Related papers: On "two important theorems" in canonical duality t…
For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving…
This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the…
We study the problem of finding good gauges for connections in higher gauge theories. We find that, for $2$-connections in strict $2$-gauge theory and $3$-connections in $3$-gauge theory, there are local "Coulomb gauges" that are more…
I argue that, on a judicious reading of two existing criteria--one syntactic and the other semantic--dual theories can be taken to be empirically equivalent. The judicious reading is straightforward, but leads to the surprising conclusion…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
We discuss why, in the determination of $\alpha_s(m_{\tau}^2)$ from hadronic $\tau$ decays, two important assumptions made in most of previous analyses, namely the neglect of higher-dimension condensates and of Duality Violations (DVs),…
The simplified Lennard-Jones (LJ) potential minimization problem is $f(x)=4\sum_{i=1}^N \sum_{j=1,j<i}^N (\frac{1}{\tau_{ij}^6} -\frac{1}{\tau_{ij}^3}) {subject to} x\in \mathbb{R}^n,$ where $\tau_{ij}=(x_{3i-2}-x_{3j-2})^2…
Superconformal sigma models with Calabi--Yau target spaces described as complete intersection subvarieties in toric varieties can be obtained as the low-energy limit of certain abelian gauge theories in two dimensions. We formulate mirror…
We prove that every quasi-projective semi log canonical pair has a quasi-log structure with several good properties. It implies that various vanishing theorems, torsion-free theorem, and the cone and contraction theorem hold for semi log…
We study various cases of dualities between $\cal{N}$$=1$ 5d supersymmetric gauge theories. We motivate the dualities using brane webs, and provide evidence for them by comparing the superconformal index. In many cases we find that the…
The paper is accompanying "A general Duality Theorem for the Monge-Kantorovich Transport Problem". We explain the methods used in this article in an elementary setting and present two examples complementing the results obtained therein.
The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as `duality' is understood in physics and (ii) equivalence of theories, as `equivalence' is understood in logic and philosophy. The…
A global analysis of duality transformations is presented. It is shown that duality between quantum field theories exists only when the geometrical structure of the quantum configuration spaces of the theories comply with certain precise…
The quantum Yang-Mills theory describing dual ($\tilde g$) and non-dual ($g$) charges and revealing the generalized duality symmetry was developed by analogy with the Zwanziger formalism in QED.
Quantum theory is a tremendously successful physical theory, but nevertheless suffers from two serious problems: the measurement problem and the problem of interpretational underdetermination. The latter, however, is largely overlooked as a…
We show by explicit computation that the recently discovered duality invariance of D=4 linearized gravity fails, already at first self-interacting, cubic, approximation of GR. In contrast, the cubic Yang-Mills correction to Maxwell does…
In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na\"ive version of Andrews' anti-telescoping technique quite well. These new theorems also put to rest any notion…
Kim, Kim, and Oh gave a minimal criterion for the 2-universality of positive-definite integer-matrix quadratic forms. We show that this 2-universality criterion is unique in the sense of the uniqueness of the Conway-Schneeberger Fifteen…
This thesis presents a thorough analysis of the links between the N=4 supersymmetric gauge theory in four dimensions and its three topological twisted counterparts. Special emphasis is put in deriving explicit results in terms of the vacuum…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…