Chiral Boundary Conditions Research Articles

Massive fermion between two parallel chiral plates

Abstract We study the system of a massive fermion field confined between two parallel plates, where the properties of both plates are discussed under chiral MIT boundary conditions. We investigate the effects of the chiral angle on the Casimir energy for a massive fermion field with the general momentum. We find that the Casimir energy as a function of the chiral angle is generally symmetric, and the attractive Casimir force in the chiral case is stronger than that in the nonchiral case. In addition, we investigate the approximate Casimir energy for light and heavy mass cases. The behavior of the discrete momentum and changes of spin orientation are also discussed.

Quantum magnetic billiards: boundary conditions and gauge transformations

We study admissible boundary conditions for a charged quantum particle in a two-dimensional region subjected to an external magnetic field, i.e. a quantum magnetic billiard. After reviewing some physically interesting classes of admissible boundary conditions (magnetic Robin and chiral boundary conditions), we turn our attention to the role of gauge transformations in a magnetic billiard: in particular, we introduce gauge covariant boundary conditions, and find a sufficient condition for gauge covariance which is satisfied by all the aforementioned examples.

Web of Seiberg-like dualities for 3D N=2 quivers

We propose a universal manipulation to obtain Seiberg-like dualities of 3d $\mathcal{N}=2$ general quiver gauge theories with unitary, symplectic and orthogonal gauge groups coupled to fundamental and bifundamental matter fields. We illustrate this with several examples of linear, circular and star-shaped quiver gauge theories. We examine the local operators in the theories by computing supersymmetric indices and also find precise matching for the proposed dualities as strong evidence. We also generalize the dualities in the presence of a boundary on which the theories obey $\mathcal{N}=(0,2)$ chiral half-BPS boundary conditions.

A mixed elliptic-parabolic boundary value problem coupling a harmonic-like map with a nonlinear spinor

Abstract In this paper, we solve a new elliptic-parabolic system arising in geometric analysis that is motivated by the nonlinear supersymmetric sigma model of quantum field theory. The corresponding action functional involves two fields, a map from a Riemann surface into a Riemannian manifold and a spinor coupled to the map. The first field has to satisfy a second-order elliptic system, which we turn into a parabolic system so as to apply heat flow techniques. The spinor, however, satisfies a first-order Dirac-type equation. We carry that equation as a nonlinear constraint along the flow. With this novel scheme, in more technical terms, we can show the existence of Dirac-harmonic maps from a compact spin Riemann surface with smooth boundary to a general compact Riemannian manifold via a heat flow method when a Dirichlet boundary condition is imposed on the map and a chiral boundary condition on the spinor.

Effects of chiral MIT boundary conditions for a Dirac particle in a box

Abstract We investigate the effects of the chiral MIT boundary conditions for a Dirac particle in a 1D box. We show how the boundary condition affects the discrete momentum, energy level, transition frequency, and spin state in a box. The effects of the chiral MIT boundary conditions on the probability and scalar densities are also demonstrated. The results show that an asymmetric distribution appears in the box depending on the parameters of the spin orientation and chiral angle.

Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor

We find a Chern-Simons propagator on the ball with the chiral boundary condition. We use it to study perturbatively Chern-Simons boundary conditions related to 2-dim σ-models and to Poisson-Lie T-duality. In particular, we find their renormalization group flow, given by the generalized Ricci tensor. Finally we briefly discuss what happens when the Chern-Simons theory is replaced by a Courant σ-model or possibly by a more general AKSZ model.

Vacancies in graphene: Dirac physics and fractional vacuum charges

The study of vacancies in graphene is a topic of growing interest. A single vacancy induces a localized stable charge of order unity interacting with other charges of the conductor through an unscreened Coulomb potential. It also breaks the symmetry between the two triangular graphene sublattices hence inducing zero energy states at the Dirac points. Here we show the fractional and pseudoscalar nature of this vacancy charge. A continuous Dirac model is presented which relates zero modes to vacuum fractional charge and to a parity anomaly. This relation constitutes an index theorem and is achieved by using particular chiral boundary conditions, which map the vacancy problem onto edge state physics. Vacancies in graphene thus allow us to realize prominent features of $2+1$ quantum electrodynamics but without coupling to a gauge field. This essential difference makes vacancy physics relatively easy to implement and an interesting playground for topological state switching.

