相关论文: On K(E_9)

We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups $G_f$ and general values of the chiral central charge $c_-$. Here $G_f$ is a…

In this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite equivariant…

We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a…

We review E$_{6(6)}$ exceptional field theory with a particular emphasis on the embedding of type IIB supergravity, which is obtained by picking the GL$(5)\times {\rm SL}(2)$ invariant solution of the section constraint. We work out the…

We extend the refined G-structure classification of supersymmetric solutions of eleven dimensional supergravity. We derive necessary and sufficient conditions for the existence of an arbitrary number of Killing spinors whose common isotropy…

Gauged off-shell Maxwell-Einstein supergravity in six dimensions with N=(1,0) supersymmetry has a higher derivative extension afforded by a supersymmetrized Riemann squared term. This theory admits a supersymmetric Minkowski x S^2…

We construct the 12-dimensional exceptional field theory associated to the group $\mathrm{SL}(2) \times \mathbb{R}^+$ . Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that…

Eleven-dimensional supergravity on $S^8\times S^1$ is conjectured to be dual to the M-theory matrix model. We prove that the dynamics of a subset of fluctuations around this background is consistently described by D=2 SO(9) gauged maximal…

We study the higher derivative corrections that occur in type II superstring theories in ten dimensions or less. Assuming invariance under a discrete duality group G(Z) we show that the generic functions of the scalar fields that occur can…

We study predictions of orbifold family unification models with $SU(9)$ gauge group on a six-dimensional space-time including the orbifold $T^2/Z_2$, and obtain relations among sfermion masses in the supersymmetric extension of models. The…

We provide an off-shell formulation of four-dimensional higher spin gravity based on a covariant Hamiltonian action on an open nine-dimensional Poisson manifold whose boundary consists of the direct product of spacetime and a noncommutative…

I build a SU(2)left x U(1) electroweak gauge theory of J=0 mesons, which transform like sets of fermion-antifermion composite fields. SU(2)left x U(1) is embedded in a natural way, compatible with the Glashow-Salam-Weinberg model for…

We review the geometrical formulation of Quantum Mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of…

Let $G$ be a linear Lie group acting properly and isometrically on a $G$-spin$^c$ manifold $M$ with compact quotient. We show that Poincar\'e duality holds between $G$-equivariant $K$-theory of $M$, defined using finite-dimensional…

The fundamental chiral nature of the observed quarks and leptons and the emergence of the gauge group itself are most puzzling aspects of the standard model. Starting from general considerations of topological properties of gauge field…

We develop a systematic theory of symmetry fractionalization for fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general $G_f$ is a central extension of the bosonic symmetry group $G_b$ by…

Totally complex submanifolds of a quaternionic K\"{a}hler manifold are analogous to complex submanifolds of a K\"{a}hler manifold. In this paper, we construct an example of a non-compact totally complex submanifold of maximal dimension of a…

We investigate the conformal window of four-dimensional gauge theories with fermionic matter fields in multiple representations. Of particularly relevant examples are the ultra-violet complete models with fermions in two distinct…

Let $G$ be a non-compact connected semisimple real Lie group with finite center. Suppose $L$ is a non-compact connected closed subgroup of $G$ acting transitively on a symmetric space $G/H$ such that $L\cap H$ is compact. We study the…

In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on…