2,059 research outputs found
Muon g-2 through a flavor structure on soft SUSY terms
In this work we analyze the possibility to explain the muon anomalous
magnetic moment discrepancy within theory and experiment through lepton flavor
violation processes. We propose a flavor extended MSSM by considering a
hierarchical family structure for the trilinear scalar Soft-Supersymmetric
terms of the Lagranagian, present at the SUSY breaking scale. We obtain
analytical results for the rotation mass matrix, with the consequence of having
non-universal slepton masses and the possibility of leptonic flavour mixing.
The one-loop supersymmetric contributions to the leptonic flavour violating
process are calculated in the physical basis, with slepton
flavour mixed states, instead of using the well known Mass Insertion Method. We
present the regions in parameter space where the muon g-2 problem is either
entirely solved or partially reduced through the contribution of these flavor
violating processes.Comment: 21 pages, 7 figures. Changes on version 3: In order to obtain the
complete result for muon g-2 in the limit of non-flavor violation we added
the terms given in the appendix. We redid the graphics and numerical analysis
including these changes. We also corrected some typos and changed the order
of figure
An Invitation to Higher Gauge Theory
In this easy introduction to higher gauge theory, we describe parallel
transport for particles and strings in terms of 2-connections on 2-bundles.
Just as ordinary gauge theory involves a gauge group, this generalization
involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie
group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes,
which play an important role in string theory and multisymplectic geometry.
Second, every group representation gives a Lie 2-group; the representation of
the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which
leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint
representation of any Lie group on its own Lie algebra gives a 'tangent
2-group', which serves as a gauge 2-group in 4d BF theory, which has
topological gravity as a special case. Fourth, every Lie group has an 'inner
automorphism 2-group', which serves as the gauge group in 4d BF theory with
cosmological constant term. Fifth, every Lie group has an 'automorphism
2-group', which plays an important role in the theory of nonabelian gerbes. And
sixth, every compact simple Lie group gives a 'string 2-group'. We also touch
upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra
that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum
Gravity and Quantum Geometry at the 2009 Corfu Summer Institut
2-Vector Spaces and Groupoids
This paper describes a relationship between essentially finite groupoids and
2-vector spaces. In particular, we show to construct 2-vector spaces of
Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding
to functors between groupoids in both a covariant and contravariant way, which
are ambidextrous adjoints. This is used to construct a representation--a weak
functor--from Span(Gpd) (the bicategory of groupoids and spans of groupoids)
into 2Vect. In this paper we prove this and give the construction in detail.Comment: 44 pages, 5 figures - v2 adds new theorem, significant changes to
proofs, new sectio
On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
We discuss various features and details of two versions of the Barrett-Crane
spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian
model and second of the SL(2,C)-symmetric Lorentzian version in which all
tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a
causal structure into the Lorentzian Barrett--Crane model from which one can
construct a path integral that corresponds to the causal (Feynman) propagator.
We show how to obtain convergent integrals for the 10j-symbols and how a
dimensionless constant can be introduced into the model. We propose a `Wick
rotation' which turns the rapidly oscillating complex amplitudes of the Feynman
path integral into positive real and bounded weights. This construction does
not yet have the status of a theorem, but it can be used as an alternative
definition of the propagator and makes the causal model accessible by standard
numerical simulation algorithms. In addition, we identify the local symmetries
of the models and show how their four-simplex amplitudes can be re-expressed in
terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible
numerical simulations, we express the matrix elements that are defined by the
model, in terms of the continuous connection variables and determine the most
general observable in the connection picture. Everything is done on a fixed
two-complex.Comment: 22 pages, LaTeX 2e, 1 figur
Dual variables and a connection picture for the Euclidean Barrett-Crane model
The partition function of the SO(4)- or Spin(4)-symmetric Euclidean
Barrett-Crane model can be understood as a sum over all quantized geometries of
a given triangulation of a four-manifold. In the original formulation, the
variables of the model are balanced representations of SO(4) which describe the
quantized areas of the triangles. We present an exact duality transformation
for the full quantum theory and reformulate the model in terms of new variables
which can be understood as variables conjugate to the quantized areas. The new
variables are pairs of S^3-values associated to the tetrahedra. These
S^3-variables parameterize the hyperplanes spanned by the tetrahedra (locally
embedded in R^4), and the fact that there is a pair of variables for each
tetrahedron can be viewed as a consequence of an SO(4)-valued parallel
transport along the edges dual to the tetrahedra. We reconstruct the parallel
transport of which only the action of SO(4) on S^3 is physically relevant and
rewrite the Barrett-Crane model as an SO(4) lattice BF-theory living on the
2-complex dual to the triangulation subject to suitable constraints whose form
we derive at the quantum level. Our reformulation of the Barrett-Crane model in
terms of continuous variables is suitable for the application of various
analytical and numerical techniques familiar from Statistical Mechanics.Comment: 33 pages, LaTeX, combined PiCTeX/postscript figures, v2: note added,
TeX error correcte
A Lorentzian Signature Model for Quantum General Relativity
We give a relativistic spin network model for quantum gravity based on the
Lorentz group and its q-deformation, the Quantum Lorentz Algebra.
