11 research outputs found
Bilocal approach to the infra-red fixed point of O (N) invariant theories in 3d and its relation to higher spins
A dissertation submitted to the Faculty of Science, University of the Witwatersrand,
Johannesburg, in fulfillment of the requirements for the degree of Doctor of Science.
Johannesburg, 2018The Klebanov-Polyakov Higher-Spin Anti-de Sitter/Conformal Field Theory conjecture
posits that the free O(N) vector model is dual to the type A Vasiliev Higher Spin Gravity
with the bulk scalar eld having conformal scaling dimension = 1. Similarly, the
critical O(N) vector model in 3d is dual to type A Vasilev Higher Spin Gravity with bulk
scalar having = 2 . This is a weak-weak duality and accordingly allows a setting where
a reconstruction of bulk physics from the boundary CFT is possible. The Jevicki-Sakita
collective eld theory provides an explicit realization of such a bulk reconstruction.
In this thesis, we use the collective eld theory description of the large-N limit of vector
models to study the O(N) infra-red interacting xed point. In particular, we compute the
two-point functions for the non-linear sigma model (which is equivalent, in the infra-red,
to the critical O(N) vector model) and the two-time bilocal propagator. The spectrum
for the O(N) vector model is then obtained by looking at the poles of the connected
Green's function. We then show that this same pole condition can be obtained from the
homogeneous equation for the bilocal
uctuations.
We then discuss the single-time Hamiltonian formalism for the critical O(N) vector
model. We derive a coupled integral equation for the single-time
uctuations. This
coupled integral equations allows us to write down the single-time pole condition. We
show that the two-time pole condition is equivalent to the single-time pole condition.
In addition, we also show that the two-time free bilocal propagator is equivalent to the
single-time free bilocal propagator. A Lagrangian formulation of the single-time descripiv
tion is given and we write down the single-time propagator.
We then explain a puzzle which is that from our study of the non-linear sigma model
and the the pole structure of both the two-time and the single-time propagators it would
seem that both the = 1 and = 2 scalars are present. By studying the quadratic
Hamiltonian determining the spectrum, we demonstrate how in the infra-red limit the
state = 1 disappears from the spectum.MT 201
Large N bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction
We study the three dimensional O(N) invariant bosonic vector model with a
interaction at its infrared fixed
point, using a bilocal field approach and in an expansion. We identify a
(negative energy squared) bound state in its spectrum about the large
conformal background. At the critical point this is identified with the
state. We further demonstrate that at the critical point the
state disappears from the spectrum.Comment: 30 page
Large N Matrix Hyperspheres and the Gauge-Gravity Correspondence
The large N dynamics of a subsector of d=0 interacting complex multi matrix
systems, which is naturally parametrized by a matrix valued radial coordinate,
and which embodies the canonical AdS/CFT relationship between 't Hooft's
coupling constant and radius, is obtained. Unlike the case of the single
complex matrix, for two or more complex matrices a new repulsive logarithmic
potential is present, as a result of which the density of radial eigenvalues
has support on an hyper annulus. For the single complex matrix, the integral
over the angular degrees of freedom of the Yang-Mills interaction can be
carried out exactly, and in the presence of an harmonic potential, the density
of radial eigenvalues is shown to be of the Wigner type.Comment: 15 pages - v2: minor text changes in abstract and introductio
Constructing the bulk at the critical point of three-dimensional large N vector theories
Please read abstract in the article.The National and Mandelstam
Institutes for Theoretical Physics; a Postdoctoral Fellowship from the National Research Foundation (NRF) and the National Institute
for Theoretical and Computational Sciences.http://www.elsevier.com/locate/physletbhj2023Physic
Six-membered ring systems: with O and/or S atoms
A large variety of publications involving O- and S-6-membered ring systems
have appeared in 2017. The importance of these heterocyclic compounds
is highlighted by the huge number of publications on the total
synthesis of natural oxygen derivatives and of other communications
dedicated to synthetic derivatives.
Reviews on stereoselective organocatalytic synthesis of tetrahydropyrans
(17EJO4666), of tetrahydropyrans and their application in total synthesis of
natural products (17CSR1661), on the synthesis of the less thermodynamically
stable 2,6-trans-tetrahydropyrans (17S4899), on enantioselective
synthesis of polyfunctionalized pyran and chromene derivatives
(17TA1462), and on enantioselective and racemic total synthesis of
camptothecins, including the formation of their pyran-2-one ring
(17SL1134), have appeared.
