2,821 research outputs found
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
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 of length 5 or more, we characterize when the number of
-avoiding reverse double lists on letters has polynomial growth. We
also determine the number of -avoiders of maximum length for any
positive integer .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
- …