Related papers: Cooking pasta with Lie groups
We define gauge theories whose gauge group includes charge conjugation as well as standard $\mathrm{SU}(N)$ transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For $N$ even,…
Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent…
The minimal supersymmetric standard model (MSSM), is perhaps the leading candidate for new physics beyond the standard model, but it encounters difficulties with string gauge unification and in addition does not shed any light on the…
Extended Higgs sectors are often introduced to explain phenomena beyond the standard model (BSM). The existence of multiple scalar fields may cause the Landau pole below the Planck scale. In this case, the low-energy theory may be replaced…
A set of coupled non-linear integral equations is derived for a class of models connected with the quantum group $U_q(\hat g)$ ($g$ simply laced Lie algebra), which are solvable using the Bethe Ansatz; these equations describe arbitrary…
We study a generalization of the Skyrme model with the inclusion of a sixth-order term and a generalized mass term. We first analyze the model in a regime where the nonlinear sigma and Skyrme terms are switched to zero which leads to…
We construct exact, regular and topologically non-trivial\ configurations of the coupled Einstein-nonlinear sigma model in (3+1) dimensions. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and circumvents Derrick's theorem…
We construct a graded Lie algebra in which a solution to the vacuum Einstein equations is any element of degree 1 whose bracket with itself is zero. Each solution generates a cochain complex, whose first cohomology is linearized gravity…
In their celebrated paper of 1976, Rothschild and Stein prove a lifting procedure that locally reduces to a free nilpotent Lie algebra any family of smooth vector fields $X_1,\dots,X_q$, over a manifold $M$. Then, a large class of…
A noncommutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: 1) although we can have noncommutative U(n) (which we denote by $U_{\star}(n)$) gauge theory we cannot have…
We show that any solution of the SU(2) Skyrme model can be used to give a topologically trivial solution of the SU(4) one. In addition, we extend the method introduced by Houghton et al. and use harmonic maps from S2 to CP(N-1) to construct…
In this article we study properties of isospin asymmetric nuclear matter in the generalized Skyrme model. This is achieved by canonically quantizing the isospin collective degrees of freedom of the recently found multi-wall skyrmion…
By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of $N$ copies of a Lie group over some diagonal subgroup and they depend on…
Within the context of the E_8 x E_8 heterotic superstring compactified on a smooth Calabi-Yau threefold with an SU(4) gauge instanton, we show the existence of simple, realistic N=1 supersymmetric vacua that are compatible with low energy…
We calculate, at the classical level, the superpotential tri-linear couplings of the only known globally consistent heterotic minimal supersymmetric Standard Model [ hep-th/0512149 ]. This recently constructed model is based on a…
We introduce an unrolled quantization $U_q^E(\mathfrak{gl}(1 \vert 1))$ of the complex Lie superalgebra $\mathfrak{gl}(1 \vert 1)$ and use its categories of weight modules to construct and study new three dimensional non-semisimple…
We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with $N$-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in…
A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an…
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\omega_4$ of $G$'s cohomology group…
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…