We propose a combinatorial model for the path integral given by an integral
over suitable representations of this algebra. This generalises the state sum
models for the case of the four-dimensional rotation group previously studied
in gr-qc/9709028.
As a technical tool, formulae for the evaluation of relativistic spin
networks for the Lorentz group are developed, with some simple examples which
show that the evaluation is finite in interesting cases. We conjecture that the
`10J' symbol needed in our model has a finite value.Comment: 22 pages, latex, amsfonts, Xypic. Version 3: improved presentation.
Version 2 is a major revision with explicit formulae included for the
evaluation of relativistic spin networks and the computation of examples
which have finite value
Positivity of Spin Foam Amplitudes
The amplitude for a spin foam in the Barrett-Crane model of Riemannian
quantum gravity is given as a product over its vertices, edges and faces, with
one factor of the Riemannian 10j symbols appearing for each vertex, and simpler
factors for the edges and faces. We prove that these amplitudes are always
nonnegative for closed spin foams. As a corollary, all open spin foams going
between a fixed pair of spin networks have real amplitudes of the same sign.
This means one can use the Metropolis algorithm to compute expectation values
of observables in the Riemannian Barrett-Crane model, as in statistical
mechanics, even though this theory is based on a real-time (e^{iS}) rather than
imaginary-time (e^{-S}) path integral. Our proof uses the fact that when the
Riemannian 10j symbols are nonzero, their sign is positive or negative
depending on whether the sum of the ten spins is an integer or half-integer.
For the product of 10j symbols appearing in the amplitude for a closed spin
foam, these signs cancel. We conclude with some numerical evidence suggesting
that the Lorentzian 10j symbols are always nonnegative, which would imply
similar results for the Lorentzian Barrett-Crane model.Comment: 15 pages LaTeX. v3: Final version, with updated conclusions and other
minor changes. To appear in Classical and Quantum Gravity. v4: corrects # of
samples in Lorentzian tabl
Self-referential Monte Carlo method for calculating the free energy of crystalline solids
A self-referential Monte Carlo method is described for calculating the free energy of crystalline solids. All Monte Carlo methods for the free energy of classical crystalline solids calculate the free-energy difference between a state whose free energy can be calculated relatively easily and the state of interest. Previously published methods employ either a simple model crystal, such as the Einstein crystal, or a fluid as the reference state. The self-referential method employs a radically different reference state; it is the crystalline solid of interest but with a different number of unit cells. So it calculates the free-energy difference between two crystals, differing only in their size. The aim of this work is to demonstrate this approach by application to some simple systems, namely, the face centered cubic hard sphere and Lennard-Jones crystals. However, it can potentially be applied to arbitrary crystals in both bulk and confined environments, and ultimately it could also be very efficient
When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?
In this work we investigate the question, under what conditions Hilbert
spaces that are induced by measures on the space of generalized connections
carry a representation of certain non-Abelian analogues of the electric flux.
We give the problem a precise mathematical formulation and start its
investigation. For the technically simple case of U(1) as gauge group, we
establish a number of "no-go theorems" asserting that for certain classes of
measures, the flux operators can not be represented on the corresponding
Hilbert spaces.
The flux-observables we consider play an important role in loop quantum
gravity since they can be defined without recourse to a background geometry,
and they might also be of interest in the general context of quantization of
non-Abelian gauge theories.Comment: LaTeX, 21 pages, 5 figures; v3: some typos and formulations
corrected, some clarifications added, bibliography updated; article is now
identical to published versio
Higher Poincare Lemma and Integrability
We prove the non-abelian Poincare lemma in higher gauge theory in two
different ways. The first method uses a result by Jacobowitz which states
solvability conditions for differential equations of a certain type. The second
method extends a proof by Voronov and yields the explicit gauge parameters
connecting a flat local connective structure to the trivial one. Finally, we
show how higher flatness appears as a necessary integrability condition of a
linear system which featured in recently developed twistor descriptions of
higher gauge theories.Comment: 1+21 pages, presentation streamlined, section on integrability for
higher linear systems significantly improved, published versio
- …