109 research outputs found
Non-Geometric Vacua of the Heterotic String and Little String Theories
We study a class of 6d non-geometric vacua of the
heterotic string which can be understood as
fibrations of genus-two curves over a complex one-dimensional base. The 6d
theories living on the defects that arise when the
genus-two fiber degenerates at a point of the base are analyzed by dualizing to
F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. We consider
all possible degenerations of genus-two curves and systematically attempt to
resolve the singularities of the dual threefolds. As in the analogous
non-geometric vacua of the heterotic string, we find that many
of the resulting dual threefolds contain singularities which do not admit a
crepant resolution. When the singularities can be resolved crepantly, we
determine the emerging effective theories which turn out to be little string
theories at a generic point on their tensor branch. We also observe a form of
duality in which theories living on distinct defects are the same.Comment: 39 pages, 3 figures, and 6 table
Algebraic Cycles and Local Anomalies in F-Theory
We introduce a set of identities in the cohomology ring of elliptic
fibrations which are equivalent to the cancellation of gauge and mixed
gauge-gravitational anomalies in F-theory compactifications to four and six
dimensions. The identities consist in (co)homological relations between complex
codimension-two cycles. The same set of relations, once evaluated on elliptic
Calabi-Yau three-folds and four-folds, is shown to universally govern the
structure of anomalies and their Green-Schwarz cancellation in six- and
four-dimensional F-theory vacua, respectively. We furthermore conjecture that
these relations hold not only within the cohomology ring, but even at the level
of the Chow ring, i.e. as relations among codimension-two cycles modulo
rational equivalence. We verify this conjecture in non-trivial examples with
Abelian and non-Abelian gauge groups factors. Apart from governing the
structure of local anomalies, the identities in the Chow ring relate different
types of gauge backgrounds on elliptically fibred Calabi-Yau four-folds.Comment: 45 page
Hypercharge Flux in IIB and F-theory: Anomalies and Gauge Coupling Unification
We analyse hypercharge flux GUT breaking in F-theory/Type IIB GUT models with
regards to its implications for anomaly cancellation and gauge coupling
unification. To this aim we exploit the Type IIB limit and consider 7-brane
configurations that for the first time are guaranteed to exhibit net
hypercharge flux restriction to matter curves. We show that local F-theory
models with anomalies of type U(1)_Y-U(1)^2 in the massless spectrum can be
consistent only if such additional U(1)s are globally geometrically massive (in
the sense that they arise from non-Kahler deformations of the Calabi-Yau
four-fold). Further, in such cases of geometrically massive U(1)s hypercharge
flux can induce new anomalies of type U(1)_Y^2-U(1) in the massless spectrum,
violating constraints in local models forbidding such anomalies. In particular
this implies that it is possible to construct models exhibiting a U(1)_{PQ}
global symmetry which have hypercharge flux doublet-triplet splitting and no
further exotics. We also show that the known hypercharge flux induced splitting
of the gauge couplings in IIB models at tree-level can be reduced by a factor
of 5 by employing a more F-theoretic twisting of U(1) flux by hypercharge flux
bringing it to well within MSSM 2-loop results. In the case of net restriction
of hypercharge flux to matter curves this tree-level splitting becomes more
involved, is tied to the vacuum expectation values of certain closed-string
fields, and therefore gauge coupling unification becomes tied to the question
of moduli stabilisation.Comment: 27 pages. v2: Expanded discussion on anomalies and showed that
geometrically massive U(1)s of Peccei-Quinn type are compatible with
hypercharge flux doublet-triplet splitting with no exotic
U(1) symmetries in F-theory GUTs with multiple sections
We present a systematic construction of F-theory compactifications with
Abelian gauge symmetries in addition to a non-Abelian gauge group G. The
formalism is generally applicable to models in global Tate form but we focus on
the phenomenologically interesting case of G=SU(5). The Abelian gauge factors
arise due to extra global sections resulting from a specific factorisation of
the Tate polynomial which describes the elliptic fibration. These
constructions, which accommodate up to four different U(1) factors, are worked
out in detail for the two possible embeddings of a single U(1) factor into E8,
usually denoted SU(5) x U(1)_X and SU(5) x U(1)_PQ. The resolved models can be
understood either patchwise via a small resolution or in terms of a
P_{1,1,2}[4] description of the elliptic fibration. We derive the U(1) charges
of the fields from the geometry, construct the U(1) gauge fluxes and exemplify
the structure of the Yukawa interaction points. A particularly interesting
result is that the global SU(5) x U(1)_PQ model exhibits extra SU(5)-singlet
states which are incompatible with a single global decomposition of the 248 of
E8. The states in turn lead to new Yukawa type couplings which have not been
considered in local model building.Comment: 46 pages, 3 figures; v2 typos corrected, citations adde
Gauge Backgrounds and Zero-Mode Counting in F-Theory
Computing the exact spectrum of charged massless matter is a crucial step
towards understanding the effective field theory describing F-theory vacua in
four dimensions. In this work we further develop a coherent framework to
determine the charged massless matter in F-theory compactified on elliptic
fourfolds, and demonstrate its application in a concrete example. The gauge
background is represented, via duality with M-theory, by algebraic cycles
modulo rational equivalence. Intersection theory within the Chow ring allows us
to extract coherent sheaves on the base of the elliptic fibration whose
cohomology groups encode the charged zero-mode spectrum. The dimensions of
these cohomology groups are computed with the help of modern techniques from
algebraic geometry, which we implement in the software gap. We exemplify this
approach in models with an Abelian and non-Abelian gauge group and observe
jumps in the exact massless spectrum as the complex structure moduli are
varied. An extended mathematical appendix gives a self-contained introduction
to the algebro-geometric concepts underlying our framework.Comment: 41 pages + extended appendice
Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications
We study F-Theory compactifications to four dimensions that exhibit discrete
gauge symmetries. Geometrically these arise by deforming elliptic fibrations
with two sections to a genus-one fibration with a bi-section. From a
four-dimensional field-theory perspective they are remnant symmetries from a
Higgsed U(1) gauge symmetry. We implement such symmetries in the presence of an
additional SU(5) symmetry and associated matter fields, giving a geometric
prescription for calculating the induced discrete charge for the matter curves
and showing the absence of Yukawa couplings that are forbidden by this charge.
