On F-theory E_6 GUTs

We approach the Minimum Supersymmetric Standard Model (MSSM) from an E_6 GUT by using the spectral cover construction and non-abelian gauge fluxes in F-theory. We start with an E_6 singularity unfolded from an E_8 singularity and obtain E_6 GUTs by using an SU(3) spectral cover. By turning on SU(2) X U(1)^2 gauge fluxes, we obtain a rank 5 model with the gauge group SU(3) X SU(2) X U(1)^2. Based on the well-studied geometric backgrounds in the literature, we demonstrate several models and discuss their phenomenology.Comment: 42 pages, 17 tables; typos corrected, clarifications added, and references adde

Exact coefficients for higher dimensional operators with sixteen supersymmetries

We consider constraints on higher dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F^n with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F^4. As the F^4 coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficient that are determined exactly. We also consider three-dimensional N=8 as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.Comment: typos corrected, minor modificatio

Teachers' recognition of school bullying according to background variables and type of bullying

How teachers identify and judge school bullying may affect their willingness to intervene in bullying situations and influence their strategies for doing so. This study aimed to investigate whether there were significant differences in teachers' identification of bullying incidents according to background variables (gender, teaching experience, and education level). The participants of this study were 150 primary school and middle school teachers in Taiwan, A 24-item Recognition of Bullying incidents Questionnaire (RBIQ) was used in this study to explore whether teachers can identify physical, verbal, and relational scenarios as bullying or non-bullying incidents. A mixed-model two way ANOVA was used to analyze this data. Results revealed that teachers' teaching experiences significantly interacted with behavioral types, and teachers' education levels also sigm candy interacted with behavioral types. In addition, no gender differences in the identification of bullying were observed. Overall, teachers were more likely to identifi physical bullying incidents than relational ones. The results of this study suggest that teachers should participate in training to help them identify bullying incidents, particularly when these involve relational bullying