Related papers: Introduction to the Maldacena Conjecture on AdS/CF…
These lectures (given at TASI 2000) provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1 (Ch. 2) is a very vanilla introduction to lattice QCD. Lecture 2 (Ch. 3) describes examples of…
Some simple facts are proved ruling the Collatz tree and the chains of vertices appearing in it, leading to the reduction of the number of significant elements appearing in the tree. Although the Collatz conjecture remains open, these fact…
Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…
These lecture notes cover the theory of convex optimization, with a particular emphasis on first-order methods.
We provide a new general setting for scalar interacting fields on the covering of a d+1-dimensional AdS spacetime. The formalism is used at first to construct a one-paramater family of field theories, each living on a corresponding…
In this note we present some of the most basic aspects of the fractional Laplacean with a self-contained and purely didactic intent, and with a somewhat different slant from the several excellent existing references. Given the interest that…
It is natural to analyse the AdS$_{d+1}$-CQFT$_{d}$ correspondence in the context of the conformal- compactification and covering formalism. In this way one obtains additional inside about Rehren's rigorous algebraic holography in…
This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…
Light-cone gauge formulation of fields in AdS space and conformal field theory in flat space adapted for the study of AdS/CFT correspondence is developed. Arbitrary spin mixed-symmetry fields in AdS space and arbitrary spin mixed-symmetry…
This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
In recent literature one-loop tests of the higher-spin AdS$_{d+1}$/CFT$_d$ correspondences were carried out. Here we extend these results to a more general set of theories in $d>2$. First, we consider the Type B higher spin theories, which…
These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum…
These lectures are a brief introduction to scattering amplitudes. We begin with a review of basic kinematical concepts like the spinor helicity formalism, followed by a tutorial on bootstrapping tree-level scattering amplitudes. Afterwards,…
I partially review our current knowledge on microquasars, making special emphasis on radio interferometric observations, and I comment on emerging trends in this field of astrophysics.
The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic…
This is an introduction to the basic elements needed for the measurements and interpretation of data in the millimeter and sub-mm wavelength range. A more complete version will be published in the proceedings of the Saas Fee Winter School…
AdS/QCD is an extra-dimensional approach to modeling hadronic physics, motivated by the AdS/CFT correspondence in string theory. AdS/QCD models are often more accurate than would have been expected at energies below a few GeV. We address…