Related papers: Anomaly-free Hyperspherical Hamiltonian spaces for…

We show that there is a class of finite groups, the so-called perfect groups, which cannot exhibit anomalies. This implies that all non-Abelian finite simple groups are anomaly-free. On the other hand, non-perfect groups generically suffer…

It is known that the second Leibniz homology group $HL_2(stl_n(R))$ of the Steinberg Leibniz algebra $stl_n(R)$ is trivial for $n\geq 5$. In this paper, we determine $HL_2(stl_n(R))$ explicitly (which are shown to be not necessarily…

We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic groups. Our results are…

We prove that all SYM theories that have a quantum modified moduli space $\m$ defined by a single constraint equation have trivial homotopy groups $\pi_j(\m)$ for $j=0,1,2,3$ and 4. This implies that none of these theories admit skyrmions…

The purpose of this paper is to give new examples of families of free singularities. We first show that a generic equidimensional subspace arrangement is free. Furthermore, we show that a product of two reduced Cohen-Macaulay subspaces is…

The paper gives analogues of some starting results in the theory of Gaussian Hilbert Spaces for semicircular distributed random variables. The transition from the commutative to the free frame is done considering matrices of increasing…

All three-dimensional matter-free spacetimes with negative cosmological constant, compatible with cyclic symmetry are identified. The only cyclic solutions are the 2+1 (BTZ) black hole with SO(2) x R isometry, and the self-dual…

(N=2)-superspace without torsion is described, which is equivalent to an 8-space with a discrete internal subspace. A number and a character of ties determine now an internal symmetry group, while in the supersymmetrical models this one is…

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a…

Assume that $G$ is a virtually torsion-free solvable group of finite rank and $A$ a $\mathbb ZG$-module whose underlying abelian group is torsion-free and has finite rank. We stipulate a condition on $A$ that ensures that $H^n(G,A)$ and…

We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^{4}$ with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with…

We consider nonholonomic systems which symmetry groups consist of two subgroups one of which represents rotations about the axis of symmetry. After nonholonomic reduction by another subgroup the corresponding vector fields on partially…

The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific $SU(4)$ vector bundle leading to the "heterotic standard model" in the…

It is shown that an alternative supersymmetric version of the Liouville equation extracted from D=3 Green-Schwarz superstring equations naturally arises as a super-Toda model obtained from a properly constrained supersymmetric WZNW theory…

We compute the equivariant $K$-homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological $K$-theory of the reduced $C^\ast$-algebra associated to the…

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is…

For semisimple Lie superalgebras over an algebraically closed field of characteristic zero, whose category of finite dimensional super representations is semisismple, we classify all irreducible super representations for which the…

Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are…

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable…

Given a quasi-split reductive group $G$ and a symmetric variety $X$, we introduce a notion of endoscopic varieties for $(G,X)$, and establish the foundational properties of these varieties such as matching of stable semi-simple orbits. To…