160,607 research outputs found
Learning non-Higgsable gauge groups in 4D F-theory
We apply machine learning techniques to solve a specific classification
problem in 4D F-theory. For a divisor on a given complex threefold base, we
want to read out the non-Higgsable gauge group on it using local geometric
information near . The input features are the triple intersection numbers
among divisors near and the output label is the non-Higgsable gauge group.
We use decision tree to solve this problem and achieved 85%-98% out-of-sample
accuracies for different classes of divisors, where the data sets are generated
from toric threefold bases without (4,6) curves. We have explicitly generated a
large number of analytic rules directly from the decision tree and proved a
small number of them. As a crosscheck, we applied these decision trees on bases
with (4,6) curves as well and achieved high accuracies. Additionally, we have
trained a decision tree to distinguish toric (4,6) curves as well. Finally, we
present an application of these analytic rules to construct local base
configurations with interesting gauge groups such as SU(3).Comment: 50 pages, 18 figures, 20 table
Atomic Classification of 6D SCFTs
We use F-theory to classify possibly all six-dimensional superconformal field
theories (SCFTs). This involves a two step process: We first classify all
possible tensor branches allowed in F-theory (which correspond to allowed
collections of contractible spheres) and then classify all possible
configurations of seven-branes wrapped over them. We describe the first step in
terms of "atoms" joined into "radicals" and "molecules," using an analogy from
chemistry. The second step has an interpretation via quiver-type gauge theories
constrained by anomaly cancellation. A very surprising outcome of our analysis
is that all of these tensor branches have the structure of a linear chain of
intersecting spheres with a small amount of possible decoration at the two
ends. The resulting structure of these SCFTs takes the form of a generalized
quiver consisting of ADE-type nodes joined by conformal matter. A collection of
highly non-trivial examples involving E8 small instantons probing an ADE
singularity is shown to have an F-theory realization. This yields a
classification of homomorphisms from ADE subgroups of SU(2) into E8 in purely
geometric terms, largely matching results obtained in the mathematics
literature from an intricate group theory analysis.Comment: v3: 123 pages, 23 figures, typos corrected. Included with the
submission are the Mathematica notebooks "Bases.nb" and
"Fiber_Enhancements.nb
Loop operators and S-duality from curves on Riemann surfaces
We study Wilson-'t Hooft loop operators in a class of N=2 superconformal
field theories recently introduced by Gaiotto. In the case that the gauge group
is a product of SU(2) groups, we classify all possible loop operators in terms
of their electric and magnetic charges subject to the Dirac quantization
condition. We then show that this precisely matches Dehn's classification of
homotopy classes of non-self-intersecting curves on an associated Riemann
surface--the same surface which characterizes the gauge theory. Our analysis
provides an explicit prediction for the action of S-duality on loop operators
in these theories which we check against the known duality transformation in
several examples.Comment: 41 page
Calabi-Yau threefolds with large h^{2, 1}
We carry out a systematic analysis of Calabi-Yau threefolds that are
elliptically fibered with section ("EFS") and have a large Hodge number h^{2,
1}. EFS Calabi-Yau threefolds live in a single connected space, with regions of
moduli space associated with different topologies connected through transitions
that can be understood in terms of singular Weierstrass models. We determine
the complete set of such threefolds that have h^{2, 1} >= 350 by tuning
coefficients in Weierstrass models over Hirzebruch surfaces. The resulting set
of Hodge numbers includes those of all known Calabi-Yau threefolds with h^{2,
1} >= 350, as well as three apparently new Calabi-Yau threefolds. We speculate
that there are no other Calabi-Yau threefolds (elliptically fibered or not)
with Hodge numbers that exceed this bound. We summarize the theoretical and
practical obstacles to a complete enumeration of all possible EFS Calabi-Yau
threefolds and fourfolds, including those with small Hodge numbers, using this
approach.Comment: 44 pages, 5 tables, 5 figures; v2: minor corrections; v3: minor
corrections, moved figure; v4: typo in Table 2 correcte
On the Defect Group of a 6D SCFT
We use the F-theory realization of 6D superconformal field theories (SCFTs)
to study the corresponding spectrum of stringlike, i.e. surface defects. On the
tensor branch, all of the stringlike excitations pick up a finite tension, and
there is a corresponding lattice of string charges, as well as a dual lattice
of charges for the surface defects. The defect group is data intrinsic to the
SCFT and measures the surface defect charges which are not screened by
dynamical strings. When non-trivial, it indicates that the associated theory
has a partition vector rather than a partition function. We compute the defect
group for all known 6D SCFTs, and find that it is just the abelianization of
the discrete subgroup of U(2) which appears in the classification of 6D SCFTs
realized in F-theory. We also explain how the defect group specifies defining
data in the compactification of a (1,0) SCFT.Comment: 24 page
Towards Classification of 5d SCFTs: Single Gauge Node
We propose a number of apparently equivalent criteria necessary for the
consistency of a 5d SCFT in its Coulomb phase and use these criteria to
classify 5d SCFTs arising from a gauge theory with simple gauge group. These
criteria include the convergence of the 5-sphere partition function; the
positivity of particle masses and monopole string tensions; and the positive
definiteness of the metric in some region in the Coulomb branch. We find that
for large rank classical groups simple classes of SCFTs emerge where the bounds
on the matter content and the Chern-Simons level grow linearly with rank. For
classical groups of rank less than or equal to 8, our classification leads to
additional cases which do not fit in the large rank analysis. We also classify
the allowed matter content for all exceptional groups.Comment: 52 pages + appendix, 11 tables, 12 figure
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