Grand Unified Theories often involve additional Abelian group factors apart from the standard model hypercharge, that generally lead to loop-induced mixing gauge kinetic terms. In this letter, we show that at the one-loop level this effect can be avoided in many cases by a suitable choice of basis in group space and present a general scheme for the construction of this basis. In supersymmetric ...

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients ...

Twist knots form a family of special two–bridge knots which include the trefoil knot and the figure eight knot. The knot group of a two–bridge knot has a particularly nice presentation with only two generators and a single relation. One could find our interest in this family of knots in the following facts: first, twist knots except the trefoil knot are hyperbolic; and second, twist knots are n...

The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H̃. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. The action of the magne...

Domain walls between different topological phases are one of the most interesting phenomena that reveal non-trivial bulk properties phases. Very recently, gapped domain have been intensively studied. In this paper, we systematically construct a large class lattice models for gapless twisted and untwisted gauge theories with arbitrary finite group $G$. As simple examples, numerically study sever...

Let $$G$$ be a non-abelian finite simple group. A famous result of Liebeck and Shalev is that there an absolute constant $$c$$ such whenever $$S$$ non-trivial normal subset in then $$S^{k} = G$$ for any integer $$k$$ at least $$c \cdot (\log|G|/\log|S|)$$ . This generalized by showing exists $$S_{1}$$ , $$\ldots $$ $$S_{k}$$ are subsets with $$\prod_{i=1}^{k} |S_{i}| \geq {|G|}^{c}$$ $$S_{1} \c...