1,712 research outputs found
Reactor mixing angle from hybrid neutrino masses
In terms of its eigenvector decomposition, the neutrino mass matrix (in the
basis where the charged lepton mass matrix is diagonal) can be understood as
originating from a tribimaximal dominant structure with small deviations, as
demanded by data. If neutrino masses originate from at least two different
mechanisms, referred to as "hybrid neutrino masses", the experimentally
observed structure naturally emerges provided one mechanism accounts for the
dominant tribimaximal structure while the other is responsible for the
deviations. We demonstrate the feasibility of this picture in a fairly
model-independent way by using lepton-number-violating effective operators,
whose structure we assume becomes dictated by an underlying flavor
symmetry. We show that if a second mechanism is at work, the requirement of
generating a reactor angle within its experimental range always fixes the solar
and atmospheric angles in agreement with data, in contrast to the case where
the deviations are induced by next-to-leading order effective operators. We
prove this idea is viable by constructing an -based ultraviolet
completion, where the dominant tribimaximal structure arises from the type-I
seesaw while the subleading contribution is determined by either type-II or
type-III seesaw driven by a non-trivial singlet (minimal hybrid model).
After finding general criteria, we identify all the symmetries
capable of producing such -based minimal hybrid models.Comment: 18 pages, 5 figures. v3: section including sum rules added, accepted
by JHE
CORE and the Haldane Conjecture
The Contractor Renormalization group formalism (CORE) is a real-space
renormalization group method which is the Hamiltonian analogue of the Wilson
exact renormalization group equations. In an earlier paper\cite{QGAF} I showed
that the Contractor Renormalization group (CORE) method could be used to map a
theory of free quarks, and quarks interacting with gluons, into a generalized
frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to
study these theories. Since generalizations of HAF's exhibit all sorts of
subtle behavior which, from a continuum point of view, are related to
topological properties of the theory, it is important to know that CORE can be
used to extract this physics. In this paper I show that despite the folklore
which asserts that all real-space renormalization group schemes are necessarily
inaccurate, simple Contractor Renormalization group (CORE) computations can
give highly accurate results even if one only keeps a small number of states
per block and a few terms in the cluster expansion. In addition I argue that
even very simple CORE computations give a much better qualitative understanding
of the physics than naive renormalization group methods. In particular I show
that the simplest CORE computation yields a first principles understanding of
how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1
HAF.Comment: 36 pages, 4 figures, 5 tables, latex; extensive additions to conten
Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras
As Lie algebras of compact connected Lie groups, semisimple Lie algebras have
wide applications in the description of continuous symmetries of physical
systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of
generators which consists of a Cartan subalgebra of mutually commuting
generators H_I and a number of step generators E^\alpha that are characterized
by a root space of non-degenerate one-forms \alpha. This simple decomposition
in terms of the root space allows for a complete classification of semisimple
Lie algebras. In this paper, we introduce the analogous concept of a
Cartan-Weyl Lie 3-algebra. We analyze their structure and obtain a complete
classification of them. Many known examples of metric Lie 3-algebras (e.g. the
Lorentzian 3-algebras) are special cases of the Cartan-Weyl 3-algebras. Due to
their elegant and simple structure, we speculate that Cartan-Weyl 3-algebras
may be useful for describing some kinds of generalized symmetries. As an
application, we consider their use in the Bagger-Lambert-Gustavsson (BLG)
theory.Comment: LaTeX. 34 pages.v2. deleted some distracting paragraphs in the
introduction to bring more out the main results of the paper. typos corrected
and references adde
Statistical Mechanics of Vacancy and Interstitial Strings in Hexagonal Columnar Crystals
Columnar crystals contain defects in the form of vacancy/interstitial loops
or strings of vacancies and interstitials bounded by column ``heads'' and
``tails''. These defect strings are oriented by the columnar lattice and can
change size and shape by movement of the ends and forming kinks along the
length. Hence an analysis in terms of directed living polymers is appropriate
to study their size and shape distribution, volume fraction, etc. If the
entropy of transverse fluctuations overcomes the string line tension in the
crystalline phase, a string proliferation transition occurs, leading to a
