, and the kernels of the equations up to any order are explicitly given. Chiral symmetry (at chiral limit) is preserved in any order truncation, so it exemplifies the symmetry preserving truncation scheme. It provides a method to study DSEs and BSE beyond the Rainbow-Ladder truncation, and is especially useful to study contributions from non-Abelian dynamics (those arise from gluon self-interactions). We also derive the equation for the quark-ghost scattering kernel, and discuss the Slavnov-Taylor identity connecting the quark-gluon vertex, the quark propagator and the quark-ghost scattering kernel.

Free energy for a damped cold atom in SU(2) non-Abelian gauge potentials

Our main aim in this work is to find out the exact formula of the equilibrium free energy for a cold atom subjected to a harmonic potential in the background of an artificial non-Abelian uniform magnetic field and linearly coupled to a heat bath. The heat bath consists of a collection of independent quantum harmonic oscillators, while its interaction with the cold atom is modeled in terms of bilinear coupling between the coordinate variables of the cold atom and the oscillators. The main thermodynamic properties of such a system are modified in comparison with the Abelian case. For a non-Abelian magnetic field generated from the laser methods employing degenerate dark states, we evaluate the effect of the non-Abelian dynamics on the magnetic moment of the cold atom.

Non-Abelian dynamics in the resonant decay of the Higgs after inflation

We study the resonant decay of the Higgs condensate into weak gauge bosons after inflation and estimate the corrections arising from the non-Abelian self-interactions of the gauge fields. We find that non-Abelian interaction terms induce an effective mass which tends to shut down the resonance. For the broad resonance relevant for the Standard Model Higgs the produced gauge particles backreact on the dynamics of the Higgs condensate before the non-Abelian terms grow large. The non-Abelian terms can however significantly affect the final stages of the resonance after the backreaction. In the narrow resonance regime, which may be important for extensions of the Standard Model, the non-Abelian terms affect already the linear stage and terminate the resonance before the Higgs condensate is affected by the backreaction of decay products.

RDuality and “instead-of-confinement” mechanism inN=1supersymmetric QCD

We consider N=2 SQCD with the U(N) gauge group and N_f flavors (N_f>N) perturbed by an N=2 breaking deformation - a small mass term \mu for the adjoint matter. We study r-vacua, with the constraint $2N_f/3 < r \le N. At large values of the parameter \xi\sim\mu m (m is a typical value of the quark masses) r quark flavors condense, by construction. The effective low-energy theory with the gauge group U(r)\times U(1)^{N-r} is at weak coupling. Upon reducing \xi the original theory undergoes a crossover transition from weak to strong coupling. As the original theory becomes strongly coupled, at low energies it is described by a weakly coupled infrared-free dual theory with the gauge group U(N_f-r)\times U(1)^{N-N_f+r} and N_f light dyon flavors. These dyons condense triggering formation of non-Abelian strings which still confine monopoles, rather than quarks, contrary to naive duality arguments. "Instead-of-confinement" mechanism for quarks and gauge bosons of the original theory takes place: screened quarks and gauge bosons of the original theory decay, on curves of the marginal stability (CMS), into confined monopole-antimonopole pairs that form stringy mesons. Next, we increase the deformation parameter \mu thus decoupling the adjoint fields. Then our theory flows to N=1 SQCD. The gauge group of the dual theory becomes U(N_f-r). We show that the dual theory is weakly coupled if we are sufficiently close to the Argyres-Douglas point. The "instead-of-confinement" mechanism for quarks and gauge bosons survives in the limit of large \mu. It determines low-energy non-Abelian dynamics in the r-vacua of N=1 SQCD.

Non-Abelian Dynamics and Heavy Multiquarks

A brief review is first presented of attempts to predict stable multiquark states within current models of hadron spectroscopy. Then a model combining flip–flop and connected Steiner trees is introduced and shown to lead to stable multiquarks, in particular for some configurations involving several heavy quarks and bearing exotic quantum numbers.

Non-linear theory for multiple M2 branes

We present a manifestly SO(8) invariant non-linear Lagrangian for describing the non-abelian dynamics of the bosonic degrees of freedom of N coinciding M2 branes in flat spacetime. The theory exhibits a gauge symmetry structure of the BF type (semidirect product of SU(N) and translations) and at low energies it reduces exactly to the bosonic part of the Lorentzian Bagger-Lambert Lagrangian for group SU(N). There are eight scalar fields satisfying a free-scalar equation. When one of them takes a large expectation value, the non-linear Lagrangian gets simplified and the theory can be connected to the non-abelian Lagrangian describing the dynamics of N coinciding D2 branes. As an application, we show that the BPS fuzzy funnel solution describing M2 branes ending into a single M5 brane is an exact solution of the non-linear system.

