1,341 research outputs found
Effective action and semiclassical limit of spin foam models
We define an effective action for spin foam models of quantum gravity by
adapting the background field method from quantum field theory. We show that
the Regge action is the leading term in the semi-classical expansion of the
spin foam effective action if the vertex amplitude has the large-spin
asymptotics which is proportional to an exponential function of the vertex
Regge action. In the case of the known three-dimensional and four-dimensional
spin foam models this amounts to modifying the vertex amplitude such that the
exponential asymptotics is obtained. In particular, we show that the ELPR/FK
model vertex amplitude can be modified such that the new model is finite and
has the Einstein-Hilbert action as its classical limit. We also calculate the
first-order and some of the second-order quantum corrections in the
semi-classical expansion of the effective action.Comment: Improved presentation, 2 references added. 15 pages, no figure
Euclidean three-point function in loop and perturbative gravity
We compute the leading order of the three-point function in loop quantum
gravity, using the vertex expansion of the Euclidean version of the new spin
foam dynamics, in the region of gamma<1. We find results consistent with Regge
calculus in the limit gamma->0 and j->infinity. We also compute the tree-level
three-point function of perturbative quantum general relativity in position
space, and discuss the possibility of directly comparing the two results.Comment: 16 page
3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
An effective field theory for matter coupled to three-dimensional quantum
gravity was recently derived in the context of spinfoam models in
hep-th/0512113. In this paper, we show how this relates to group field theories
and generalized matrix models. In the first part, we realize that the effective
field theory can be recasted as a matrix model where couplings between matrices
of different sizes can occur. In a second part, we provide a family of
classical solutions to the three-dimensional group field theory. By studying
perturbations around these solutions, we generate the dynamics of the effective
field theory. We identify a particular case which leads to the action of
hep-th/0512113 for a massive field living in a flat non-commutative space-time.
The most general solutions lead to field theories with non-linear redefinitions
of the momentum which we propose to interpret as living on curved space-times.
We conclude by discussing the possible extension to four-dimensional spinfoam
models.Comment: 17 pages, revtex4, 1 figur
Spin foams with timelike surfaces
Spin foams of 4d gravity were recently extended from complexes with purely
spacelike surfaces to complexes that also contain timelike surfaces. In this
article, we express the associated partition function in terms of vertex
amplitudes and integrals over coherent states. The coherent states are
characterized by unit 3--vectors which represent normals to surfaces and lie
either in the 2--sphere or the 2d hyperboloids. In the case of timelike
surfaces, a new type of coherent state is used and the associated completeness
relation is derived. It is also shown that the quantum simplicity constraints
can be deduced by three different methods: by weak imposition of the
constraints, by restriction of coherent state bases and by the master
constraint.Comment: 22 pages, no figures; v2: remarks on operator formalism added in
discussion; correction: the spin 1/2 irrep of the discrete series does not
appear in the Plancherel decompositio
Coupling gauge theory to spinfoam 3d quantum gravity
We construct a spinfoam model for Yang-Mills theory coupled to quantum
gravity in three dimensional riemannian spacetime. We define the partition
function of the coupled system as a power series in g_0^2 G that can be
evaluated order by order using grasping rules and the recoupling theory. With
respect to previous attempts in the literature, this model assigns the
dynamical variables of gravity and Yang-Mills theory to the same simplices of
the spinfoam, and it thus provides transition amplitudes for the spin network
states of the canonical theory. For SU(2) Yang-Mills theory we show explicitly
that the partition function has a semiclassical limit given by the Regge
discretization of the classical Yang-Mills action.Comment: 18 page
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
The amplitude for the 4-simplex in a spin foam model for quantum gravity is
defined using a graphical calculus for the unitary representations of the
Lorentz group. The asymptotics of this amplitude are studied in the limit when
the representation parameters are large, for various cases of boundary data. It
is shown that for boundary data corresponding to a Lorentzian simplex, the
asymptotic formula has two terms, with phase plus or minus the Lorentzian
signature Regge action for the 4-simplex geometry, multiplied by an Immirzi
parameter. Other cases of boundary data are also considered, including a
surprising contribution from Euclidean signature metrics.Comment: 30 pages. v2: references now appear. v3: presentation greatly
improved (particularly diagrammatic calculus). Definition of "Regge state"
now the same as in previous work; signs change in final formula as a result.
