1,625 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
Heterotic and M-theory Compactifications for String Phenomenology
In this thesis, we explore two approaches to string phenomenology. In the
first half of the work, we investigate M-theory compactifications on spaces
with co-dimension four, orbifold singularities. We construct M-theory on
C^2/Z_N by coupling 11-dimensional supergravity to a seven-dimensional
Yang-Mills theory located on the orbifold fixed-plane. The resulting action is
supersymmetric to leading non-trivial order in the 11-dim Newton constant. We
thereby reduce M-theory on a G2 orbifold with C^2/Z_N singularities, explicitly
incorporating the additional gauge fields at the singularities. We derive the
Kahler potential, gauge-kinetic function and superpotential for the resulting
N=1 four-dimensional theory. Blowing-up of the orbifold is described by a Higgs
effect and the results are consistent with the corresponding ones obtained for
smooth G2 spaces. Further, we consider flux and Wilson lines on singular loci
of the G2 space, and discuss the relation to N=4 SYM theory.
In the second half, we develop an algorithmic framework for E8 x E8 heterotic
compactifications with monad bundles. We begin by considering cyclic Calabi-Yau
manifolds where we classify positive monad bundles, prove stability, and
compute the complete particle spectrum for all bundles. Next, we generalize the
construction to bundles on complete intersection Calabi-Yau manifolds. We show
that the class of positive monad bundles, subject to the heterotic anomaly
condition, is finite (~7000 models). We compute the particle spectrum for these
models and develop new techniques for computing the cohomology of line bundles.
There are no anti-generations of particles and the spectrum is manifestly
moduli-dependent. We further study the slope-stability of positive monad
bundles and develop a new method for proving stability of SU(n) vector bundles.Comment: PhD Thesis, 230 pages; University of Oxford (2008
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
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