Vibrations and elastic waves in chiral multi-structures

We develop a new asymptotic model of the dynamic interaction between an elastic structure and a system of gyroscopic spinners that make the overall multi-structure chiral. An important result is the derivation and analysis of effective chiral boundary conditions describing the interaction between an elastic beam and a gyroscopic spinner. These conditions are applied to the analysis of waves in systems of beams connected by gyroscopic spinners. A new asymptotic and physical interpretation of the notion of a Rayleigh gyrobeam is also presented. The theoretical findings are accompanied by illustrative numerical examples and simulations.

Mechanical behavior enhancement of defective graphene sheet employing boron nitride coating via atomistic study

The most stable form of boron nitride polymorph naming hexagonal boron nitride sheet has recently been widely concerned like graphite due to its interesting features such as electrical insulation and high thermal conductivity. In this study, the molecular dynamic simulations are implemented to investigate the mechanical properties of single-layer graphene sheets under tensile and compressive loadings in the absence and presence of boron–nitride coating layers. In this introduced hybrid nanostructure, the benefit of combining both individual interesting features of graphene and boron–nitride sheets such as exceptional mechanical and electrical properties can be simultaneously achieved for future potential application in nano devices. The influences of chiral indices, boundary conditions and presence of mono-atomic vacancy defects as well as coating dimension on the mechanical behavior of the resulted hybrid structure are reported. The interatomic forces between the atoms are modeled by employing the AIREBO and Tersoff–Brenner potentials for carbon–carbon and boron–nitrogen atoms in each layer, respectively. Furthermore, the van der Waal interlayer forces of carbon–boron and carbon–nitrogen are estimated by the Lennard–Jones potential field. Besides the potential improvement in electrical and physical properties of the nanostructure, it is demonstrated that the buckling load capacity of the fully coated graphene sheet with 3% concentration of mono-atomic vacancy defects noticeably enhances by amounts of 24.1%.

Tweaking one-loop determinants in AdS3

We revisit the subject of one-loop determinants in AdS3 gravity via the quasi-normal mode method. Our goal is to evaluate a one-loop determinant with chiral boundary conditions for the metric field; chirality is achieved by imposing Dirichlet boundary conditions on certain components while others satisfy Neumann. Along the way, we give a generalization of the quasinormal mode method for stationary (non-static) thermal backgrounds, and propose a treatment for Neumann boundary conditions in this framework. We evaluate the graviton one-loop determinant on the Euclidean BTZ background with parity-violating boundary conditions (CSS), and find excellent agreement with the dual warped CFT. We also discuss a more general falloff in AdS3 that is related to two dimensional quantum gravity in lightcone gauge. The behavior of the ghost fields under both sets of boundary conditions is novel and we discuss potential interpretations.

Chiral boundary conditions for singletons and W-branes

We revisit the holographic dictionary for a free massless scalar in AdS3, focusing on the ‘singleton’ solutions for which the boundary profile is an arbitrary chiral function. We look for consistent boundary conditions which include this class of solutions. On one hand, we give a no-go argument that they cannot be interpreted within any boundary condition which preserves full conformal invariance. On the other hand, we show that such solutions fit naturally in a generalization of the Compère-Song-Strominger boundary conditions, which preserve a chiral Virasoro and current algebra. These observations have implications for the black hole deconstruction proposal, which proposes singleton solutions as candidate black hole microstate geometries. Our results suggest that the chiral boundary condition, which also contains the extremal BTZ black hole, is the natural setting for holographically interpreting the black hole deconstruction proposal.

Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession

We consider the reflection of a Dirac plane wave on a perfectly reflecting plane described by chiral MIT boundary conditions and determine the rotation of the spin in the reflected component of the wave. We solve the analogous problem for a classical particle using the evolution of the spin defined by the Thomas precession and make a comparison with the quantum result. We find that the rotation axes of the spin in the two problems coincide only for a vanishing chiral angle, in which case the rotation angles coincide in the nonrelativistic limit, and also remain remarkably close in the relativistic regime. The result shows that in the nonrelativistic limit the interaction between the spin and a reflecting surface with nonchiral boundary conditions is completely contained in the Thomas precession effect, in conformity with the fact that these boundary conditions are equivalent to an infinite repulsive scalar potential outside the boundary. By contrast, in the ultrarelativistic limit the rotation angle in the quantum problem remains finite, while in the classical one the rotation angle diverges. We comment on the possible implications of this discrepancy on the validity of the Mathisson-Papapetrou-Dixon equations at large accelerations.

