96 research outputs found
Toric Duality Is Seiberg Duality
We study four N=1 SU(N)^6 gauge theories, with bi-fundamental chiral matter
and a superpotential. In the infrared, these gauge theories all realize the
low-energy world-volume description of N coincident D3-branes transverse to the
complex cone over a del Pezzo surface dP_3 which is the blowup of P^2 at three
generic points. Therefore, the four gauge theories are expected to fall into
the same universality class--an example of a phenomenon that has been termed
"toric duality." However, little independent evidence has been given that such
theories are infrared-equivalent.
In fact, we show that the four gauge theories are related by the N=1 duality
of Seiberg, vindicating this expectation. We also study holographic aspects of
these gauge theories. In particular we relate the spectrum of chiral operators
in the gauge theories to wrapped D3-brane states in the AdS dual description.
We finally demonstrate that the other known examples of toric duality are
related by N=1 duality, a fact which we conjecture holds generally.Comment: 46 pages, 2 figures, harvma
Special Lagrangian torus fibrations of complete intersection Calabi-Yau manifolds: a geometric conjecture
For complete intersection Calabi-Yau manifolds in toric varieties, Gross and
Haase-Zharkov have given a conjectural combinatorial description of the special
Lagrangian torus fibrations whose existence was predicted by Strominger, Yau
and Zaslow. We present a geometric version of this construction, generalizing
an earlier conjecture of the first author.Comment: 23 pagers, 10 figure
Enhanced Gauge Symmetry in Type II String Theory
We show how enhanced gauge symmetry in type II string theory compactified on
a Calabi--Yau threefold arises from singularities in the geometry of the target
space. When the target space of the type IIA string acquires a genus curve
of singularities, we find that an gauge theory with
adjoint hypermultiplets appears at the singularity. The new massless states
correspond to solitons wrapped about the collapsing cycles, and their dynamics
is described by a twisted supersymmetric gauge theory on . We
reproduce this result from an analysis of the -dual -manifold. We check
that the predictions made by this model about the nature of the Higgs branch,
the monodromy of period integrals, and the asymptotics of the one-loop
topological amplitude are in agreement with geometrical computations. In one of
our examples we find that the singularity occurs at strong coupling in the
heterotic dual proposed by Kachru and Vafa.Comment: 43 pages using harvmac's `big' option. (Minor correction concerning
magnetically charged states.
Conifold Transitions in M-theory on Calabi-Yau Fourfolds with Background Fluxes
We consider topology changing transitions for M-theory compactifications on
Calabi-Yau fourfolds with background G-flux. The local geometry of the
transition is generically a genus g curve of conifold singularities, which
engineers a 3d gauge theory with four supercharges, near the intersection of
Coulomb and Higgs branches. We identify a set of canonical, minimal flux quanta
which solve the local quantization condition on G for a given geometry,
including new solutions in which the flux is neither of horizontal nor vertical
type. A local analysis of the flux superpotential shows that the potential has
flat directions for a subset of these fluxes and the topologically different
phases can be dynamically connected. For special geometries and background
configurations, the local transitions extend to extremal transitions between
global fourfold compactifications with flux. By a circle decompactification the
M-theory analysis identifies consistent flux configurations in four-dimensional
F-theory compactifications and flat directions in the deformation space of
branes with bundles.Comment: 93 pages; v2: minor changes and references adde
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