181 research outputs found
Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
We use the resolution procedure of Esole and Yau arXiv:1107.0733 to study
Yukawa couplings, G-flux, and the emergence of spectral covers from
elliptically fibered Calabi-Yau's with a surface of A_4 singularities. We
provide a global description of the Esole-Yau resolution and use it to
explicitly compute Chern classes of the resolved 4-fold, proving the conjecture
of arXiv:0908.1784 for the Euler character in the process. We comment on the
physical implications of the surprising singular fibers in codimension 2 and 3
in arXiv:1107.0733 and emphasize a group theoretic interpretation based on the
A_4 weight lattice. We then construct explicit G-fluxes by brute force in one
of the 6 birationally equivalent Esole-Yau resolutions, quantize them
explicitly using our result for the second Chern class, and compute the
spectrum and flux-induced 3-brane charges, finding agreement with results and
conjectures of local models in all cases. Finally, we provide a precise
description of the spectral divisor formalism in this setting and sharpen the
procedure described in arXiv:1107.1718 in order to explicitly demonstrate how
the Higgs bundle spectral cover of the local model emerges from the resolved
Calabi-Yau geometry. Along the way, we demonstrate explicitly how the
quantization rules for fluxes in the local and global models are related.Comment: 68 pages (41 pages + 4 appendices
D-Brane Charges in Gepner Models
We construct Gepner models in terms of coset conformal field theories and
compute their twisted equivariant K-theories. These classify the D-brane
charges on the associated geometric backgrounds and therefore agree with the
topological K-theories. We show this agreement for various cases, in particular
the Fermat quintic.Comment: 25 pages, 2 figures. LaTeX. v2: typos and references corrected. v3:
reference adde
Six-dimensional Origin of SYM with Duality Defects
We study the topologically twisted compactification of the 6d
M5-brane theory on an elliptically fibered K\"ahler three-fold preserving two
supercharges. We show that upon reducing on the elliptic fiber, the 4d theory
is Super-Yang Mills, with varying complexified coupling ,
in the presence of defects. For abelian gauge group this agrees with the
so-called duality twisted theory, and we determine a non-abelian generalization
to . When the elliptic fibration is singular, the 4d theory contains 3d
walls (along the branch-cuts of ) and 2d surface defects, around which
the 4d theory undergoes duality transformations. Such
duality defects carry chiral fields, which from the 6d point of view arise as
modes of the two-form in the tensor multiplet. Each duality defect has a
flavor symmetry associated to it, which is encoded in the structure of the
singular elliptic fiber above the defect. Generically 2d surface defects will
intersect in points in 4d, where there is an enhanced flavor symmetry. The 6d
point of view provides a complete characterization of this 4d-3d-2d-0d
`Matroshka'-defect configuration.Comment: 62 pages, 4 figure
The Tate Form on Steroids: Resolution and Higher Codimension Fibers
F-theory on singular elliptically fibered Calabi-Yau four-folds provides a
setting to geometrically study four-dimensional N=1 supersymmetric gauge
theories, including matter and Yukawa couplings. The gauge degrees of freedom
arise from the codimension 1 singular loci, the matter and Yukawa couplings are
generated at enhanced singularities in higher codimension. We construct the
resolution of the singular Tate form for an elliptic Calabi-Yau four-fold with
an ADE type singularity in codimension 1 and study the structure of the fibers
in codimension 2 and 3. We determine the fibers in higher codimension which in
general are of Kodaira type along minimal singular loci, and are thus
consistent with the low energy gauge-theoretic intuition. Furthermore, we
provide a complementary description of the fibers in higher codimension, which
will also be applicable to non-minimal singularities. The irreducible
components in the fiber in codimension 2 correspond to weights of
representations of the ADE gauge group. These can split further in codimension
3 in a way that is consistent with the generation of Yukawa couplings. Applying
this reasoning, we then venture out to study non-minimal singularities, which
occur for A type along codimension 3, and for D and E also in codimension 2.
The fibers in this case are non-Kodaira, however some insight into these
singularities can be gained by considering the splitting of fiber components
along higher codimension, which are shown to be consistent with matter and
Yukawa couplings for the corresponding gauge groups.Comment: 75 pages, v2: clarifications and references added, JHEP versio
F-theory and 2d (0,2) Theories
F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds
gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry.
In this paper we initiate the study of such compactifications and determine the
dictionary between the geometric data of the elliptic fibration and the 2d
gauge theory such as the matter content in terms of (0,2) superfields and their
supersymmetric couplings. We study this setup both from a gauge-theoretic point
of view, in terms of the partially twisted 7-brane theory, and provide a global
geometric description based on the structure of the elliptic fibration and its
singularities. Global consistency conditions are determined and checked against
the dual M-theory compactification to one dimension. This includes a discussion
of gauge anomalies, the structure of the Green-Schwarz terms and the
Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics.
Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic
worldsheet theories, we propose a correspondence between the geometric data of
elliptically fibered Calabi-Yau five-folds and the target space of a heterotic
gauged linear sigma-model (GLSM). In particular the correspondence between the
Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via
different T-branes or gluing data in F-theory.Comment: 124 pages, 5 figures, v2: ref added, v3: typos corrected, discussion
of interactions extended, v4: updated section 12, v5: typos corrected and
refs adde
Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories
M-theory on compact eight-manifolds with -holonomy is a
framework for geometric engineering of 3d gauge theories
coupled to gravity. We propose a new construction of such
-manifolds, based on a generalized connected sum, where the
building blocks are a Calabi-Yau four-fold and a -holonomy manifold times
a circle, respectively, which both asymptote to a Calabi-Yau three-fold times a
cylinder. The generalized connected sum construction is first exemplified for
Joyce orbifolds, and is then used to construct examples of new compact
manifolds with -holonomy. In instances when there is a
K3-fibration of the -manifold, we test the spectra using
duality to heterotic on a -fibered -holonomy manifold, which are
shown to be precisely the recently discovered twisted-connected sum
constructions.Comment: 49 pages, 4 figures; v2: added reference
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