Related papers: U-Duality and the Leech Lattice
Generators for the discrete U-duality groups of toroidally compactified M-theory in d>3 are presented and used to determine the d=3 U-duality group. This contribution summarizes the results of hep-th/9909150.
Electromagnetic duality is a symmetry of the source-free Einstein-Maxwell equations that rotates electric and magnetic fields while leaving the stress-energy tensor invariant. We present the first fully nonlinear realization of this…
We show that the Mathieu groups $M_{24}$ and $M_{23}$ in the isometry group of the odd Leech lattice do not lift to subgroups of the automorphism group of its lattice vertex operator (super)algebra. In other words, the subgroups…
After defining the concept of duality in the context of general $n$-form abelian gauge fields in 2$n$ dimensions, we show by explicit example the difference between apparent but unrealizable duality transformations, namely those in…
We study the gauge/gravity duality for supersymmetric SU(N) Yang-Mills theory in 1+0 dimension with sixteen supercharges using lattice simulations. The conjectured duality states that the gravity side is described by N D0-branes in type IIA…
Freudenthal duality can be defined as an anti-involutive, non-linear map acting on symplectic spaces. It was introduced in four-dimensional Maxwell-Einstein theories coupled to a non-linear sigma model of scalar fields. In this short…
In this article we study a second example of the phenomenon studied in "Complex Lorentzian Leech lattice and bimonster".(Arxiv. math.GR/0508228). The results and methods of proof are similar. We find 14 roots in the automorphism group of…
We show that the full global symmetry groups of all the D-dimensional maximal supergravities can be described in terms of the closure of the internal general coordinate transformations of the toroidal compactifications of D=11 supergravity…
We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their U-duality…
In the first three sections, we develop some basic facts about hypergeometric sheaves on the multiplicative group ${\mathbb G}_m$ in characteristic $p >0$. In the fourth and fifth sections, we specialize to quite special classses of…
We demonstrate the emergence of the U-duality group in compactification of Matrix theory on a 4-torus. The discussion involves non-trivial effects in strongly coupled 4+1 dimensional gauge theory, and highlights some interesting phenomena…
Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic…
It is mentioned that there is a subalgebra isomorphic to the alternating group $2 \cdot A_4$ as a subalgebra of the Quaternion over integers and half-integers called Hurwitz quaternionic integers $\mathscr{H}$ in the book by J.H.Conway and…
For $G(\mathbb{R})$ a split, simply connected, semisimple Lie group of rank $n$ and $K$ the maximal compact subgroup of $G$, we give a method for computing Iwasawa coordinates of $G/K$ using the Chevalley generators and the Steinberg…
We use the connection between the U-duality groups in d=5 and d=4 to derive properties of the N=8 black hole potential and its critical points (attractors). This approach allows to study and compare the supersymmetry features of different…
We study "minimal degree" complete bases of duality- and "horizontal"- invariant homogeneous polynomials in the flux representation of two-centered black hole solutions in two classes of D=4 Einstein supergravity models with symmetric…
The dimensional reduction of (the bosonic sector of) five-dimensional minimal supergravity to four dimensions leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields (one of which has Chern-Simons…
In 4-dimensional supergravity theories, covariant under symplectic electric-magnetic duality rotations, a significant role is played by the symplectic matrix M({\phi}), related to the coupling of scalars {\phi} to vector field-strengths. In…
Starting from basic identities of the group E8, we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E7xSU(2) and then of E6xU(1). This procedure provides a systematic approach to…
This work is intended as a pedagogical introduction to M-theory and to its maximally supersymmetric toroidal compactifications, in the frameworks of 11D supergravity, type II string theory and M(atrix) theory. U-duality is used as the main…