28 research outputs found
Discrete and continuum third quantization of Gravity
We give a brief introduction to matrix models and the group field theory
(GFT) formalism as realizations of the idea of a third quantization of gravity,
and present in some more detail the idea and basic features of a continuum
third quantization formalism in terms of a field theory on the space of
connections, building up on the results of loop quantum gravity that allow to
make the idea slightly more concrete. We explore to what extent one can
rigorously define such a field theory. Concrete examples are given for the
simple case of Riemannian GR in 3 spacetime dimensions. We discuss the relation
between GFT and this formal continuum third quantized gravity, and what it can
teach us about the continuum limit of GFTs.Comment: 21 pages, 5 eps figures; submitted as a contribution to the
proceedings of the conference "Quantum Field Theory and Gravity Conference
Regensburg 2010" (28 September - 1 October 2010, Regensburg/Bavaria); v2:
preprint number include
Random volumes from matrices
We propose a class of models which generate three-dimensional random volumes,
where each configuration consists of triangles glued together along multiple
hinges. The models have matrices as the dynamical variables and are
characterized by semisimple associative algebras A. Although most of the
diagrams represent configurations which are not manifolds, we show that the set
of possible diagrams can be drastically reduced such that only (and all of the)
three-dimensional manifolds with tetrahedral decompositions appear, by
introducing a color structure and taking an appropriate large N limit. We
examine the analytic properties when A is a matrix ring or a group ring, and
show that the models with matrix ring have a novel strong-weak duality which
interchanges the roles of triangles and hinges. We also give a brief comment on
the relationship of our models with the colored tensor models.Comment: 33 pages, 31 figures. Typos correcte
Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories
Using localization, matrix model and saddle-point techniques, we determine
exact behavior of circular Wilson loop in N=2 superconformal (quiver) gauge
theories. Focusing at planar and large `t Hooft couling limits, we compare its
asymptotic behavior with well-known exponential growth of Wilson loop in N=4
super Yang-Mills theory. For theory with gauge group SU(N) coupled to 2N
fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential
growth -- at most, it can grow a power of `t Hooft coupling. For theory with
gauge group SU(N) x SU(N) and bifundamental hypermultiplets, there are two
Wilson loops associated with two gauge groups. We find Wilson loop in untwisted
sector grows exponentially large as in N=4 super Yang-Mills theory. We then
find Wilson loop in twisted sector exhibits non-analytic behavior with respect
to difference of two `t Hooft coupling constants. By letting one gauge coupling
constant hierarchically larger/smaller than the other, we show that Wilson
loops in the second type theory interpolate to Wilson loop in the first type
theory. We infer implications of these findings from holographic dual
description in terms of minimal surface of dual string worldsheet. We suggest
intuitive interpretation that in both type theories holographic dual background
must involve string scale geometry even at planar and large `t Hooft coupling
limit and that new results found in the gauge theory side are attributable to
worldsheet instantons and infinite resummation therein. Our interpretation also
indicate that holographic dual of these gauge theories is provided by certain
non-critical string theories.Comment: 52 pages, 7 figures v2. more figures embedded v3. minor stylistic
changes, v4. published versio
Phases of planar 5-dimensional supersymmetric Chern-Simons theory
In this paper we investigate the large- behavior of 5-dimensional
super Yang-Mills with a level Chern-Simons term and an
adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must
choose an integration contour to completely define the theory. Using
localization, we reduce the path integral to a matrix model with a cubic action
and compute its free energy in various scenarios. In the limit of infinite
Yang-Mills coupling and for particular choices of the contours, we find that
the free-energy scales as for gauge groups with large values
of the Chern-Simons 't\,Hooft coupling, . If we also
set the hypermultiplet mass to zero, then this limit is a superconformal fixed
point and the behavior parallels other fixed points which have known
supergravity duals. We also demonstrate that gauge groups cannot have
this scaling for their free-energy. At finite Yang-Mills coupling we
establish the existence of a third order phase transition where the theory
crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase
transition exists for any value of , although the details differ
between small and large values of . For pure Chern-Simons
theories we present evidence for a chain of phase transitions as
is increased.
We also find the expectation values for supersymmetric circular Wilson loops
in these various scenarios and show that the Chern-Simons term leads to
different physical properties for fundamental and anti-fundamental Wilson
loops. Different choices of the integration contours also lead to different
properties for the loops.Comment: 40 pages, 17 figures, Minor corrections, Published versio
The Spin Foam Approach to Quantum Gravity
This article reviews the present status of the spin foam approach to the
quantization of gravity. Special attention is payed to the pedagogical
presentation of the recently introduced new models for four dimensional quantum
gravity. The models are motivated by a suitable implementation of the path
integral quantization of the Plebanski formulation of gravity on a simplicial
regularization. The article also includes a self-contained treatment of the 2+1
gravity. The simple nature of the latter provides the basis and a perspective
for the analysis of both conceptual and technical issues that remain open in
four dimensions.Comment: To appear in Living Reviews in Relativit