60 research outputs found
Bose-Fermi duality and entanglement entropies
Entanglement (Renyi) entropies of spatial regions are a useful tool for
characterizing the ground states of quantum field theories. In this paper we
investigate the extent to which these are universal quantities for a given
theory, and to which they distinguish different theories, by comparing the
entanglement spectra of the massless Dirac fermion and the compact free boson
in two dimensions. We show that the calculation of Renyi entropies via the
replica trick for any orbifold theory includes a sum over orbifold twists on
all cycles. In a modular-invariant theory of fermions, this amounts to a sum
over spin structures. The result is that the Renyi entropies respect the
standard Bose-Fermi duality. Next, we investigate the entanglement spectrum for
the Dirac fermion without a sum over spin structures, and for the compact boson
at the self-dual radius. These are not equivalent theories; nonetheless, we
find that (1) their second Renyi entropies agree for any number of intervals,
(2) their full entanglement spectra agree for two intervals, and (3) the
spectrum generically disagrees otherwise. These results follow from the
equality of the partition functions of the two theories on any Riemann surface
with imaginary period matrix. We also exhibit a map between the operators of
the theories that preserves scaling dimensions (but not spins), as well as OPEs
and correlators of operators placed on the real line. All of these coincidences
can be traced to the fact that the momentum lattice for the bosonized fermion
is related to that of the self-dual boson by a 45 degree rotation that mixes
left- and right-movers.Comment: 40 pages; v3: improvements to presentation, new section discussing
entanglement negativit
Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm
The discrete-time Toda equation arises as a universal equation for the
relevant Hankel determinants associated with one-variable orthogonal
polynomials through the mechanism of adjacency, which amounts to the inclusion
of shifted weight functions in the orthogonality condition. In this paper we
extend this mechanism to a new class of two-variable orthogonal polynomials
where the variables are related via an elliptic curve. This leads to a `Higher
order Analogue of the Discrete-time Toda' (HADT) equation for the associated
Hankel determinants, together with its Lax pair, which is derived from the
relevant recurrence relations for the orthogonal polynomials. In a similar way
as the quotient-difference (QD) algorithm is related to the discrete-time Toda
equation, a novel quotient-quotient-difference (QQD) scheme is presented for
the HADT equation. We show that for both the HADT equation and the QQD scheme,
there exists well-posed -periodic initial value problems, for almost all
\s\in\Z^2. From the Lax-pairs we furthermore derive invariants for
corresponding reductions to dynamical mappings for some explicit examples.Comment: 38 page
Symmetry Decomposition of Potentials with Channels
We discuss the symmetry decomposition of the average density of states for
the two dimensional potential and its three dimensional
generalisation . In both problems, the energetically
accessible phase space is non-compact due to the existence of infinite channels
along the axes. It is known that in two dimensions the phase space volume is
infinite in these channels thus yielding non-standard forms for the average
density of states. Here we show that the channels also result in the symmetry
decomposition having a much stronger effect than in potentials without
channels, leading to terms which are essentially leading order. We verify these
results numerically and also observe a peculiar numerical effect which we
associate with the channels. In three dimensions, the volume of phase space is
finite and the symmetry decomposition follows more closely that for generic
potentials --- however there are still non-generic effects related to some of
the group elements
Relativistic wave equations for interacting massive particles with arbitrary half-intreger spins
New formulation of relativistic wave equations (RWE) for massive particles
with arbitrary half-integer spins s interacting with external electromagnetic
fields are proposed. They are based on wave functions which are irreducible
tensors of rank n=s-\frac12$) antisymmetric w.r.t. n pairs of indices,
whose components are bispinors. The form of RWE is straightforward and free of
inconsistencies associated with the other approaches to equations describing
interacting higher spin particles
S4 Flavor Symmetry and Fermion Masses: Towards a Grand Unified theory of Flavor
Pursuing a bottom-up approach to explore which flavor symmetry could serve as
an explanation of the observed fermion masses and mixings, we discuss an
extension of the standard model (SM) where the flavor structure for both quarks
and leptons is determined by a spontaneously broken S4 and the requirement that
its particle content is embeddable simultaneously into the conventional SO(10)
grand unified theory (GUT) and a continuous flavor symmetry G_f like SO(3)_f or
SU(3)_f. We explicitly provide the Yukawa and the Higgs sector of the model and
show its viability in two numerical examples which arise as small deviations
from rank one matrices. In the first case, the corresponding mass matrix is
democratic and in the second one only its 2-3 block is non-vanishing. We
demonstrate that the Higgs potential allows for the appropriate vacuum
