Related papers: Higher Order Conformal Invariance of String Backgr…

This is the second of two papers devoted to the proof of conformal invariance of the critical double random current on the square lattice. More precisely, we show convergence of loop ensembles obtained by taking the cluster boundaries in…

Motivated by examples that appeared in the context of string theory - gauge theory duality, we consider corrections to supergravity backgrounds induced by higher derivative R^4+... terms in superstring effective action. We argue that…

There are two main approaches to duality covariant first order higher derivative corrections to the heterotic string, one extending the duality structure and the other deforming the gauge transformations. In this paper we introduce a…

One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…

Starting with a manifestly conformal ($O(d,2)$ invariant) mechanics model in $d$ space and 2 time dimensions, we derive the action for a massless spinning particle in $d$-dimensional anti-de Sitter space. The action obtained possesses both…

We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configurat$ of dynamical…

We present further mathematical results on a function appearing in the conformal blocks of four-point correlation functions with arbitrary quasi-primary operators. The $H$-function was introduced in a previous article and it has several…

String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string…

The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…

A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…

We present the string Lagrangian with manifest T-duality. Not only zero-modes but also all string modes are doubled. The gravitational field is an O(D,D) gauge field. We give a Lagrangian version of the section condition for the gauge…

QCD in $d=4-2\epsilon$ space-time dimensions possesses a nontrivial critical point. Scale invariance usually implies conformal symmetry so that there are good reasons to expect that QCD at the critical point restricted to the gauge…

Invariants are the predominant approach to verify the correctness of loops. As an alternative, loop contracts, which make explicit the premise and conclusion of the underlying induction proof, can sometimes capture correctness conditions…

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…

Using independent left and right vierbeins to describe graviton plus axion as suggested by string mechanics, O(d,d) duality can be realized linearly.

In this work, we exploit the operator content of the $(D_{4}, A_{6})$ conformal algebra. By constructing a $Z_{2}$-invariants fusion rules of a chosen subalgebra and by resolving the bootstrap equations consistent with these rules, we…

In the large N limit, conditions for the conformal invariance of the generalized Thirring model are derived, using two different approaches: the background field method and the Hamiltonian method based on an operator algebra, and the…

We present a way of constructing string solutions around non-trivial gravitational backgrounds. The proposed solutions are constructed using $N = 4$ superconformal building blocks with $\hat c = 4$. We give two different and inequivalent…