88 research outputs found
Asymptotics of 4d spin foam models
We study the asymptotic properties of four-simplex amplitudes for various
four-dimensional spin foam models. We investigate the semi-classical limit of
the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the
boundary data. For some classes of geometrical boundary data, the asymptotic
formulae are given, in all three cases, by simple functions of the Regge action
for the four-simplex geometry.Comment: 10 pages, Proceedings for the 2nd Corfu summer school and workshop on
quantum gravity and quantum geometry, talk given by Winston J. Fairbair
Holography in the EPRL Model
In this research announcement, we propose a new interpretation of the EPR
quantization of the BC model using a functor we call the time functor, which is
the first example of a CLa-ren functor. Under the hypothesis that the universe
is in the Kodama state, we construct a holographic version of the model.
Generalisations to other CLa-ren functors and connections to model category
theory are considered.Comment: research announcement. Latex fil
Holomorphic Factorization for a Quantum Tetrahedron
We provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of
SU(2)-invariant tensors (intertwiners) and establish a holomorphically
factorized formula for the decomposition of identity in H(j_1,..,j_n).
Interestingly, the integration kernel that appears in the decomposition formula
turns out to be the n-point function of bulk/boundary dualities of string
theory. Our results provide a new interpretation for this quantity as being, in
the limit of large conformal dimensions, the exponential of the Kahler
potential of the symplectic manifold whose quantization gives H(j_1,..,j_n).
For the case n=4, the symplectic manifold in question has the interpretation of
the space of "shapes" of a geometric tetrahedron with fixed face areas, and our
results provide a description for the quantum tetrahedron in terms of
holomorphic coherent states. We describe how the holomorphic intertwiners are
related to the usual real ones by computing their overlap. The semi-classical
analysis of these overlap coefficients in the case of large spins allows us to
obtain an explicit relation between the real and holomorphic description of the
space of shapes of the tetrahedron. Our results are of direct relevance for the
subjects of loop quantum gravity and spin foams, but also add an interesting
new twist to the story of the bulk/boundary correspondence.Comment: 45 pages; published versio
Colored Group Field Theory
Group field theories are higher dimensional generalizations of matrix models.
Their Feynman graphs are fat and in addition to vertices, edges and faces, they
also contain higher dimensional cells, called bubbles. In this paper, we
propose a new, fermionic Group Field Theory, posessing a color symmetry, and
take the first steps in a systematic study of the topological properties of its
graphs. Unlike its bosonic counterpart, the bubbles of the Feynman graphs of
this theory are well defined and readily identified. We prove that this graphs
are combinatorial cellular complexes. We define and study the cellular homology
of this graphs. Furthermore we define a homotopy transformation appropriate to
this graphs. Finally, the amplitude of the Feynman graphs is shown to be
related to the fundamental group of the cellular complex
Bubble divergences from cellular cohomology
We consider a class of lattice topological field theories, among which are
the weak-coupling limit of 2d Yang-Mills theory, the Ponzano-Regge model of 3d
quantum gravity and discrete BF theory, whose dynamical variables are flat
discrete connections with compact structure group on a cell 2-complex. In these
models, it is known that the path integral measure is ill-defined in general,
because of a phenomenon called `bubble divergences'. A common expectation is
that the degree of these divergences is given by the number of `bubbles' of the
2-complex. In this note, we show that this expectation, although not realistic
in general, is met in some special cases: when the 2-complex is simply
connected, or when the structure group is Abelian -- in both cases, the
divergence degree is given by the second Betti number of the 2-complex.Comment: 5 page
Complex Ashtekar variables and reality conditions for Holst's action
From the Holst action in terms of complex valued Ashtekar variables
additional reality conditions mimicking the linear simplicity constraints of
spin foam gravity are found. In quantum theory with the results of You and
Rovelli we are able to implement these constraints weakly, that is in the sense
of Gupta and Bleuler. The resulting kinematical Hilbert space matches the
original one of loop quantum gravity, that is for real valued Ashtekar
connection. Our result perfectly fit with recent developments of Rovelli and
Speziale concerning Lorentz covariance within spin-form gravity.Comment: 24 pages, 2 picture
Dichromatic state sum models for four-manifolds from pivotal functors
A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category.
A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant.
A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models.
Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed
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
The complete 1/N expansion of colored tensor models in arbitrary dimension
In this paper we generalize the results of [1,2] and derive the full 1/N
expansion of colored tensor models in arbitrary dimensions. We detail the
expansion for the independent identically distributed model and the topological
Boulatov Ooguri model
J/ψ polarization in p+p collisions at s=200 GeV in STAR
AbstractWe report on a polarization measurement of inclusive J/ψ mesons in the di-electron decay channel at mid-rapidity at 2<pT<6 GeV/c in p+p collisions at s=200 GeV. Data were taken with the STAR detector at RHIC. The J/ψ polarization measurement should help to distinguish between different models of the J/ψ production mechanism since they predict different pT dependences of the J/ψ polarization. In this analysis, J/ψ polarization is studied in the helicity frame. The polarization parameter λθ measured at RHIC becomes smaller towards high pT, indicating more longitudinal J/ψ polarization as pT increases. The result is compared with predictions of presently available models
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