An sl(2, $ \mathbb{R} $ ) current algebra from AdS 3 gravity

We provide a set of chiral boundary conditions for three-dimensional gravity that allow for asymptotic symmetries identical to those of two-dimensional induced gravity in light-cone gauge considered by Polyakov. These are the most general boundary conditions consistent with the boundary terms introduced by Compère, Song and Strominger recently. We show that the asymptotic symmetry algebra of our boundary conditions is a Virasoro algebra with Brown-Henneaux central charge c and an sl(2, $ \mathbb{R} $ ) current algebra with level given by c/6. The fully non-linear solution in Fefferman-Graham coordinates is also provided along with its charges.

Edge states: topological insulators, superconductors and QCD chiral bags

The dynamics of the magnetic field in a superconducting phase is described by an effective massive bosonic field theory. If the superconductor is confined in a domain M with boundary \partial M, the boundary conditions of the electromagnetic fields are predetermined by physics. They are time-reversal and also parity invariant for adapted geometry. They lead to edge excitations while in comparison, the bulk energies have a large gap. A similar phenomenon occurs for topological insulators where appropriate boundary conditions for the Dirac Hamiltonian also lead to similar edge states and an 'incompressible bulk'. They give spin-momentum locking as well. In addition time-reversal and parity invariance emerge for adapted geometry. Similar edge states appear in QCD bag models with chiral boundary conditions.

New boundary conditions for AdS3

New chiral boundary conditions are found for quantum gravity with matter on AdS3. The associated asymptotic symmetry group is generated by a single right-moving U(1) Kac-Moody-Virasoro algebra with c_R = 3l/2G. The Kac-Moody zero mode generates global left-moving translations and equals, for a BTZ black hole, the sum of the total mass and spin. The level is positive about the global vacuum and negative in the black hole sector, corresponding to ergosphere formation. Realizations arising in Chern-Simons gravity and string theory are analyzed. The new boundary conditions are shown to naturally arise for warped AdS3 in the limit that the warp parameter is taken to zero.

Experimental study of influence of external electric field on the photonic band gap of chiral liquid crystals

Influence of an external electric field on the boundaries of photonic band gap of a chiral liquid crystal has been studied experimentally. It is shown that by using a negative chiral liquid crystal and homeotropic boundary conditions one can increase the abruptness of photonic band gap boundaries and control thus the band gap width by application of the external electric field.

Tadpoles and commutative spectral triples

Using the Chamseddine–Connes approach of the noncommutative action on spectral triples, we show that there are no tadpoles of any order for compact spin manifolds without boundary, and also consider a case of a chiral boundary condition. Using pseudodifferential techniques, we study noncommutative integrals in commutative geometries.

SLAB BAG FERMIONIC CASIMIR EFFECT, CHIRAL BOUNDARIES AND VECTOR BOSON — MAJORANA FERMION PISTONS

In this paper we consider the Casimir energy and force of massless Majorana fermions and vector bosons between parallel plates. The vector bosons satisfy perfect electric conductor boundary conditions, while the Majorana fermions satisfy bag and chiral boundary conditions. We consider various piston configurations containing one vector boson and one fermion. We make use of supersymmetry, broken on the boundaries, to explain the number of fields that appear in all the studied cases. The effect of chiral boundary conditions in a fermion–boson system is investigated. Concerning the supersymmetry issue and the vanishing of the Casimir energy, we study a massive Dirac fermion–scalar boson system with bag and specific Robin type boundary conditions for which the Casimir energy vanishes. Finally, a two-scalar-boson system between parallel plates is presented in which the singularities vanish in the total Casimir energy.

Spectral triples and manifolds with boundary

We investigate manifolds with boundary in noncommutative geometry. Spectral triples associated to a symmetric differential operator and a local boundary condition are constructed. We show that there is no tadpole for classical Dirac operators with a chiral boundary condition on spin manifolds.

Fermionic states in pure 4D deconstruction

We study the structure of fermionic mass eigenstates in a pure four-dimensional deconstruction approach. Unlike the case with the usual higher dimensional deconstruction (or latticized extra dimension), here the doubling of fermionic degrees of freedom is physical, thus there is no need to invoke Wilson terms to eliminate them. The fermionic structure is shaped by two key factors, namely, the boundary conditions on fermions and the ratio of two breaking scales involved. The singular value decomposition of linear algebra is employed to shed light into the phenomenologically crucial role of chiral boundary conditions. In this approach, we can explain the localization or ``delocalization'' nature of fermionic zero-mode in flavor space and obtain analytically all higher modes. The application of boundary conditions on fermions to the implementation of CKM quark mixing is also found.