Related papers: Cooking pasta with Lie groups

The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to "sausage" shape by a deformation parameter \nu. This…

We study asymptotically non-free gauge theories and search for renormalization group invariant (i.e. technically natural) relations among the couplings which lead to successful gauge-Yukawa unification. To be definite, we consider a…

In this paper we classify in terms of Lie point symmetries the three-dimensional nonrelativistic motion of charged particles in arbitrary time-independent electromagnetic fields. The classification is made on the ground of equivalence…

For a simply connected (non-nilpotent) solvable Lie group $G$ with a lattice $\Gamma$ the de Rham and Dolbeault cohomologies of the solvmanifold $G/\Gamma$ are not in general isomorphic to the cohomologies of the Lie algebra $\mathfrak g$…

We developed a unified framework based on a special (non-regular) embedding of the exceptional group $E_6$ in which the main stage of symmetry breaking chain realizes $E_6\to G(2) \times SU(3)_A$. The exceptional factor $G(2)$ plays the…

Let $G$ be a simply connected Lie group with Lie algebra $\mathfrak{g}$ and denote by $\mathrm{C}_{\bullet}(G)$ the DG Hopf algebra of smooth singular chains on $G$. In a companion paper it was shown that the category of sufficiently smooth…

We construct an effective theory for the SM with extra dimensions. We start from a theory governed by the extra-dimensional groups ISO$(1,3+n)$ and $G_{\rm SM}({\cal M}^{4+n})=SU_C(3,{\cal M}^{4+n})\times SU_L(2,{\cal M}^{4+n})\times…

Let $F \hookrightarrow X \to B$ be a fibre bundle with structure group $G$, where $B$ is $(d{-}1)$-connected and of finite dimension, $d \geq 1$. We prove that the strong L-S category of $X$ is less than or equal to $m + \frac{\dim B}{d}$,…

We make a comprehensive study of the theory and phenomenology of a low energy supersymmetric standard model originating from a string-inspired $E_6$ grand unified gauge group. The Exceptional Supersymmetric Standard Model (ESSM) considered…

In this paper, we obtain an infinite dimensional Lie algebra of exotic gauge invariant observables that is closed under Goldman-type bracket associated with monodromy matrices of flat connections on a compact Riemann surface for $G_{2}$…

All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using…

The extension of the noncommutative u*(N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u*(N) can consistently be restricted to o*(N)…

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target space is a flag manifold of simple G, and…

We point out that type I string theory in the presence of internal magnetic fields provides a concrete realization of split supersymmetry. To lowest order, gauginos are massless while squarks and sleptons are superheavy. We build such…

Gauge theories with the orthogonal Cayley-Klein gauge groups $SO(2;j)$ and $SO(3;{\bf j})$ are regarded. For nilpotent values of the contraction parameters ${\bf j}$ these groups are isomorphic to the non-semisimple Euclid, Newton, Galilei…

We revisit the study of singular points in N=2 SQCD with classical gauge groups. Using a technique proposed recently by Gaiotto, Seiberg and Tachikawa we find that the low-energy physics at the maximally singular point involves two…

We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E_{10}-approach to M-theory. We focus on the solutions with non zero electric field determined by geometric configurations (n_m,…