v4: two references adde
Limit on the mass of a long-lived or stable gluino
We reinterpret the generic CDF charged massive particle limit to obtain a
limit on the mass of a stable or long-lived gluino. Various sources of
uncertainty are examined. The -hadron spectrum and scattering cross sections
are modeled based on known low-energy hadron physics and the resultant
uncertainties are quantified and found to be small compared to uncertainties
from the scale dependence of the NLO pQCD production cross sections. The
largest uncertainty in the limit comes from the unknown squark mass: when the
squark -- gluino mass splitting is small, we obtain a gluino mass limit of 407
GeV, while in the limit of heavy squarks the gluino mass limit is 397 GeV. For
arbitrary (degenerate) squark masses, we obtain a lower limit of 322 GeV on the
gluino mass. These limits apply for any gluino lifetime longer than
ns, and are the most stringent limits for such a long-lived or stable gluino.Comment: 15 pages, 5 figures, accepted for publication in JHE
Observables in 3d spinfoam quantum gravity with fermions
We study expectation values of observables in three-dimensional spinfoam
quantum gravity coupled to Dirac fermions. We revisit the model introduced by
one of the authors and extend it to the case of massless fermionic fields. We
introduce observables, analyse their symmetries and the corresponding proper
gauge fixing. The Berezin integral over the fermionic fields is performed and
the fermionic observables are expanded in open paths and closed loops
associated to pure quantum gravity observables. We obtain the vertex amplitudes
for gauge-invariant observables, while the expectation values of gauge-variant
observables, such as the fermion propagator, are given by the evaluation of
particular spin networks.Comment: 32 pages, many diagrams, uses psfrag
A new look at loop quantum gravity
I describe a possible perspective on the current state of loop quantum
gravity, at the light of the developments of the last years. I point out that a
theory is now available, having a well-defined background-independent
kinematics and a dynamics allowing transition amplitudes to be computed
explicitly in different regimes. I underline the fact that the dynamics can be
given in terms of a simple vertex function, largely determined by locality,
diffeomorphism invariance and local Lorentz invariance. I emphasize the
importance of approximations. I list open problems.Comment: 15 pages, 5 figure
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
The present paper studies the large-j asymptotics of the Lorentzian EPRL
spinfoam amplitude on a 4d simplicial complex with an arbitrary number of
simplices. The asymptotics of the spinfoam amplitude is determined by the
critical configurations. Here we show that, given a critical configuration in
general, there exists a partition of the simplicial complex into three type of
regions R_{Nondeg}, R_{Deg-A}, R_{Deg-B}, where the three regions are
simplicial sub-complexes with boundaries. The critical configuration implies
different types of geometries in different types of regions, i.e. (1) the
critical configuration restricted into R_{Nondeg} is degenerate of type-A in our definition of degeneracy, but implies
a nondegenerate discrete Euclidean geometry on R_{Deg-A}, (3) the critical
configuration restricted into R_{Deg-B} is degenerate of type-B, and implies a
vector geometry on R_{Deg-B}. With the critical configuration, we further make
a subdivision of the regions R_{Nondeg} and R_{Deg-A} into sub-complexes (with
boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume
V_4(v), such that sgn(V_4(v)) is a constant sign on each sub-complex. Then in
the each sub-complex, the spinfoam amplitude at the critical configuration
gives the Regge action in Lorentzian or Euclidean signature respectively on
R_{Nondeg} or R_{Deg-A}. The Regge action reproduced here contains a sign
factor sgn(V_4(v)) of the oriented 4-simplex volume. Therefore the Regge action
reproduced here can be viewed a discretized Palatini action with on-shell
connection. Finally the asymptotic formula of the spinfoam amplitude is given
by a sum of the amplitudes evaluated at all possible critical configurations,
which are the products of the amplitudes associated to different type of
geometries.Comment: 54 pages, 2 figures, reference adde
- …