Related papers: Quantum symmetries for exceptional SU(4) modular i…
This is a set of notes describing several aspects of the space of paths on ADE Dynkin diagrams, with a particular attention paid to the graph E6. Many results originally due to A. Ocneanu are here described in a very elementary way…
Starting with the partition functions for quantum group invariant systems we calculate the metric in the two-dimensional space defined by the parameters $\beta$ and $\gamma=-\beta\mu$ and the corresponding scalar curvature for these systems…
We study implications of exact conformal invariance of scalar quantum field theories at the critical point in non-integer dimensions for the evolution kernels of the light-ray operators in physical (integer) dimensions. We demonstrate that…
Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group $SU(3)$ and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to…
We present the maximally supersymmetric three-dimensional gauged supergravities. Owing to the special properties of three dimensions -- especially the on-shell duality between vector and scalar fields, and the purely topological character…
We introduce two spectral invariants of finite metric spaces, the $q$-spectrum and the transition $q$-spectrum, defined from similarity matrices. These invariants extend the adjacency and Laplacian spectra of graphs to general finite metric…
Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the…
Maximal supergravities in ten and eleven dimensions admit consistent truncations on particular spheres to maximal supergravities in lower dimensions. Concurrently, the truncation to singlets under any subgroup of the sphere isometry group…
We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of non-conformal (Einstein) gravity. As an `existence proof' that this is indeed possible we show how to derive N=4 super Yang…
We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincar\'e series of the minimal set of generators of the graded algebra of regular functions, provided that the link of the…
We argue that $\mathcal N=8$ supergravity in four dimensions exhibits an exceptional $E_{8(8)}$ symmetry, enhanced from the known $E_{7(7)}$ invariance. Our procedure to demonstrate this involves dimensional reduction of the $\mathcal N=8$…
The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain $N=2$ supergravity theories, where dimensional reduction induces a mapping between {\em special} real, K\"ahler…
F(4) supergravity, the gauge theory of the exceptional six-dimensional Anti-de Sitter superalgebra, is coupled to an arbitrary number of vector multiplets whose scalar components parametrize the quaternionic manifold SO(4,n)/SO(4)\times…
We study the quantum moduli spaces and dynamical superpotentials of four dimensional $SU(2)^r$ linear and ring moose theories with $\mathcal{N}=1$ supersymmetry and link chiral superfields in the fundamental representation. Nontrivial…
Using geometric engineering method of 4D $\mathcal{N}=2$ quiver gauge theories and results on the classification of Kac-Moody (KM) algebras, we show on explicit examples that there exist three sectors of $\mathcal{N}=2$ infrared CFT$_{4}$s.…
We formulate the locally supersymmetric E$_{7(7)}$ exceptional field theory in a $(4+56|32)$ dimensional superspace, corresponding to a 4D $N\!=\!8$ "external" superspace augmented with an "internal" 56-dimensional space. This entails the…
The category of finite dimensional module over the quantum superalgebra U_q(sl(2|1)) is not semi-simple and the quantum dimension of a generic U_q(sl(2|1))-module vanishes. This vanishing happens for any value of q (even when q is not a…
This paper works as an appendix of the paper titled Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group and for paper titled Yang-Mills-Connes Theory and Quantum Principal SU(N)-Bundles. Here, we are going to prove…
Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of…
Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely…