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S. -Y. Pi

Publications and source records attributed to S. -Y. Pi.

At least 19 recordsLinked to original sources
arXiv2012

Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics

Extending previous work on 2 -- and 3 -- point functions, we study the 4 -- point function and its conformal block structure in conformal quantum mechanics CFT$_1$, which realizes the SO(2,1) symmetry group. Conformal covariance is preserved even though the operators with which we work need not be primary and the states are not conformally invariant. We find that only one conformal block contributes to the four-point function. We describe some further properties of the states that we use and we construct dynamical evolution generated by the compact generator of SO(2.1).

hep-th↗
arXiv2011

State Space for Planar Majorana Zero Modes

Zero modes arising from a planar Majorana equation in the presence of $N$ vortices require an $\mathcal{N}$-dimensional state-space, where $\mathcal{N} = 2^{N/2}$ for $N$ even and $\mathcal{N} = 2^{(N + 1)/2}$ for $N$ odd. The mode operators form a restricted $\mathcal{N}$-dimensional Clifford algebra.

cond-mat.str-el↗
arXiv2011

Quantizing Majorana Fermions in a Superconductor

A Dirac-type matrix equation governs surface excitations in a topological insulator in contact with an s-wave superconductor. The order parameter can be homogenous or vortex valued. In the homogenous case a winding number can be defined whose non-vanishing value signals topological effects. A vortex leads to a static, isolated, zero energy solution. Its mode function is real, and has been called "Majorana." Here we demonstrate that the reality/Majorana feature is not confined to the zero energy mode, but characterizes the full quantum field. In a four-component description a change of basis for the relevant matrices renders the Hamiltonian imaginary and the full, space-time dependent field is real, as is the case for the relativistic Majorana equation in the Majorana matrix representation. More broadly, we show that the Majorana quantization procedure is generic to superconductors, with or without the Dirac structure, and follows from the constraints of fermionic statistics on the symmetries of Bogoliubov-de Gennes Hamiltonians. The Hamiltonian can always be brought to an imaginary form, leading to equations of motion that are real with quantized real field solutions. Also we examine the Fock space realization of the zero mode algebra for the Dirac-type systems. We show that a two-dimensional representation is natural, in which fermion parity is preserved.

cond-mat.str-el↗
arXiv2011

Conformal quantum mechanics as the CFT$_1$ dual to AdS$_2$

A 0+1-dimensional candidate theory for the CFT$_1$ dual to AdS$_2$ is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose "non-primary character" conspires with the "non-invariance of the vacuum" to give precisely the correlation functions in a conformally invariant theory.

hep-th↗
arXiv2009

Induced Current and Aharonov-Bohm Effect in Graphene

The effect of vacuum polarization in the field of an infinitesimally thin solenoid at distances much larger than the radius of solenoid is investigated. The induced charge density and induced current are calculated. Though the induced charge density turned out to be zero, the induced current is finite periodical function of the magnetic flux $Φ$. The expression for this function is found exactly in a value of the flux. The induced current is equal to zero at the integer values of $Φ/Φ_0$ as well as at half-integer values of this ratio, where $Φ_0=2π\hbar c/e$ is the elementary magnetic flux. The latter is a consequence of the Furry theorem and periodicity of the induced current with respect to magnetic flux. As an example we consider the graphene in the field of solenoid perpendicular to the plane of a sample.

cond-mat.mes-hall↗
arXiv2008

Persistence of zero modes in a gauged Dirac model for bilayer graphene

A recently constructed model for low lying excitations in bilayer graphene exhibits mid-gap, zero energy modes in its Dirac-like spectrum, when a scalar order parameter takes a vortex profile. We show that these modes persist when the dynamics is extended by a gauge field interaction, which also renders finite the vortex energy. The effect of the gauge field on the zero energy wave function is to shift the phase of the (damped) oscillatory component of the wave function in the absence of the gauge field.

cond-mat.str-el↗
arXiv2007

Chiral Gauge Theory for Graphene

We construct a chiral gauge theory to describe fractionalization of fermions in graphene. Thereby we extend a recently proposed model, which relies on vortex formation. Our chiral gauge fields provide dynamics for the vortices and also couple to the fermions.

cond-mat.str-el↗
arXiv2005

Quantum Relaxation of the Cosmological Constant

We describe a mechanism that drives the Cosmological Constant to zero value. This mechanism is based on the quantum triviality of $λϕ^4$ field theory and works in $AdS$ space. Some subtleties of the model are discussed.

hep-th↗
arXiv2004

Cotton Blend Gravity $pp$ Waves

We study conformal gravity in d=2+1, where the Cotton tensor is equated to a--necessarily traceless--matter stress tensor, for us that of the improved scalar field. We first solve this system exactly in the $pp$ wave regime, then show it to be equivalent to topologically massive gravity.

gr-qc↗
arXiv2004

Perfect Fluid Theory and its Extensions

We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization, as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern-Simons terms (= vortex or magnetic helicity).

hep-ph↗
arXiv2003

Chern-Simons Modification of General Relativity

General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v_μ-- an external quantity, which we fix to be a non-vanishing constant in its time component. The theory is identical to one in which the embedding coordinate is itself a dynamical variable, rather than a fixed, external quantity. Consequently diffeomorphism symmetry breaking is hidden in the modified theory: the Schwarzschild metric is a solution; gravitational waves possess two polarizations, each traveling at the velocity of light; a conserved energy-momentum (pseudo-) tensor can be constructed. The modification is visible in the intensity of gravitational radiation: the two polarizations of a gravity wave carry intensities that are suppressed/enchanced by the extension.

gr-qc↗
arXiv2003

Dimensionally Reduced Gravitational Chern-Simons Term and its Kink

When the gravitational Chern-Simons term is reduced from 3 to 2 dimensions, the lower dimensional theory supports a symmetry breaking solution and an associated kink. Kinks in general relativity bear a close relation to flat space kinks, governed by identical potentials.

hep-th↗
arXiv2002

Non-Abelian Fluid Dynamics in Lagrangian Formulation

Non-Abelian extensions of fluid dynamics, which can have applications to the quark-gluon plasma, are given. These theories are presented in a symplectic/Lagrangian formulation and involve a fluid generalization of the Kirillov-Kostant form well known in Lie group theory. In our simplest model the fluid flows with velocity v and in presence of non-Abelian chromoelectric/magnetic E^a / B^a fields, the fluid feels a Lorentz force of the form Q_a E^a + (v / c) \times Q_a B^a, where Q_a is a space-time local non-Abelian charge satisfying a fluid Wong equation [ (D_t + v \cdot D) Q ]_a = 0 with gauge covariant derivatives.

hep-th↗
arXiv2002

Noncommuting Gauge Fields as a Lagrange Fluid

The Lagrange description of an ideal fluid gives rise in a natural way to a gauge potential and a Poisson structure that are classical precursors of analogous noncommuting entities. With this observation we are led to construct gauge-covariant coordinate transformations on a noncommuting space. Also we recognize the Seiberg-Witten map from noncommuting to commuting variables as the quantum correspondent of the Lagrange to Euler map in fluid mechanics.

hep-th↗
arXiv2002

Noncommutative 1-cocycle in the Seiberg-Witten map

We show that the Seiberg-Witten map for a noncommutative gauge theory involves a noncommutative 1-cocycle. The cocycle condition enforces a consistency requirement, which has been previously derived.

hep-th↗