Advances in the transition metal-catalyzed synthesis of pyran-2/4-ones
(17TL263), N-heterocyclic carbene (NHC)-catalyzed achiral synthesis of
pyran-2-one, coumarin and (thio)chromone derivatives (17OBC4731), on
the synthesis and transformation of 2H-pyran-2-ones (17T2529) and
2-styrylchromones (17EJO3115) into other heterocyclic compounds, have
been surveyed. The strategies to build up the tetrahydropyranyl core of
brevisamide (17H(95)81) and the reactions of ketyl radicals, generated from
carbonyl derivatives under transition-metal photoredox-catalyzed conditions,
leading to isochromen- and chroman-type compounds (17CC13093) were
disclosed. Developments in the synthesis of pentafluorosulfanyl(chromene
and coumarin) derivatives (17TL4803), photoswitchable D9-tetrahydrocannabinol
derivatives (17JA18206), and aminobenzopyranoxanthenes
with nitrogen-containing rings (17JOC13626) have been studied.info:eu-repo/semantics/publishedVersio
The large-N limit of matrix models and AdS/CFT
Random matrix models have found numerous applications in both Theoretical Physics
and Mathematics. In the gauge-gravity duality, for example, the dynamics of the half-
BPS sector can be fully described by the holomorphic sector of a single complex matrix
model.
In this thesis, we study the large-N limit of multi-matrix models at strong-coupling. In
particular, we explore the significance of rescaling the matrix fields. In order to investigate
this, we consider the matrix quantum mechanics of a single Hermitian system with a
quartic interaction. We “compactify” this system on a circle and compute the first-order
perturbation theory correction to the ground-state energy. The exact ground-state energy
is obtained using the Das-Jevicki-Sakita Collective Field Theory approach.
We then discuss the multi-matrix model that results from the compactification of the
Higgs sector of N = 4 SYM on S4 (or T S3). For the radial subsector, the saddle-point
equations are solved exactly and hence the radial density of eigenvalues for an arbitrary
number of even Hermitian matrices is obtained. The single complex matrix model is
parametrized in terms of the matrix valued polar coordinates and the first-order perturbation theory density of eigenstates is obtained. We make use of the Harish-Chandra- Itzykson-Zuber (HCIZ) formula to write down the exact saddle-point equations.
We then give a complementary approach - based on the Dyson-Schwinger (loop) equations formalism - to the saddle-point method. We reproduce the results obtained for the radial (single matrix) subsector. The two-matrix integral does not close on the original
set of variables and thus we map the system onto an auxiliary Penner-type two
matrix model. In the absence of a logarithmic potential we derive a radial hemispherical
density of eigenvalues. The system is regulated with a logarithm potential, and the
Dobroliubov-Makeenko-Semenoff (DMS) loop equations yield an equation of third degree
that is satisfied by the generating function. This equation is solved at strong coupling
and, accordingly, we obtain the radial density of eigenvalues
Constructing the bulk at the critical point of three-dimensional large vector theories
In the context of the correspondence between higher spin
fields and vector theories, we use the constructive bilocal fields based
approach to this correspondence, to demonstrate, at the critical point of
the interacting vector theory and directly in the bulk, the removal of the
() state from the higher spins field spectrum, and to exhibit
simple Klein-Gordon higher spin Hamiltonians. The bulk variables and higher
spin fields are obtained in a simple manner from boundary bilocals, by the
change of variables previously derived for the critical point (in momentum
space), together with a field redefinition.Comment: Derivation of the \Delta=2 Hamiltonian added to Section 3.3; 19 pages
including reference
NaHSO<sub>4</sub>–SiO<sub>2</sub>-catalyzed aza-Diels–Alder reaction of <i>o</i>-hydroxybenzaldimines with 2,3-dihydrofuran: Diastereoselective synthesis of furanobenzopyrans
<p>NaHSO<sub>4</sub> supported on silica gel catalyzes the aza-Diels–Alder reaction of <i>o</i>-hydroxybenzaldimines with 2,3-dihydrofuran to provide furanobenzopyrans in reasonable yields and diastereoselectivity. The catalyst is recyclable and reusable up to two times without a significant loss of activity.</p