16 research outputs found
On ADE Quiver Models and F-Theory Compactification
Based on mirror symmetry, we discuss geometric engineering of N=1 ADE quiver
models from F-theory compactifications on elliptic K3 surfaces fibered over
certain four-dimensional base spaces. The latter are constructed as
intersecting 4-cycles according to ADE Dynkin diagrams, thereby mimicking the
construction of Calabi-Yau threefolds used in geometric engineering in type II
superstring theory. Matter is incorporated by considering D7-branes wrapping
these 4-cycles. Using a geometric procedure referred to as folding, we discuss
how the corresponding physics can be converted into a scenario with D5-branes
wrapping 2-cycles of ALE spaces.Comment: 21 pages, Latex, minor change
A Geometric Unification of Dualities
We study the dynamics of a large class of N=1 quiver theories, geometrically
realized by type IIB D-brane probes wrapping cycles of local Calabi-Yau
threefolds. These include N=2 (affine) A-D-E quiver theories deformed by
superpotential terms, as well as chiral N=1 quiver theories obtained in the
presence of vanishing 4-cycles inside a Calabi-Yau. We consider the various
possible geometric transitions of the 3-fold and show that they correspond to
Seiberg-like dualities (represented by Weyl reflections in the A-D-E case or
`mutations' of bundles in the case of vanishing 4-cycles) or large N dualities
involving gaugino condensates (generalized conifold transitions). Also duality
cascades are naturally realized in these classes of theories, and are related
to the affine Weyl group symmetry in the A-D-E case.Comment: 94 pages, 18 figures. Added referenc
Geometrically Induced Phase Transitions at Large N
Utilizing the large N dual description of a metastable system of branes and
anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau
threefold, we study phase transitions induced by changing the positions of the
S^2's. At leading order in 1/N the effective potential for this system is
computed by the planar limit of an auxiliary matrix model. Beginning at the two
loop correction, the degenerate vacuum energy density of the discrete confining
vacua split, and a potential is generated for the axion. Changing the relative
positions of the S^2's causes discrete jumps in the energetically preferred
confining vacuum and can also obstruct direct brane/anti-brane annihilation
processes. The branes must hop to nearby S^2's before annihilating, thus
significantly increasing the lifetime of the corresponding non-supersymmetric
vacua. We also speculate that misaligned metastable glueball phases may
generate a repulsive inter-brane force which stabilizes the radial mode present
in compact Calabi-Yau threefolds.Comment: 47 pages, 7 figure
The unwarped, resolved, deformed conifold: fivebranes and the baryonic branch of the Klebanov-Strassler theory
We study a gravity solution corresponding to fivebranes wrapped on the
of the resolved conifold. By changing a parameter the solution continuously
interpolates between the deformed conifold with flux and the resolved conifold
with branes. Therefore, it displays a geometric transition, purely in the
supergravity context. The solution is a simple example of torsional geometry
and may be thought of as a non-K\"ahler analog of the conifold. By U-duality
transformations we can add D3 brane charge and recover the solution in the form
originally derived by Butti et al. This describes the baryonic branch of the
Klebanov-Strassler theory. Far along the baryonic branch the field theory gives
rise to a fuzzy two-sphere. This corresponds to the D5 branes wrapping the
two-sphere of the resolved conifold in the gravity solution.Comment: 41 pages, 7 figure
M5-branes, toric diagrams and gauge theory duality
In this article we explore the duality between the low energy effective
theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge
theories compactified on S^1. The theories we study are the five-dimensional
uplifts of four-dimensional superconformal linear quivers. We study this
duality by comparing the Seiberg-Witten curves and the Nekrasov partition
functions of the two dual theories. The Seiberg-Witten curves are obtained by
minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov
partition functions are computed using topological string theory. The result of
our study is a map between the gauge theory parameters, i.e., Coulomb moduli,
masses and UV coupling constants, of the two dual theories. Apart from the
obvious physical interest, this duality also leads to compelling mathematical
identities. Through the AGTW conjecture these five-dimentional gauge theories
are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The
duality we study implies the relations between Liouville and Toda correlation
functions through the map we derive.Comment: 58 pages, 17 figures; v2: minor corrections, references adde