We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) × U(1) 2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate's algorithm to elliptic fibrations with two U(1) symmetries, which are realized in terms of a cubic in P 2 . In the process, we find fibers which are not characterized solely in terms of vanishing orders, but with some additional specialization, which plays a key role in the construction of these novel SU(5) models with multiple 10 matter. We also determine a table of Tate-like forms for Kodaira fibers with two U(1)s.
We present a generalization of the six-dimensional (2, 0) system of arXiv:1007.2982 to include a constant abelian 3-form. For vanishing 3-form this system is known to provide a variety descriptions of parallel M5-branes. For a particular choice of 3-form the system is shown to reduce to that of two M2-branes. Thus this generalised (2, 0) system provides a unified description of two parallel M2-branes or M5-branes.
This essay follows the productive discussion of Giorgio Agamben’s The Open: Man and Animal that took place as part of the ‘Openness in Medieval Culture’ conference at the ICI Berlin. The essay attempts to develop a speculative notion of openness within Agamben’s work, in particular by connecting the question of openness to the question of the promise: the promise of the resolution of the question of man and animal (The Open); the promise of the Franciscans’ vow, or sacramentum (The Highest Poverty); and the promise of language (The Sacrament of Language).
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