Related papers: Higher ideles and class field theory
These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…
It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different…
We propose a notion of idele class groups of finitely generated fields using the concept of Parshin chains. This new class group allows us to give an idelic interpretation of the higher class field theory of Kato and Saito.
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
New constructions in the theory of fields for multiple integrals are designed. Generalizations of the Legendre - Weyl - Caratheodory transforms and corresponding invariant integrals are introduced and explored. Connection and curvature of…
In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
Viewing higher local fields as ring objects in the category of iterated pro-ind-objects, a definition of open subgroups in Milnor K-groups of the fields is given. The self-duality of the additive group of a higher local field is proved. By…
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
We explain and explore class-theoretic potentialism -- the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning…
The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.
From the method of realization of bialgebras developped in a preceding paper, we obtain the Duality Theorem and apply it to the study of the ideal of relations for each realized bialgebra. This is detailed in the english version of the…
A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.
We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to…
This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and…
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to…
A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…
In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this paper, we propose the extention of these characters to include the dual fields. The unified treatment of the…