35 research outputs found
The Toric SO(10) F-Theory Landscape
Supergravity theories in more than four dimensions with grand unified gauge
symmetries are an important intermediate step towards the ultraviolet
completion of the Standard Model in string theory. Using toric geometry, we
classify and analyze six-dimensional F-theory vacua with gauge group SO(10)
taking into account Mordell-Weil U(1) and discrete gauge factors. We determine
the full matter spectrum of these models, including charged and neutral SO(10)
singlets. Based solely on the geometry, we compute all matter multiplicities
and confirm the cancellation of gauge and gravitational anomalies independent
of the base space. Particular emphasis is put on symmetry enhancements at the
loci of matter fields and to the frequent appearance of superconformal points.
They are linked to non-toric K\"ahler deformations which contribute to the
counting of degrees of freedom. We compute the anomaly coefficients for these
theories as well by using a base-independent blow-up procedure and
superconformal matter transitions. Finally, we identify six-dimensional
supergravity models which can yield the Standard Model with high-scale
supersymmetry by further compactification to four dimensions in an Abelian flux
background.Comment: 64 pages, 40 pages appendices, 18 figures, 6 Tables, references
added, published versio
The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
We study global anomalies of discrete gauge symmetries in six-dimensional
supergravities and their realizations in F-theory. We explicitly construct a
discrete Green-Schwarz mechanism that depends on the choice of a coupling
constant and on a certain quadratic refinement in differential cohomology. By
geometrically engineering theories with gauge symmetry and no
tensor multiplets, we observe that a particular choice of the quadratic
refinement is singled out in F-theory. This implies new Swampland constraints
on the discrete charge spectra of 6d supergravities. On the other hand, the
discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We
use anomaly inflow to relate this to a 't Hooft anomaly of the induced global
symmetry in the worldsheet theories of non-critical strings. Using topological
symmetry lines, we further relate this anomaly to the modular properties of
twisted-twined elliptic genera. We then argue that the latter are encoded in
the A-model topological string partition functions on different torus
fibrations that are equipped with a flat torsional B-field. This allows us to
derive a geometric expression for the global discrete anomaly in terms of the
height-pairing of a multi-section on a genus one fibered Calabi-Yau.Comment: 35+16 pages, 21 figure
Gauged 2-form symmetries in 6D SCFTs coupled to gravity
We study six dimensional supergravity theories with superconformal sectors (SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both (2, 0) and (1, 0) theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2-form symmetry embeds into the 2-form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions
6D Heterotic Little String Theories and F-theory Geometry: An Introduction
We review here some aspects of our recent works about the geometric
engineering of heterotic little string theories using F-theory. Building on the
seminal work by Aspinwall and Morrison as well as Intrilligator and Blum, we
solve some longstanding open questions thanks to recent progress in our
understanding of 6D (1,0) theories and their generalized symmetries. On the
geometry side, these systems correspond to non-compact elliptically fibered
Calabi-Yau varieties that must admit the structure of an elliptic K3 fibration.
From fiberwise F-theory/Heterotic duality the K3 plays a central role - it
determines the 6D flavor group, as well as different T-dual LSTs via
inequivalent elliptic fibration structures. The geometries we obtain are some
finer versions of Kulikov degenerations: the point where the K3 fiber
degenerates is the locus where the LST arises. This structure serve on one hand
to check our field theory predictions on LST dualities via the match of Coulomb
branch dimension, flavor symmetries, and 2-group structure constants, and also
on the other hand to deduce novel LST models and their networks of dualities,
thus allowing exploring non-geometric Heterotic regimes.Comment: Contribution to the proceedings of String Math 202