69 research outputs found
D-branes with Lorentzian signature in the Nappi-Witten model
Lorentzian signature D-branes of all dimensions for the Nappi-Witten string
are constructed. This is done by rewriting the gluing condition for
the model chiral currents on the brane as a well posed first order differential
problem and by solving it for Lie algebra isometries other than Lie algebra
automorphisms. By construction, these D-branes are not twined conjugacy
classes. Metrically degenerate D-branes are also obtained.Comment: 22 page
Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
We define a theory of Galilean gravity in 2+1 dimensions with cosmological
constant as a Chern-Simons gauge theory of the doubly-extended Newton-Hooke
group, extending our previous study of classical and quantum gravity in 2+1
dimensions in the Galilean limit. We exhibit an r-matrix which is compatible
with our Chern-Simons action (in a sense to be defined) and show that the
associated bi-algebra structure of the Newton-Hooke Lie algebra is that of the
classical double of the extended Heisenberg algebra. We deduce that, in the
quantisation of the theory according to the combinatorial quantisation
programme, much of the quantum theory is determined by the quantum double of
the extended q-deformed Heisenberg algebra.Comment: 22 page
Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity
In this work we investigate the canonical quantization of 2+1 gravity with
cosmological constant in the canonical framework of loop quantum
gravity. The unconstrained phase space of gravity in 2+1 dimensions is
coordinatized by an SU(2) connection and the canonically conjugate triad
field . A natural regularization of the constraints of 2+1 gravity can be
defined in terms of the holonomies of . As a first step
towards the quantization of these constraints we study the canonical
quantization of the holonomy of the connection on the
kinematical Hilbert space of loop quantum gravity. The holonomy operator
associated to a given path acts non trivially on spin network links that are
transversal to the path (a crossing). We provide an explicit construction of
the quantum holonomy operator. In particular, we exhibit a close relationship
between the action of the quantum holonomy at a crossing and Kauffman's
q-deformed crossing identity. The crucial difference is that (being an operator
acting on the kinematical Hilbert space of LQG) the result is completely
described in terms of standard SU(2) spin network states (in contrast to
q-deformed spin networks in Kauffman's identity). We discuss the possible
implications of our result.Comment: 19 pages, references added. Published versio
Defect loops in gauged Wess-Zumino-Witten models
We consider loop observables in gauged Wess-Zumino-Witten models, and study
the action of renormalization group flows on them. In the WZW model based on a
compact Lie group G, we analyze at the classical level how the space of
renormalizable defects is reduced upon the imposition of global and affine
symmetries. We identify families of loop observables which are invariant with
respect to an affine symmetry corresponding to a subgroup H of G, and show that
they descend to gauge-invariant defects in the gauged model based on G/H. We
study the flows acting on these families perturbatively, and quantize the fixed
points of the flows exactly. From their action on boundary states, we present a
derivation of the "generalized Affleck-Ludwig rule, which describes a large
class of boundary renormalization group flows in rational conformal field
theories.Comment: 43 pages, 2 figures. v2: a few typos corrected, version to be
published in JHE
Geometric construction of D-branes in WZW models
The geometric description of D-branes in WZW models is pushed forward. Our
starting point is a gluing condition\, that matches the model's
chiral currents at the worldsheet boundary through a linear map acting on
the WZW Lie algebra. The equivalence of boundary and gluing conditions of this
type is studied in detail. The analysis involves a thorough discussion of
Frobenius integrability, shows that must be an isometry, and applies to
both metrically degenerate and nondegenerate D-branes. The isometry need
not be a Lie algebra automorphism nor constantly defined over the brane. This
approach, when applied to isometries of the form with a constant Lie
algebra automorphism, validates metrically degenerate -twined conjugacy
classes as D-branes. It also shows that no D-branes exist in semisimple WZW
models for constant\, .Comment: 23 pages, discussion of limitations of the gluing condition approach
adde
Geometry of the Grosse-Wulkenhaar Model
We define a two-dimensional noncommutative space as a limit of finite-matrix
spaces which have space-time dimension three. We show that on such space the
Grosse-Wulkenhaar (renormalizable) action has natural interpretation as the
action for the scalar field coupled to the curvature. We also discuss a natural
generalization to four dimensions.Comment: 16 pages, version accepted in JHE
Evidence for F(uzz) Theory
We show that in the decoupling limit of an F-theory compactification, the
internal directions of the seven-branes must wrap a non-commutative four-cycle
S. We introduce a general method for obtaining fuzzy geometric spaces via toric
geometry, and develop tools for engineering four-dimensional GUT models from
this non-commutative setup. We obtain the chiral matter content and Yukawa
couplings, and show that the theory has a finite Kaluza-Klein spectrum. The
value of 1/alpha_(GUT) is predicted to be equal to the number of fuzzy points
on the internal four-cycle S. This relation puts a non-trivial restriction on
the space of gauge theories that can arise as a limit of F-theory. By viewing
the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the
geometry, we argue that this theory admits a holographic dual description in
the large N limit. We also entertain the possibility of constructing string
models with large fuzzy extra dimensions, but with a high scale for quantum
gravity.Comment: v2: 66 pages, 3 figures, references and clarifications adde
Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions
We propose gauge-Higgs unification in fuzzy extra dimensions as a possible
solution to the Higgs naturalness problem. In our approach, the fuzzy extra
dimensions are created spontaneously as a vacuum solution of certain
four-dimensional gauge theory. As an example, we construct a model which has a
fuzzy torus as its vacuum. The Higgs field in our model is associated with the
Wilson loop wrapped on the fuzzy torus. We show that the quadratic divergence
in the mass of the Higgs field in the one-loop effective potential is absent.
We then argue based on symmetries that the quantum corrections to the Higgs
mass is suppressed including all loop contributions. We also consider a
realization on the worldvolume theory of D3-branes probing orbifold with discrete torsion.Comment: 1+38 pages, 4 figures v2: refs adde
Quasitriangular structure and twisting of the 3D bicrossproduct model
We show that the bicrossproduct model...SCOAP
Limits of minimal models and continuous orbifolds
The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be
equivalent to the singlet sector of a free boson theory, thus paralleling
exactly the structure of the free theory in the Klebanov-Polyakov proposal. In
2d, the singlet sector does not describe a consistent theory by itself since
the corresponding partition function is not modular invariant. However, it can
be interpreted as the untwisted sector of a continuous orbifold, and this point
of view suggests that it can be made consistent by adding in the appropriate
twisted sectors. We show that these twisted sectors account for the `light
states' that were not included in the original 't Hooft limit. We also show
that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold
agrees precisely with the limit theory of Runkel & Watts. In particular, this
implies that our construction satisfies crossing symmetry.Comment: 33 pages; v2: minor improvements and references added, published
versio
- …