Variations on stability

We explore the effects of non-abelian dynamics of D-branes on their stability and introduce Hitchin-like modifications to previously-known stability conditions. The relation to brane–antibrane systems is used in order to rewrite the equations in terms of superconnections and arrive at deformed vortex equations.

Extended QCD versus Skyrme-Faddeev theory

We discuss the physical impacts of the ``Cho decomposition'' (or the ``Cho-Faddeev-Niemi-Shabanov decomposition'') of the non-Abelian gauge potential on QCD. We show how the decomposition makes a subtle but important modification on the non-Abelian dynamics, and present three physically equivalent quantization schemes of QCD which are consistent with the decomposition. In particular, we show that the decomposition enlarges the dynamical degrees of QCD by making the topological degrees of the non-Abelian gauge symmetry dynamical. Furthermore with the decomposition we show that the Skyrme-Faddeev theory of non-linear sigma model and QCD have almost identical topological structures. In specific we show that an essential ingredient in both theories is the Wu-Yang type non-Abelian monopole, and that the Faddeev-Niemi knots of the Skyrme-Faddeev theory can actually be interpreted to describe the multiple vacua of the SU(2) QCD. Finally we argue that the Skyrme-Faddeev theory is, just like QCD, a theory of confinement which confines the magnetic flux of the monopoles.

Diagrammatic approach to soft non-Abelian dynamics at high temperature

The dynamics of soft (| p |∼ g 2 T) non-Abelian gauge fields at finite temperature is non-perturbative. The effective theory for the soft scale is determined by diagrams with external momenta p 0≲ g 2 T, | p |∼ g 2 T and loop momenta larger than g 2 T. We consider the polarization tensor beyond the hard thermal loop approximation, which accounts for loop momenta of order T. There are higher loop diagrams, involving also the scale gT, which are as important as the hard thermal loops. These higher loop contributions are characteristic for non-Abelian gauge theories and their calculation is simplified by using the hard thermal loop effective theory. Remarkably, the effective one-loop polarization tensor is found to be gauge fixing independent and transverse at leading order in the gauge coupling g. The transversality indicates that this approach leads to a gauge invariant effective theory.

Spacetime quantization from non-AbelianD-particle dynamics

We describe the short-distance properties of the spacetime of a system of D-particles by viewing their matrix-valued coordinates as coupling constants of a deformed worldsheet $\sigma$-model. We show that the Zamolodchikov metric on the associated moduli space naturally encodes properties of the non-abelian dynamics, and from this we derive new spacetime uncertainty relations directly from the quantum string theory. The non-abelian uncertainties exhibit decoherence effects which suggest the interplay of quantum gravity in multiple D-particle dynamics.

Heuristic approach to non-abelian quantum kinematics and dynamics in configuration spacetime

New plausible kinematic foundations of quantum dynamics are discussed in a heuristic manner in which the quantum rule stems directly from the non-Abelian configuration symmetries of a system. Upon quantizing the ‘complete’ configuration symmetry group itself, irreducible generalized configuration-state representations can be calculated, whose transition amplitudes yield the propagation kernel. These states results from solving a set of ‘generalized Schrodinger equations’ corresponding to the superselection rules dictated by the quantized group. The propagation kernel of the system is thus obtained as an invariant Hurwitz integral, defined over the manifold of the complete symmetry group. A heuristic argument is given in favor of this approach to non-Abelian quantum kinematics, in which sums over physical world lines are evaluated instead of sums over arbitrary paths, for obtaining the propagation kernel of quantum systems having a classical Lagrangian analog. The attained quantum kinematic formalism, however, is completely general and does not depend on this particular interpretation. Nevertheless, the heuristic argument strongly suggests that non-Abelian quantum kinematics contains the formalism of standard nonrelativistic quantum mechanics as a very special case. No examples of the issues involved are presented in this paper.

Configuration ray representations in non-Abelian quantum kinematics and dynamics

Ray extensions of the regular representation of noncompact non-Abelian Lie groups are examined as generalizations of the Cartesian coordinate representation of ordinary quantum mechanics to the case of generalized non-Cartesian coordinates and generalized noncommuting momenta. (The momenta are in fact the generators of the representation, and so they satisfy the Lie algebra of the group.) The concept of configuration ray representation is introduced within this new kinematic formalism as subrepresentations of the regular representation which are embossed with the “relativity theory” of a given system. The main features of the mathematical formalism leading to these representations in configuration spacetime are discussed, and their importance for non-Abelian quantum kinematics and dynamics is emphasized. Two miscellaneous examples on the calculus of phase functions for configuration ray representations are given.