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 $S^2$ 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