Toric Methods in F-theory Model Building

In this review article we discuss recent constructions of global F-theory GUT models and explain how to make use of toric geometry to do calculations within this framework. After introducing the basic properties of global F-theory GUTs we give a self-contained review of toric geometry and introduce all the tools that are necessary to construct and analyze global F-theory models. We will explain how to systematically obtain a large class of compact Calabi-Yau fourfolds which can support F-theory GUTs by using the software package PALP.Comment: 19 pages. Prepared for the special issue "Computational Algebraic Geometry in String and Gauge Theory" of Advances in High Energy Physics, v2: references added, typos correcte

Λ\Lambda-symmetry and background independence of noncommutative gauge theory on Rn\mathbb R^n

Background independence of noncommutative Yang-Mills theory on $\mathbb R^n$ is discussed. The quantity $\theta \hat F \theta - \theta$ is found to be background dependent at subleading order, and it becomes background independent only when the ordinary gauge field strength $F$ is constant. It is shown that, at small values of $B$, the noncommutative Dirac-Born-Infeld action possesses $\Lambda$-symmetry at least to subleading order in $\theta$ if $F$ damps fast enough at infinity.Comment: 16 pages, LaTeX2e, minor revisions (version published in JHEP