Geometric constraints in dual F-theory and heterotic string compactifications

We systematically analyze a broad class of dual heterotic and F-theory models that give four-dimensional supergravity theories, and compare the geometric constraints on the two sides of the duality. Specifically, we give a complete classification of models where the heterotic theory is compactified on a smooth Calabi-Yau threefold that is elliptically fibered with a single section and carries smooth irreducible vector bundles, and the dual F-theory model has a corresponding threefold base that has the form of a P^1 bundle. We formulate simple conditions for the geometry on the F-theory side to support an elliptically fibered Calabi-Yau fourfold. We match these conditions with conditions for the existence of stable vector bundles on the heterotic side, and show that F-theory gives new insight into the conditions under which such bundles can be constructed. In particular, we find that many allowed F-theory models correspond to vector bundles on the heterotic side with exceptional structure groups, and determine a topological condition that is only satisfied for bundles of this type. We show that in many cases the F-theory geometry imposes a constraint on the extent to which the gauge group can be enhanced, corresponding to limits on the way in which the heterotic bundle can decompose. We explicitly construct all (4962) F-theory threefold bases for dual F-theory/heterotic constructions in the subset of models where the common twofold base surface is toric, and give both toric and non-toric examples of the general results.Comment: 81 pages, 2 figures; v2, v3: references added, minor corrections; v4: minor errors, Table 5 correcte

M-Theory on the Orbifold C^2/Z_N

We construct M-theory on the orbifold C^2/Z_N by coupling 11-dimensional supergravity to a seven-dimensional Yang-Mills theory located on the orbifold fixed plane. It is shown that the resulting action is supersymmetric to leading non-trivial order in the 11-dimensional Newton constant. This action provides the starting point for a reduction of M-theory on G_2 spaces with co-dimension four singularities.Comment: 33 pages, Late

T-Branes and Geometry

T-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of this open string data for six-dimensional F-theory vacua. We show that in the dual M-theory / IIA compactification on a smooth Calabi-Yau threefold X, the geometric remnant of T-brane data translates to periods of the three-form potential valued in the intermediate Jacobian of X. Starting from a smoothing of a singular Calabi-Yau, we show how to track this data in singular limits using the theory of limiting mixed Hodge structures, which in turn directly points to an emergent Hitchin-like system coupled to defects. We argue that the physical data of an F-theory compactification on a singular threefold involves specifying both a geometry as well as the remnant of three-form potential moduli and flux which is localized on the discriminant. We give examples of T-branes in compact F-theory models with heterotic duals, and comment on the extension of our results to four-dimensional vacua.Comment: v2: 80 pages, 2 figures, clarifications and references added, typos correcte

Monad Bundles in Heterotic String Compactifications

In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 x E8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly condition, is finite and consists of about 7000 models. We explain how to compute the complete particle spectrum for these models. In particular, we prove the absence of vector-like family anti-family pairs in all cases. We also verify a set of highly non-trivial necessary conditions for the stability of the bundles. A full stability proof will appear in a companion paper. A scan over all models shows that even a few rudimentary physical constraints reduces the number of viable models drastically.Comment: 35 pages, 4 figure

Pattern Avoidance in Reverse Double Lists

In this paper, we consider pattern avoidance in a subset of words on $\{1,1,2,2,\dots,n,n\}$ called reverse double lists. In particular a reverse double list is a word formed by concatenating a permutation with its reversal. We enumerate reverse double lists avoiding any permutation pattern of length at most 4 and completely determine the corresponding Wilf classes. For permutation patterns $\rho$ of length 5 or more, we characterize when the number of $\rho$-avoiding reverse double lists on $n$ letters has polynomial growth. We also determine the number of $1\cdots k$-avoiders of maximum length for any positive integer $k$.Comment: 24 pages, 5 figures, 4 table

Out of the Class and into the Gallery: Teaching Spanish through Fine Arts

Der Beitraguntersucht die Rolle vonKunstgalerien im Spanischprogramm der University of Melbourne, Australien, und zeigt, wie sich durch Kunstwerke bestimmte Unterrichtsformen fürden fach-und sprachenintegrierende Unterricht eröffnenund gleichzeitigdie Motivation der Lernendenerhöhen. Die Integration von Kultur und Sprache stellt für Anfänger eine besondere Herausforderung dar, doch die bildende Kunst hat sich dann als besonders fruchtbar erwiesen, wenn Kunst ohne Sprache auskommt. Bildende Kunst im Sprachunterricht wurde bereits im Hinblick auf die Motivation der Lernendendiskutiert (Bevilacqua Martello 2017). In diesem Beitrag gehtes um die Motivation der Lernendenin Bezug auf unsere fortgeschrittenen Studierenden, die mit den Mitarbeiternder National Gallery of Victoria (NGV's) zusammenarbeiten, um ein auf Anfänger zugeschnittenes Programm zu entwickeln, das während des Galeriebesuchs als Lehrende oder Führerfür die Studierende fungieren kann. This paper explores the role of art galleries in the Spanish program at the University of Melbourne, Australia, illustrating how teaching language via artworks opens up particular modes of teaching that integrate language and content while increasing student motivation. The integration of culture and language is particularly challenging in the case of beginning level students, yet visual art has provided particularly fruitful, given that art bypasses linguistics. Visual arts in language instruction has already been discussed in terms of student motivation (Bevilacqua Martello2017). I discuss student motivation in relation to our advanced level students who work with the National Gallery of Victoria’s (NGV’s) education team to design a program tailored to beginners students, acting as teachers or guides for the students during thegallery visit

Matter in transition

We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, where a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the three-index antisymmetric representation of SU(N) require Weierstrass models that cannot be realized from the standard SU(N) Tate form. We also briefly describe some other situations, with groups such as Sp(3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.Comment: 107 pages, 3 figures, 32 tables. In version 2, one figure and comments added on the geometry of matter transition