expectation value (VEV) configurations in both cases, if CP is conserved. For
the first case, the chosen Yukawa couplings can be made natural by invoking an
auxiliary Z2 symmetry. The numerical study we perform shows that the best-fit
values for the lepton mixing angles theta_12 and theta_23 can be accommodated
for normal neutrino mass hierarchy. The results for the quark mixing angles
turn out to be too small. Furthermore the CP-violating phase delta can only be
reproduced correctly in one of the examples. The small mixing angle values are
likely to be brought into the experimentally allowed ranges by including
radiative corrections. Interestingly, due to the S4 symmetry the mass matrix of
the right-handed neutrinos is proportional to the unit matrix.Comment: 27 pages, published version with minor change
Leptons in Holographic Composite Higgs Models with Non-Abelian Discrete Symmetries
We study leptons in holographic composite Higgs models, namely in models
possibly admitting a weakly coupled description in terms of five-dimensional
(5D) theories. We introduce two scenarios leading to Majorana or Dirac
neutrinos, based on the non-abelian discrete group which is
responsible for nearly tri-bimaximal lepton mixing. The smallness of neutrino
masses is naturally explained and normal/inverted mass ordering can be
accommodated. We analyze two specific 5D gauge-Higgs unification models in
warped space as concrete examples of our framework. Both models pass the
current bounds on Lepton Flavour Violation (LFV) processes. We pay special
attention to the effect of so called boundary kinetic terms that are the
dominant source of LFV. The model with Majorana neutrinos is compatible with a
Kaluza-Klein vector mass scale TeV, which is roughly the
lowest scale allowed by electroweak considerations. The model with Dirac
neutrinos, although not considerably constrained by LFV processes and data on
lepton mixing, suffers from a too large deviation of the neutrino coupling to
the boson from its Standard Model value, pushing TeV.Comment: 37 pages, 4 figures; v2: Note added in light of recent T2K and MINOS
results, figures updated with new limit from MEG, references added, various
minor improvements, matches JHEP published versio
Conformal linear gravity in de Sitter space II
From the group theoretical point of view, it is proved that the theory of
linear conformal gravity should be written in terms of a tensor field of rank-3
and mixed symmetry [Binegar, et al, Phys. Rev. D 27, (1983) 2249]. We obtained
such a field equation in de Sitter space [Takook, et al, J. Math. Phys. 51,
(2010) 032503]. In this paper, a proper solution to this equation is obtained
as a product of a generalized polarization tensor and a massless scalar field
and then the conformally invariant two-point function is calculated. This
two-point function is de Sitter invariant and free of any pathological
large-distance behavior.Comment: 16 pages, no figure, published versio
Photochemical dihydrogen production using an analogue of the active site of [NiFe] hydrogenase
The photoproduction of dihydrogen (H2) by a low molecular weight analogue of the active site of [NiFe] hydrogenase has been investigated by the reduction of the [NiFe2] cluster, 1, by a photosensitier PS (PS = [ReCl(CO)3(bpy)] or [Ru(bpy)3][PF6]2). Reductive quenching of the 3MLCT excited state of the photosensitiser by NEt3 or N(CH2CH2OH)3 (TEOA) generates PS•−, and subsequent intermolecular electron transfer to 1 produces the reduced anionic form of 1. Time-resolved infrared spectroscopy (TRIR) has been used to probe the intermediates throughout the reduction of 1 and subsequent photocatalytic H2 production from [HTEOA][BF4], which was monitored by gas chromatography. Two structural isomers of the reduced form of 1 (1a•− and 1b•−) were detected by Fourier transform infrared spectroscopy (FTIR) in both CH3CN and DMF (dimethylformamide), while only 1a•− was detected in CH2Cl2. Structures for these intermediates are proposed from the results of density functional theory calculations and FTIR spectroscopy. 1a•− is assigned to a similar structure to 1 with six terminal carbonyl ligands, while calculations suggest that in 1b•− two of the carbonyl groups bridge the Fe centres, consistent with the peak observed at 1714 cm−1 in the FTIR spectrum for 1b•− in CH3CN, assigned to a ν(CO) stretching vibration. The formation of 1a•− and 1b•− and the production of H2 was studied in CH3CN, DMF and CH2Cl2. Although the more catalytically active species (1a•− or 1b•−) could not be determined, photocatalysis was observed only in CH3CN and DMF
Supersymmetric QCD corrections to and the Bernstein-Tkachov method of loop integration
The discovery of charged Higgs bosons is of particular importance, since
their existence is predicted by supersymmetry and they are absent in the
Standard Model (SM). If the charged Higgs bosons are too heavy to be produced
in pairs at future linear colliders, single production associated with a top
and a bottom quark is enhanced in parts of the parameter space. We present the
next-to-leading-order calculation in supersymmetric QCD within the minimal
supersymmetric SM (MSSM), completing a previous calculation of the SM-QCD
corrections. In addition to the usual approach to perform the loop integration
analytically, we apply a numerical approach based on the Bernstein-Tkachov
theorem. In this framework, we avoid some of the generic problems connected
with the analytical method.Comment: 14 pages, 6 figures, accepted for publication in Phys. Rev.
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