Related papers: Cooking pasta with Lie groups

We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…

We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary…

We revisit a recent solution to the flavor hierarchy problem based on the paradigm that Yukawa couplings are, rather than fundamental constants, effective low energy couplings radiatively generated by interactions in a hidden sector of the…

We explore various aspects of 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space $B^2G$ of the symmetry group $G$, and they are classified by…

Classical mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter or EKF, respectively), rely on…

In the search for vacuum solutions, with or without a cosmological constant, of the Einstein field equations of Petrov type N with twisting principal null directions, the CR structures to describe the parameter space for a congruence of…

We present a metric condition ${\LARGE{\tau}}'$ which describes the geometry of classical small cancellation groups and applies also to other known classes of groups such as two-dimensional Artin groups. We prove that presentations…

We study a generalization of the loosely bound Skyrme model which consists of the Skyrme model with a sixth-order derivative term - motivated by its fluid-like properties - and the second-order loosely bound potential - motivated by…

We report analytically known states at non-zero temperature which may serve as a powerful tool to reveal common topological and thermodynamic properties of systems ranging from the QCD phase diagram to topological phase transitions in…

We study the effective field theory of a weakly coupled 3+1d gauged $\phi^4$ type model at high temperature. Our model has $4N$ real scalars ($N$ complex Higgs doublets) and a gauge group $SU(2)$ which is spontaneously broken by a nonzero…

Let $\gg$ be the Lie algebra of a compact Lie group and let $\theta$ be any automorphism of $\gg$. Let $\gk$ denote the fixed point subalgebra $\gg^\theta$. In this paper we present LiE programs that, for any finite dimensional complex…

A generalized set of asymptotic conditions for higher spin gravity without cosmological constant in three spacetime dimensions is constructed. They include the most general temporal components of the gauge fields that manifestly preserve…

Let $G$ be a connected complex semisimple Lie group, $\Gamma$ be a cocompact, irreducible and torsionless lattice in $G$ and $K$ be a maximal compact subgroup of $G$. Assume $\Gamma$ acts by left multiplication and $K$ acts by right…

We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an $SU(4)\times Sp(6)_L \times Sp(6)_R$ anomaly-free gauge model. All the SM fermions are packaged into two…

Let $\Gamma$ be a discrete subgroup of a simply connected, solvable Lie group~$G$, such that $\Ad_G\Gamma$ has the same Zariski closure as $\Ad G$. If $\alpha \colon \Gamma \to \GL_n(\real)$ is any finite-dimensional representation…

We present an explicit construction of the basic bundle gerbes with connection over all connected compact simple Lie groups. These are geometric objects that appear naturally in the Lagrangian approach to the WZW conformal field theories.…

We study a recently proposed modification of the Skyrme model that possesses an exact self-dual sector leading to an infinity of exact Skyrmion solutions with arbitrary topological (baryon) charge. The self-dual sector is made possible by…

In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…

We study gauge symmetry in F-theory in light of global aspects. For this, we consider not only a simple (local) group, but also a semi-simple group with Abelian factors. Once we specify the complete gauge group by decomposing the…

The success of SU(5)-like gauge coupling unification boundary conditions $g_3^2=g_2^2=5/3 g_1^2$ has biased most attempts to embed the SM interactions into a unified structure. After discussing the limitations of the orthodox approach, we…