Related papers: Some simple predictions from E_{11} symmetry
In this note we present three representations of a 248-dimensional Lie algebra, namely the algebra of Lie point symmetries admitted by a system of five trivial ordinary differential equations each of order forty-four, that admitted by a…
We study the modular symmetry in four-dimensional low-energy effective field theory, which is derived from type IIB magnetized D-brane models and type IIA intersecting D-brane models. We analyze modular symmetric behaviors of perturbative…
In this paper we derive geometric consequences from the presence of a long strand of linear syzygies in the minimal free resolution of a closed scheme in projective space whose homogeneous ideal is generated by quadrics. These consequences…
Type II string theory or M-theory contains a broad spectrum of gauge potentials. In addition to the standard $p$-form potentials, various mixed-symmetry potentials have been predicted, which may couple to exotic branes with non-standard…
We study dynamics of two-dimensional N=(0,1) supersymmetric gauge theories. In particular, we propose that there is an infrared triality between certain triples of theories with orthogonal and symplectic gauge groups. The proposal is…
We obtain symmetry results for solutions of an elliptic system of equation possessing a cooperative structure. The domain in which the problem is set may possess "holes" or "small vacancies" (measured in terms of capacity) along which the…
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…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…
Consideration of the Noether variational problem for any theory whose action is invariant under global and/or local gauge transformations leads to three distinct theorems. These include the familiar Noether theorem, but also two equally…
The consequences of certain simple assumptions like smoothness of ground state properties and vanishing of the vacuum energy (at least perturbatively) are explored. It would be interesting from the point of view of building realistic…
In any dimension, the positive level generators of the very-extended Kac-Moody algebra $E_{11}$ with completely antisymmetric spacetime indices are associated to the form fields of the corresponding maximal supergravity. We consider the…
Four dimensional N=1 supersymmetric gauge theories with unitary gauge groups and matter in the adjoint and fundamental representations give rise to a series of non-trivial fixed points with an ADE classification. Many of these models…
I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of…
We prove a structure theorem for Lie n-algebras possessing an invariant inner product. We define the notion of a double extension of a metric Lie n-algebra by another Lie n-algebra and prove that all metric Lie n-algebras are obtained from…
In addition to the very good theoretical motivations for supersymmetry, there are now at least nine phenomenological indications that nature is supersymmetric. All are indirect, so more is better. They are enumerated here. Some discussion…
The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts.…
In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.
Asymptotic symmetry plays an important role in determining physical observables of a theory. Recently, in the context of four dimensional asymptotically flat pure gravity and $\mathcal{N}=1$ supergravity, it has been proposed that OPEs of…