41 research outputs found
Non-perturbative \lambda\Phi^4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
During the '70, several relativistic quantum field theory models in
and also in have been constructed in a non-perturbative way. That was
done in the so-called {\it constructive quantum field theory} approach, whose
main results have been obtained by a clever use of Euclidean functional
methods. Although in the construction of a single model there are several
technical steps, some of them involving long proofs, the constructive quantum
field theory approach contains conceptual insights about relativistic quantum
field theory that deserved to be known and which are accessible without
entering in technical details. The purpose of this note is to illustrate such
insights by providing an oversimplified schematic exposition of the simple case
of (with ) in . Because of the absence of
ultraviolet divergences in its perturbative version, this simple example
-although does not capture all the difficulties in the constructive quantum
field theory approach- allows to stress those difficulties inherent to the
non-perturbative definition. We have made an effort in order to avoid several
of the long technical intermediate steps without missing the main ideas and
making contact with the usual language of the perturbative approach.Comment: 63 pages. Typos correcte
Quantization of BMS orbits: a perturbative approach
We compute characters of the BMS group in three dimensions. The approach is
the same as that performed by Witten in the case of coadjoint orbits of the
Virasoro group in the eighties, within the large central charge approximation.
The procedure involves finding a Poisson bracket between classical variables
and the corresponding commutator of observables in a Hilbert space, explaining
why we call this a quantization. We provide first a pedagogical warm up by
applying the method to both SL(2,R) and Poincar\'{e}3 groups. As for BMS3, our
results coincide with the characters of induced representations recently
studied in the literature. Moreover, we relate the 'coadjoint representations'
to the induced representations.Comment: 17 pages. v2: references added. v3: minor changes and published in
Nucelar Physics
Scalar field dynamics in a BTZ background with generic boundary conditions
The revisit the dynamics of a massive scalar field in a BTZ background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically-sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window −3/4≤m2eℓ2<0 can be well-defined within a one-parametric family of distinct boundary conditions (−3/4 being the conformally-coupled case), while for m2eℓ2≥0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m2eℓ2<−1, and also shown that in the range m2eℓ2∈[−1,−3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly in describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved.Fil: Garbarz, Alan Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: La Madrid, Joan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin
Quasilocal energy for three-dimensional massive gravity solutions with chiral deformations of AdS boundary conditions
We consider critical gravity in three dimensions; that is, the New Massive
Gravity theory formulated about Anti-de Sitter (AdS) space with the specific
value of the graviton mass for which it results dual to a two-dimensional
conformal field theory with vanishing central charge. As it happens with Kerr
black holes in four-dimensional critical gravity, in three-dimensional critical
gravity the Banados-Teitelboim-Zanelli black holes have vanishing mass and
vanishing angular momentum. However, provided suitable asymptotic conditions
are chosen, the theory may also admit solutions carrying non-vanishing charges.
Here, we give simple examples of exact solutions that exhibit falling-off
conditions that are even weaker than those of the so-called Log-gravity. For
such solutions, we define the quasilocal stress-tensor and use it to compute
conserved charges. Despite the drastic deformation of AdS3 asymptotic, these
solutions have finite mass and angular momentum.Comment: 7 pages. v3: Typos corrected. Version accepted for publicatio
Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point
Chiral gravity admits asymptotically AdS3 solutions that are not locally
equivalent to AdS3; meaning that solutions do exist which, while obeying the
strong boundary conditions usually imposed in General Relativity, happen not to
be Einstein spaces. In Topologically Massive Gravity (TMG), the existence of
non-Einstein solutions is particularly connected to the question about the role
played by complex saddle points in the Euclidean path integral. Consequently,
studying (the existence of) non-locally AdS3 solutions to chiral gravity is
relevant to understand the quantum theory. Here, we discuss a special family of
non-locally AdS3 solutions to chiral gravity. In particular, we show that such
solutions persist when one deforms the theory by adding the higher-curvature
terms of the so-called New Massive Gravity (NMG). Moreover, the addition of
higher-curvature terms to the gravity action introduces new non-locally AdS3
solutions that have no analogues in TMG. Both stationary and time-dependent,
axially symmetric solutions that asymptote AdS3 space without being locally
equivalent to it appear. Defining the boundary stress-tensor for the full
theory, we show that these non-Einstein geometries have associated vanishing
conserved charges.Comment: 8 pages. v2 minor typos correcte
Classification of boundary gravitons in AdS3 gravity
We revisit the description of the space of asymptotically AdS3 solutions of pure gravity in three dimensions with a negative cosmological constant as a collection of coadjoint orbits of the Virasoro group. Each orbit corresponds to a set of metrics related by diffeomorphisms which do not approach the identity fast enough at the boundary. Orbits contain more than a single element and this fact manifests the global degrees of freedom of AdS3 gravity, being each element of an orbit what we call boundary graviton. We show how this setup allows to learn features about the classical phase space that otherwise would be quite difficult. Most important are the proof of energy bounds and the characterization of boundary gravitons unrelated to BTZs and AdS3. In addition, it makes manifest the underlying mathematical structure of the space of solutions close to infinity. Notably, because of the existence of a symplectic form in each orbit, being this related with the usual Dirac bracket of the asymptotic charges, this approach is a natural starting point for the quantization of different sectors of AdS3 gravity. We finally discuss previous attempts to quantize coadjoint orbits of the Virasoro group and how this is relevant for the formulation of AdS3 quantum gravity.Facultad de Ciencias ExactasInstituto de Física La Plat
A Special Class of Rank 10 and 11 Coxeter Groups
In the course of investigating regular subalgebras of E(10) related to
cosmological solutions of 11-dimensional supergravity supporting an electric
4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E(10)
was uncovered (hep-th/0606123). These Coxeter groups all share the property
that their Coxeter graphs have incidence index 3, i.e. that each node is
incident to three and only three single lines. Furthermore, the Coxeter
exponents are either 2 or 3, but never infinity. We here go beyond subgroups of
the Weyl group of E(10) and classify all rank 10 Coxeter groups with these
properties. We find 21 distinct Coxeter groups of which 7 were already
described in hep-th/0606123. Moreover, we extend the classification to the rank
11 case and we find 252 inequivalent rank 11 Coxeter groups with incidence
index 4, of which at least 28 can be regularly embedded into E(11).Comment: 20 pages, Typos corrected, Erratum added correcting the total number
of rank 11 Coxeter graphs with incidence index
Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT
Crossing symmetry (CS) is the main tool in the bootstrap program applied to CFT. This consists in an equality which imposes restrictions on the CFT data of a model, i.e., the OPE coefficients and the conformal dimensions. Reflection positivity (RP) has also played a role in this program, since this condition is what leads to the unitary bound and reality of the OPE coefficients. In this paper, we show that RP can still reveal more information, explaining how RP itself can capture an important part of the restrictions imposed by the full CS equality. In order to do that, we use a connection used by us in a previous work between RP and positive definiteness of a function of a single variable. This allows us to write constraints on the OPE coefficients in a concise way. These constraints are encoded in the conditions that certain functions of the cross-ratio will be positive defined and in particular completely monotonic. We will consider how the bounding of scalar conformal dimensions and OPE coefficients arise in this RP based approach. We will illustrate the conceptual and practical value of this view trough examples of general CFT models in d-dimensions.Fil: Lanosa, Leandro Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Leston, Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Passaglia, Mario. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin