248 research outputs found
The new vertices and canonical quantization
We present two results on the recently proposed new spin foam models. First,
we show how a (slightly modified) restriction on representations in the EPRL
model leads to the appearance of the Ashtekar-Barbero connection, thus bringing
this model even closer to LQG. Second, we however argue that the quantization
procedure used to derive the new models is inconsistent since it relies on the
symplectic structure of the unconstraint BF theory.Comment: 16 pages, 1 figure; added subsection on ordering of Casimir
operators, more details on imposing simplicity constraint
c-map as c=1 string
We show the existence of a duality between the c-map space describing the
universal hypermultiplet at tree level and the matrix model description of
two-dimensional string theory compactified at a self-dual radius and perturbed
by a sine-Liouville potential. It appears as a particular case of a general
relation between the twistor description of four-dimensional quaternionic
geometries and the Lax formalism for Toda hierarchy. Furthermore, we give an
evidence that the instanton corrections to the c-map metric coming from
NS5-branes can be encoded into the Baker-Akhiezer function of the integrable
hierarchy.Comment: 19 pages, 2 figure
Bi-gravity with a single graviton
We analyze a bi-gravity model based on the first order formalism, having as
fundamental variables two tetrads but only one Lorentz connection. We show that
on a large class of backgrounds its linearization agrees with general
relativity. At the non-linear level, additional degrees of freedom appear, and
we reveal the mechanism hiding them around the special backgrounds. We further
argue that they do not contain a massive graviton, nor the Boulware-Deser
ghost. The model thus propagates only one graviton, whereas the nature of the
additional degrees of freedom remains to be investigated. We also present a
foliation-preserving deformation of the model, which keeps all symmetries
except time diffeomorphisms and has three degrees of freedom.Comment: 29 page
Non-perturbative scalar potential inspired by type IIA strings on rigid CY
Motivated by a class of flux compactifications of type IIA strings on rigid
Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we
derive a non-perturbative potential of all scalar fields from the exact
D-instanton corrected metric on the hypermultiplet moduli space. Applying this
potential to moduli stabilization, we find a discrete set of exact vacua for
axions. At these critical points, the stability problem is decoupled into two
subspaces spanned by the axions and the other fields (dilaton and Kahler
moduli), respectively. Whereas the stability of the axions is easily achieved,
numerical analysis shows instabilities in the second subspace.Comment: 38 pages; some changes in presentatio
Theta series, wall-crossing and quantum dilogarithm identities
Motivated by mathematical structures which arise in string vacua and gauge
theories with N=2 supersymmetry, we study the properties of certain generalized
theta series which appear as Fourier coefficients of functions on a twisted
torus. In Calabi-Yau string vacua, such theta series encode instanton
corrections from Neveu-Schwarz five-branes. The theta series are determined
by vector-valued wave-functions, and in this work we obtain the transformation
of these wave-functions induced by Kontsevich-Soibelman symplectomorphisms.
This effectively provides a quantum version of these transformations, where the
quantization parameter is inversely proportional to the five-brane charge .
Consistency with wall-crossing implies a new five-term relation for Faddeev's
quantum dilogarithm at , which we prove. By allowing the torus to
be non-commutative, we obtain a more general five-term relation valid for
arbitrary and , which may be relevant for the physics of five-branes at
finite chemical potential for angular momentum.Comment: 26 pages; v2: added discussion on relation to complex Chern-Simons,
misprints correcte
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