We present a detailed map between the field theory and the geometry, including
an identification of the Higgs field and the massless states before and after
the Higgsing. Finally we show that the Higgsing of the U(1) induces a G-flux
which precisely accounts for the change in the Calabi-Yau Euler number so as to
leave the D3 tadpole invariant.Comment: 30 pages; v2: substantially improved presentation, refs added; v3:
refs. added, appendix A on remnant discrete subgroups included; v4: refs.
adde
Fluxes in F-theory Compactifications on Genus-One Fibrations
We initiate the construction of gauge fluxes in F-theory compactifications on
genus-one fibrations which only have a multi-section as opposed to a section.
F-theory on such spaces gives rise to discrete gauge symmetries in the
effective action. We generalize the transversality conditions on gauge fluxes
known for elliptic fibrations by taking into account the properties of the
available multi-section. We test these general conditions by constructing all
vertical gauge fluxes in a bisection model with gauge group SU(5) x Z2. The
non-abelian anomalies are shown to vanish. These flux solutions are dynamically
related to fluxes on a fibration with gauge group SU(5) x U(1) by a conifold
transition. Considerations of flux quantization reveal an arithmetic constraint
on certain intersection numbers on the base which must necessarily be satisfied
in a smooth geometry. Combined with the proposed transversality conditions on
the fluxes these conditions are shown to imply cancellation of the discrete Z2
gauge anomalies as required by general consistency considerations.Comment: 30 pages; v2: typos correcte
Exchange effects in spin polarized transport through carbon nanotube quantum dots
We investigate linear and nonlinear transport across single-walled carbon
nanotube quantum dots weakly coupled to spin-polarized leads. We consider tubes
of finite length and small diameter, where not only forward scattering
contributions of the Coulomb potential, but also short-ranged processes play an
important role. In particular, they induce exchange effects leading for
electron fillings 4n+2 either to a non-degenerate groundstate of spin S=0 or to
a triplet groundstate. In the linear regime we present analytical results for
the conductance - for both the S=0 and the triplet groundstate - and
demonstrate that an external magnetic field is crucial to reveal the spin
nature of the groundstates. In the nonlinear regime we show stability diagrams
that clearly distinguish between the different groundstates. We observe a
negative differential conductance (NDC) effect in the S=0 groundstate for
antiparallel lead magnetization. In presence of an external magnetic field spin
blockade effects can be detected, again leading to NDC effects for both
groundstates.Comment: 13 pages, 15 figures, 2 tables; revised published versio
On Discrete Symmetries and Torsion Homology in F-Theory
We study the relation between discrete gauge symmetries in F-theory
compactifications and torsion homology on the associated Calabi-Yau manifold.
Focusing on the simplest example of a symmetry, we show that
there are two physically distinct ways that such a discrete gauge symmetry can
arise. First, compactifications of M-Theory on Calabi-Yau threefolds which
support a genus-one fibration with a bi-section are known to be dual to
six-dimensional F-theory vacua with a gauge symmetry. We show
that the resulting five-dimensional theories do not have a
symmetry but that the latter emerges only in the F-theory decompactification
limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit
discrete torsion. Associated to the bi-section fibration is a Jacobian
fibration which does support a section. Compactifying on these related but
distinct varieties does lead to a symmetry in five dimensions
and, accordingly, we find explicitly an associated discrete torsion. We
identify the expected particle and membrane system of the discrete symmetry in
terms of wrapped M2 and M5 branes and present a field-theory description of the
physics for both cases in terms of circle reductions of six-dimensional
theories. Our results and methods generalise straightforwardly to larger
discrete symmetries and to four-dimensional compactifications.Comment: 12 pages in 2-column style, 4 figures; v2: references adde
- …