53 research outputs found
Spectral networks and higher web-like structures
We derive traffic rule for spectral networks for A_2 theory for Riemann
surface with punctures and use it to study in details the moduli space M of
flat GL(3,C) connections on P^1 with 3 full punctures. We apply the simplified
traffic rule to find the global description of M as the fibration with
symplectic fibers and to study the space of line defects in 4d theory
corresponding to the conformal point in the base of M. We define higher
web-like structures, not previously discussed in the literature. They give rise
to line defects independent of the defects corresponding to the traces of
holonomies.Comment: 22 pages, 14 figure
Gauge Mediation in F-Theory GUT Models
We study a simple framework for gauge-mediated supersymmetry-breaking in
local GUT models based on F-theory 7-branes and demonstrate that a mechanism
for solving both the \mu and \mu/B_{\mu} problems emerges in a natural way. In
particular, a straightforward coupling of the messengers to the Higgs sector
leads to a geometry which not only provides us with an approximate U(1)_{PQ}
symmetry that forbids the generation of \mu at the GUT scale, it also forces
the SUSY-breaking spurion field to carry a nontrivial PQ charge. This connects
the breaking of SUSY to the generation of \mu so that the same scale enters
both. Moreover, the messenger sector naturally realizes the D3-instanton
triggered Polonyi model of arXiv:0808.1286 so this scale is exponentially
suppressed relative to M_{GUT}. The effective action at low scales is in fact
precisely of the form of the "sweet spot supersymmetry" scenario studied by Ibe
and Kitano in arXiv:0705.3686.Comment: 34 pages, 4 figures; v4 revisions to section
Global Gluing and G-flux
Local models that capture the 7-brane physics of F-theory compactifications
for supersymmetric GUTs are conveniently described in terms of an E_8 gauge
theory in the presence of a Higgs bundle. Though the Higgs bundle data is
usually determined by the local geometry and G-flux, additional gluing data
must be specified whenever the Higgs bundle spectral cover is not smooth. In
this paper, we argue that this additional information is determined by data of
the M-theory 3-form that is not necessarily captured by the cohomology class of
the G-flux. More specifically, we show that when the 3-form is specified in
terms of a line bundle on a spectral divisor, which is a global extension of
the Higgs bundle spectral cover, the gluing data of the local model is uniquely
determined in a way that ensures agreement with Heterotic results whenever a
Heterotic dual exists.Comment: 22 page
Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory
We study surface operators in 3d Topological Field Theory and their relations
with 2d Rational Conformal Field Theory. We show that a surface operator gives
rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT.
The algebraic properties of the resulting 2d RCFT, such as the classification
of symmetry-preserving boundary conditions, are expressed in terms of
properties of the surface operator. We show that to every surface operator one
may attach a Morita-equivalence class of symmetric Frobenius algebras in the
ribbon category of bulk line operators. This provides a simple interpretation
of the results of Fuchs, Runkel and Schweigert on the construction of 2d RCFTs
from Frobenius algebras. We also show that every topological boundary condition
in a 3d TFT gives rise to a commutative Frobenius algebra in the category of
bulk line operators. We illustrate these general considerations by studying in
detail surface operators in abelian Chern-Simons theory.Comment: 20 pages, latex; 17 jpg figure
F-theory GUTs with U(1) Symmetries: Generalities and Survey
We study the structure of SU(5) F-theory GUT models that engineer additional
U(1) symmetries. These are highly constrained by a set of relations observed by
Dudas and Palti (DP) that originate from the physics of 4D anomaly
cancellation. Using the DP relations, we find a general tension between
unification and the suppression of dimension 5 proton decay when one or more
U(1)'s are PQ symmetries and hypercharge flux is used to break the SU(5) GUT
group. We then specialize to spectral cover models, whose global completions in
F- theory we know how to construct. In that setting, we provide a technical
derivation of the DP relations, construct spectral covers that yield all
possible solutions to them, and provide a complete survey of spectral cover
models for SU(5) GUTs that exhibit two U(1) symmetries.Comment: 27 pages plus 5 appendices (70 pages total) ; v2 references adde
Monodromies, fluxes, and compact three-generation F-theory GUTs
We analyze constraints for embedding local SU(5) F-theory GUTs into consistent compactifications and construct explicit three-generation models based on the geometry of [1]. The key tool for studying constraints in this problem when there is an underlying E_8 structure is the spectral cover, which encodes all of the symmetries that fix the allowed couplings in the superpotential, as well as the consistent, supersymmetric G-fluxes. Imposing phenomenological requirements such as the existence of three generations, top and bottom Yukawa couplings, good flavor structure and absence of exotics and of a tree-level ÎĽ-term, we derive stringent constraints on the allowed spectral covers. The resulting spectral covers are in conflict with the neutrino scenarios that have been studied in local F-theory models unless we allow for the possibility of additional charged fields, perhaps playing the role of gauge messengers, that do not comprise complete GUT multiplets. Quite remarkably, the existence of additional incomplete GUT multiplets below the GUT scale is necessary for consistency with gauge coupling "unification", as their effect can precisely cancel that of the internal hypercharge flux, which distorts the gauge couplings already at M_(GUT)
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