supersolid phase. We estimate the wandering entropy and examine the behaviour
in the transition regime. We also calculate numerically the line tension of
various species of vacancies and interstitials in a triangular lattice for
power-law potentials as well as for a modified Bessel function interaction
between columns as occurs in the case of flux lines in type-II superconductors
or long polyelectrolytes in an ionic solution. We find that the centered
interstitial is the lowest energy defect for a very wide range of interactions;
the symmetric vacancy is preferred only for extremely short interaction ranges.Comment: 22 pages (revtex), 15 figures (encapsulated postscript
Metal-Insulator Transition in a Disordered Two-Dimensional Electron Gas in GaAs-AlGaAs at zero Magnetic Field
A metal-insulator transition in two-dimensional electron gases at B=0 is
found in Ga(Al)As heterostructures, where a high density of self-assembled InAs
quantum dots is incorporated just 3 nm below the heterointerface. The
transition occurs at resistances around h/e^2 and critical carrier densities of
1.2 10^11cm^-2. Effects of electron-electron interactions are expected to be
rather weak in our samples, while disorder plays a crucial role.Comment: 4 pages, 3 figures, 21 reference
Tensor model and dynamical generation of commutative nonassociative fuzzy spaces
Rank-three tensor model may be regarded as theory of dynamical fuzzy spaces,
because a fuzzy space is defined by a three-index coefficient of the product
between functions on it, f_a*f_b=C_ab^cf_c. In this paper, this previous
proposal is applied to dynamical generation of commutative nonassociative fuzzy
spaces. It is numerically shown that fuzzy flat torus and fuzzy spheres of
various dimensions are classical solutions of the rank-three tensor model.
Since these solutions are obtained for the same coupling constants of the
tensor model, the cosmological constant and the dimensions are not fundamental
but can be regarded as dynamical quantities. The symmetry of the model under
the general linear transformation can be identified with a fuzzy analog of the
general coordinate transformation symmetry in general relativity. This symmetry
of the tensor model is broken at the classical solutions. This feature may make
the model to be a concrete finite setting for applying the old idea of
obtaining gravity as Nambu-Goldstone fields of the spontaneous breaking of the
local translational symmetry.Comment: Adding discussions on effective geometry, a note added, four
references added, other minor changes, 27 pages, 17 figure
Mixed-symmetry massive fields in AdS(5)
Free mixed-symmetry arbitrary spin massive bosonic and fermionic fields
propagating in AdS(5) are investigated. Using the light-cone formulation of
relativistic dynamics we study bosonic and fermionic fields on an equal
footing. Light-cone gauge actions for such fields are constructed. Various
limits of the actions are discussed.Comment: v3: 24 pages, LaTeX-2e; typos corrected, footnote 7 and 2 references
added, published in Class. Quantum Gra
Maxwell-like Lagrangians for higher spins
We show how implementing invariance under divergence-free gauge
transformations leads to a remarkably simple Lagrangian description of massless
bosons of any spin. Our construction covers both flat and (A)dS backgrounds and
extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless
fields produce single-particle actions, while whenever trace constraints can be
dispensed with the resulting Lagrangians display the same reducible,
multi-particle spectra as those emerging from the tensionless limit of free
open-string field theory. For all explored options the corresponding kinetic
operators take essentially the same form as in the spin-one, Maxwell case.Comment: 77 pages, revised version. Erroneous interpretation and proof of the
gauge-fixing procedure for mixed-symmetry fields corrected. As a consequence,
the mixed-symmetry, one-particle Lagrangians are to be complemented with
conditions on the divergences of the fields; all other conclusions unchanged.
Additional minor changes including references added. To appear in JHE
Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model
We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to
a zero-dimensional 3-Lie algebra model and construct various stable solutions
corresponding to quantized Nambu-Poisson manifolds. A recently proposed Higgs
mechanism reduces this model to the IKKT matrix model. We find that in the
strong coupling limit, our solutions correspond to ordinary noncommutative
spaces arising as stable solutions in the IKKT model with D-brane backgrounds.
In particular, this happens for S^3, R^3 and five-dimensional Neveu-Schwarz
Hpp-waves. We expand our model around these backgrounds and find effective
noncommutative field theories with complicated interactions involving
higher-derivative terms. We also describe the relation of our reduced model to
a cubic supermatrix model based on an osp(1|32) supersymmetry algebra.Comment: 22 page
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