Related papers: Exponentially Closed Fields and the Conjecture on …
Recently proposed exceptional field theories (EFTs) making manifest the duality $E_{n(n)}$ symmetry, first observed as nonlinearly realized symmetries of the maximal $d=3,4,...,9$ supergravity ($n=11-d$) and containing 11D and type IIB…
Open-closed Deligne--Mumford field theories are chain-level field theories based on moduli spaces of stable curves with boundary. We associate to a relatively spin embedded Lagrangian $L \subset (X,\omega)$ such an open-closed DMFT. It…
In this paper we show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way string and string field theories. A new Lagrangian for the closed string is obtained and shown to be equivalent…
We obtain the elliptic curve and the Seiberg-Witten differential for an $N=2$ superconformal field theory which has an $E_8$ global symmetry at the strong coupling point $\tau=e^{\pi i/3}$. The differential has 120 poles corresponding to…
We develop a first-order theory of ordered transexponential fields in the language $\{+,\cdot,0,1,<,e,T\}$, where $e$ and $T$ stand for unary function symbols. While the archimedean models of this theory are readily described, the study of…
We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle…
Let $T$ be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let $K$ be a model of $T$ equipped with a $T$-convex valuation ring and a $T$-derivation. If this derivation is continuous with respect…
Enochs Conjecture asserts that each covering class of modules (over any ring) has to be closed under direct limits. Although various special cases of the conjecture have been verified, the conjecture remains open in its full generality. In…
We show that the $\ell$-adic Tate conjecture for divisors on smooth proper varieties over finitely generated fields of positive characteristic follows from the $\ell$-adic Tate conjecture for divisors on smooth projective surfaces over…
We construct an infinite system of non-linear duality equations, including fermions, that are invariant under global E11 and gauge invariant under generalised diffeomorphisms upon the imposition of a suitable section constraint. We use…
Suppose $E$ is an elliptic curve defined over $\Q$. At the 1983 ICM the first author formulated some conjectures that propose a close relationship between the explicit class field theory construction of certain abelian extensions of…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
Relative entropy is a non-negative quantity and offers a powerful means of achieving a unified understanding of fundamental properties in physics, including the second law of thermodynamics and positivity bounds on effective field theories…
The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential…
We demonstrate that exceptional field theory is a truncation of the non-linear realisation of the semi-direct product of E11 and its first fundamental as proposed in 2003. Evaluating the simple equations of the E11 approach, and using the…
This article initiates the study of topological transcendental fields $\FF$ which are subfields of the topological field $\CC$ of all complex numbers such that $\FF$ consists of only rational numbers and a nonempty set of transcendental…
We prove that asymptotically almost all vectorial functions over finite fields have trivial extended-affine stabilizers. As a consequence, the number of EA-equivalence classes is asymptotically equal to the naive estimate, namely the total…
We solve a case of the Abelian Exponential-Algebraic Closedness Conjecture, a conjecture due to Bays and Kirby, building on work of Zilber, which predicts sufficient conditions for systems of equations involving algebraic operations and the…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
We study (1,0) and (2,0) 6D superconformal field theories (SCFTs) that can be constructed in F-theory. Quite surprisingly, all of them involve an orbifold singularity C^2 / G with G a discrete subgroup of U(2). When G is a subgroup of…