5,556 research outputs found
On F-theory E_6 GUTs
We approach the Minimum Supersymmetric Standard Model (MSSM) from an E_6 GUT
by using the spectral cover construction and non-abelian gauge fluxes in
F-theory. We start with an E_6 singularity unfolded from an E_8 singularity and
obtain E_6 GUTs by using an SU(3) spectral cover. By turning on SU(2) X U(1)^2
gauge fluxes, we obtain a rank 5 model with the gauge group SU(3) X SU(2) X
U(1)^2. Based on the well-studied geometric backgrounds in the literature, we
demonstrate several models and discuss their phenomenology.Comment: 42 pages, 17 tables; typos corrected, clarifications added, and
references adde
Algebraic Quantum Error-Correction Codes
Based on the group structure of a unitary Lie algebra, a scheme is provided
to systematically and exhaustively generate quantum error correction codes,
including the additive and nonadditive codes. The syndromes in the process of
error-correction distinguished by different orthogonal vector subspaces, the
coset subspaces. Moreover, the generated codes can be classified into four
types with respect to the spinors in the unitary Lie algebra and a chosen
initial quantum state
A Generalized Jarque-Bera Test of Conditional Normality
We consider testing normality in a general class of models that admits nonlinear conditional mean and conditional variance functions. We derive the asymptotic distribution of the skewness and kurtosis coefficients of the modelâs standardized residuals and propose an asymptotic x2 test of normality. This test simplifies to the Jarque-Bera test only when: (i) the conditional mean function contains an intercept term but does not depend on past errors, and (ii) the errors are conditionally homoskedastic. Beyond this context, it is shown that the Jarque-Bera test has size distortion but the proposed test does not.conditional heteroskedsaticity, conditional normality, Jarque-Bera test
Quench Dynamics of Topological Maximally-Entangled States
We investigate the quench dynamics of the one-particle entanglement spectra
(OPES) for systems with topologically nontrivial phases. By using dimerized
chains as an example, it is demonstrated that the evolution of OPES for the
quenched bi-partite systems is governed by an effective Hamiltonian which is
characterized by a pseudo spin in a time-dependent pseudo magnetic field
. The existence and evolution of the topological
maximally-entangled edge states are determined by the winding number of
in the -space. In particular, the maximally-entangled edge
states survive only if nontrivial Berry phases are induced by the winding of
. In the infinite time limit the equilibrium OPES can be
determined by an effective time-independent pseudo magnetic field
\vec{S}_{\mb{eff}}(k). Furthermore, when maximally-entangled edge states are
unstable, they are destroyed by quasiparticles within a characteristic
timescale in proportional to the system size.Comment: 5 pages, 3 figure
Partition Function of Chiral Boson on 2-Torus from Floreanini-Jackiw Lagrangian
We revisit the problem of quantizing a chiral boson on a torus. The
conventional approach is to extract the partition function of a chiral boson
from the path integral of a non-chiral boson. Instead we compute it directly
from the chiral boson Lagrangian of Floreanini and Jackiw modified by
topological terms involving auxiliary fields. A careful analysis of the
gauge-fixing condition for the extra gauge symmetry reproduces the correct
results for the free chiral boson, and has the advantage of being applicable to
a wider class of interacting chiral boson theories.Comment: 31 pages, minor modificatio
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