Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves

We consider the F-theory description of non-simply-connected gauge groups appearing in the E8 x E8 heterotic string. The analysis is closely tied to the arithmetic of torsion points on an elliptic curve. The general form of the corresponding elliptic fibration is given for all finite subgroups of E8 which are applicable in this context. We also study the closely-related question of point-like instantons on a K3 surface whose holonomy is a finite group. As an example we consider the case of the heterotic string on a K3 surface having the E8 gauge symmetry broken to (E6 x SU(3))/Z3 or SU(9)/Z3 by point-like instantons with Z3 holonomy.Comment: 15 pages, 2 embedded figures, some spurious U(1)'s remove

Three-generation Asymmetric Orbifold Models from Heterotic String Theory

Using Z3 asymmetric orbifolds in heterotic string theory, we construct N=1 SUSY three-generation models with the standard model gauge group SU(3)_C \times SU(2)_L \times U(1)_Y and the left-right symmetric group SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}. One of the models possesses a gauge flavor symmetry for the Z3 twisted matter.Comment: 24 page

Standard Model Compactifications of IIA Z3 x Z3 Orientifolds from Intersecting D6-branes

We discuss the construction of chiral four dimensional ${\bf T^6/(Z_3 \times Z_3)}$ orientifold compactifications of IIA theory, using D6-branes intersecting at angles and not aligned with the orientifold O6 planes. Cancellation of mixed U(1) anomalies requires the presence of a generalized Green-Schwarz mechanism mediated by RR partners of closed string untwisted moduli. In this respect we describe the appearance of three quark and lepton family $SU(3)_C \times SU(2)_L \times U(1)_Y$ non-supersymmetric orientifold models with only the massless spectrum of the SM at low energy that can have either no exotics present and three families of $\nu_R$'s (A$^{\prime}$-model class) or the massless fermion spectrum of the N=1 SM with a small number of massive non-chiral colour exotics and in one case with extra families of $\nu_R$'s (B$^{\prime}$-model class). Moreover we discuss the construction of SU(5), flipped SU(5) and Pati-Salam $SU(4)_c \times SU(2)_L \times SU(2)_R$ GUTS - the latter also derived from adjoint breaking - with only the SM at low energy. Some phenomenological features of these models are also briefly discussed. All models are constructed with the Weinberg angle to be 3/8 at the string scale.Comment: 31 pages, 1 figure; v2: typos corrected, comments in the introduction added v3:35 pages, Pati-Salam G422 models & comments on split susy scenario and refs added; to appear in NP

Phase diagram in the imaginary chemical potential region and extended Z3 symmetry

Phase transitions in the imaginary chemical potential region are studied by the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model that possesses the extended Z3 symmetry. The extended Z3 invariant quantities such as the partition function, the chiral condensate and the modifed Polyakov loop have the Roberge-Weiss (RW) periodicity. There appear four types of phase transitions; deconfinement, chiral, Polykov-loop RW and chiral RW transitions. The orders of the chiral and deconfinement transitions depend on the presence or absence of current quark mass, but those of the Polykov-loop RW and chiral RW transitions do not. The scalar-type eightquark interaction newly added in the model makes the chiral transition line shift to the vicinity of the deconfiment transition line.Comment: 22 pages,17 figure

Chiral symmetry restoration and the Z3 sectors of QCD

Quenched SU(3) lattice gauge theory shows three phase transitions, namely the chiral, the deconfinement and the Z3 phase transition. Knowing whether or not the chiral and the deconfinement phase transition occur at the same temperature for all Z3 sectors could be crucial to understand the underlying microscopic dynamics. We use the existence of a gap in the Dirac spectrum as an order parameter for the restoration of chiral symmetry. We find that the spectral gap opens up at the same critical temperature in all Z3 sectors in contrast to earlier claims in the literature.Comment: 4 pages, 4 figure

Topological Classification of Crystalline Insulators with Point Group Symmetry

We show that in crystalline insulators point group symmetry alone gives rise to a topological classification based on the quantization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the polarization is quantized and can only take three inequivalent values. Therefore, a Z3 topological classification exists. A concrete tight-binding model is derived to demonstrate the Z3 topological phase transition. Using first-principles calculations, we identify graphene on BN substrate as a possible candidate to realize the Z3 topological states. To complete our analysis we extend the classification of band structures to all 17 two-dimensional space groups. This work will contribute to a complete theory of symmetry conserved topological phases and also elucidate topological properties of graphene like systems