Related papers: Modular Groups for Twisted Narain Models
We give a complete list of orbifolds uniformised by discrete non-elementary two-generator subgroups of PSL(2,C) without invariant plane whose generators and their commutator have real traces.
A simple method for breaking gauge groups by orbifolding is presented. We extend the method of Kac and Peterson to include Wilson lines. The complete classification of the gauge group breaking, e.g. from heterotic string, is now possible.…
We investigate deformations of $\mathbb{Z}_2$ orbifold singularities on the toroidal orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_6)$ with discrete torsion in the framework of Type IIA orientifold model building with intersecting D6-branes…
We derive D-brane gauge theories for C^3/Z_n x Z_n orbifolds with discrete torsion and study the moduli space of a D-brane at a point. We show that, as suggested in previous work, closed string moduli do not fully resolve the singularity,…
We present a supersymmetric SU(5) GUT model with a discrete non-Abelian flavor symmetry that is broken by Wilson lines. The model is formulated in 4+3 dimensions compactified on a manifold S^3/Z_n. Symmetry breaking by Wilson lines is…
We here present, in modern notation, the classification of the discrete finite subgroups of SU(4) as well as the character tables for the exceptional cases thereof (Cf. https://github.com/yanghuihe/SU4Subgroups). We hope this catalogue will…
This paper aims to derive new anomaly cancellation formulas by combining modular forms with E8 and E8*E8 bundles. To this end, we systematically twist and generalize known SL(2,Z) modular forms to define new modular forms associated with…
We consider a class of four parameter D=4, N=2 string models, namely heterotic strings compactified on K3 times T2 together with their dual type II partners on Calabi-Yau three-folds. With the help of generalized modular forms (such as…
In a previous paper we outlined how discrete torsion can be understood geometrically as an analogue of orbifold U(1) Wilson lines. In this paper we shall prove the remaining details. More precisely, in this paper we describe gerbes in terms…
We review the stabilisation of complex structure moduli in Type IIA orientifolds, especially on $T^6 / (\mathbb{Z}_2 \times \mathbb{Z}_6^\prime \times \Omega \mathcal{R})$ with discrete torsion, via deformations of $\mathbb{Z}_2 \times…
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures…
We study the modular symmetry in magnetized $T^{2g}$ torus and orbifold models. The $T^{2g}$ torus has the modular symmetry $\Gamma_{g}=Sp(2g,\mathbb{Z})$. Magnetic flux background breaks the modular symmetry to a certain normalizer…
If $X\subset\operatorname{Gr}(2,6)$ is the Fano variety of lines of a smooth cubic fourfold, then we show that the restriction to $X$ of any Schur functor of the tautological quotient bundle is modular and slope polystable. Moreover it is…
We study non-Abelian flavor symmetries on orbifolds, $S^1/Z_2$ and $T^2/Z_3$. Our extra dimensional models realize $D_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$ and $\Delta(6N^2)$ including $A_4$ and $S_4$. In addition, one can also realize their…
We study of fermion zero-modes on magnetized $T^6/\mathbb{Z}_N$ orbifolds. In particular, we focus on non-factorizable orbifolds, i.e. $T^6/\mathbb{Z}_7$ and $T^6/\mathbb{Z}_{12}$ corresponding to $SU(7)$ and $E_6$ Lie lattices…
We study D3 branes at orbifolded conifold singularities in the presence of discrete torsion. The vacuum moduli space of open strings becomes non-commutative due to a deformation of the superpotential and is studied via the representation…
We study heterotic asymmetric orbifold models. By utilizing the lattice engineering technique, we classify (22,6)-dimensional Narain lattices with right-moving non-Abelian group factors which can be starting points for Z3 asymmetric…
In this article, we derive explicit combinatorial formulas, depending only on $q$, for the Wedderburn decomposition of the rational group algebras of the finite linear groups $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$.…
We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten…
Recently, an attractive model of GUT breaking has been proposed in which a 5 dimensional supersymmetric SU(5) gauge theory on an S^1/(Z_2\times Z_2') orbifold is broken down to the 4d MSSM by SU(5)-violating boundary conditions. Motivated…