172 research outputs found

### Non-Associative Geometry and the Spectral Action Principle

Chamseddine and Connes have argued that the action for Einstein gravity,
coupled to the SU(3)\times SU(2)\times U(1) standard model of particle physics,
may be elegantly recast as the "spectral action" on a certain "non-commutative
geometry." In this paper, we show how this formalism may be extended to
"non-associative geometries," and explain the motivations for doing so. As a
guiding illustration, we present the simplest non-associative geometry (based
on the octonions) and evaluate its spectral action: it describes Einstein
gravity coupled to a G_2 gauge theory, with 8 Dirac fermions (which transform
as a singlet and a septuplet under G_2). This is just the simplest example: in
a forthcoming paper we show how to construct more realistic models that include
Higgs fields, spontaneous symmetry breaking and fermion masses.Comment: 24 pages, no figures, matches JHEP versio

### A new algebraic structure in the standard model of particle physics

We introduce a new formulation of the real-spectral-triple formalism in
non-commutative geometry (NCG): we explain its mathematical advantages and its
success in capturing the structure of the standard model of particle physics.
The idea, in brief, is to represent $A$ (the algebra of differential forms on
some possibly-noncommutative space) on $H$ (the Hilbert space of spinors on
that space), and to reinterpret this representation as a simple super-algebra
$B=A\oplus H$ with even part $A$ and odd part $H$. $B$ is the fundamental
object in our approach: we show that (nearly) all of the basic axioms and
assumptions of the traditional real-spectral-triple formalism of NCG are
elegantly recovered from the simple requirement that $B$ should be a
differential graded $\ast$-algebra (or "$\ast$-DGA"). Moreover, this
requirement also yields other, new, geometrical constraints. When we apply our
formalism to the NCG traditionally used to describe the standard model of
particle physics, we find that these new constraints are physically meaningful
and phenomenologically correct. In particular, these new constraints provide a
novel interpretation of electroweak symmetry breaking that is geometric rather
than dynamical. This formalism is more restrictive than effective field theory,
and so explains more about the observed structure of the standard model, and
offers more guidance about physics beyond the standard model.Comment: 30 pages, no figures, matches JHEP versio

### Binary black hole merger: symmetry and the spin expansion

We regard binary black hole (BBH) merger as a map from a simple initial state
(two Kerr black holes, with dimensionless spins {\bf a} and {\bf b}) to a
simple final state (a Kerr black hole with mass m, dimensionless spin {\bf s},
and kick velocity {\bf k}). By expanding this map around {\bf a} = {\bf b} = 0
and applying symmetry constraints, we obtain a simple formalism that is
remarkably successful at explaining existing BBH simulations. It also makes
detailed predictions and suggests a more efficient way of mapping the parameter
space of binary black hole merger. Since we rely on symmetry rather than
dynamics, our expansion complements previous analytical techniques.Comment: 4 pages, 4 figures, matches Phys. Rev. Lett. versio

### Testing Inflation: A Bootstrap Approach

We note that the essential idea of inflation, that the universe underwent a
brief period of accelerated expansion followed by a long period of decelerated
expansion, can be encapsulated in a "closure condition" which relates the
amount of accelerated expansion during inflation to the amount of decelerated
expansion afterward. We present a protocol for systematically testing the
validity of this condition observationally.Comment: 4 pages, 2 figures, matches Phys. Rev. Lett. versio

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