Abstract
We use large N duality to study brane/antibrane configurations on a class of Calabi–Yau manifolds. With only branes present, the Calabi–Yau manifolds in question give rise to N = 2 ADE quiver theories deformed by superpotential terms. We show that the large N duality conjecture of [M. Aganagic, C. Beem, J. Seo, C. Vafa, Geometrically induced metastability and holography, hep-th/0610249] reproduces correctly the known qualitative features of the brane/antibrane physics. In the supersymmetric case, the gauge theories have Seiberg dualities, which are represented as flops in the geometry. Moreover, the holographic dual geometry encodes the whole RG flow of the gauge theory. In the non-supersymmetric case, the large N duality predicts that the brane/antibrane theories also enjoy such dualities, and allows one to pick out the good description at a given energy scale.
Highlights
Geometric transitions have proven to be a powerful means of studying the dynamics of supersymmetric D-branes
String theory relates these transitions to large N dualities, where before the transition, at small ’t Hooft coupling, one has D-branes wrapping cycles in the geometry, and after the transition, at large ’t Hooft coupling, the system is represented by a different geometry, with branes replaced by fluxes
In [1] it was conjectured that topological strings and large N dualities can be used to study non-supersymmetric, metastable configurations of branes in Calabi-Yau manifolds, that confine at low energies
Summary
Geometric transitions have proven to be a powerful means of studying the dynamics of supersymmetric D-branes. When all the branes are D5 branes and supersymmetry is preserved, the low energy theory geometrically realizes [24,25] a 4d N = 2 supersymmetric quiver gauge theory with a superpotential for the world-volume adjoints which breaks N = 2 to N = 1 These theories are known to have Seiberg-like dualities [29] in which the dual theories flow to the same IR fixed point, and where different descriptions are more weakly coupled, and . We can use holography to follow the varying sizes of 2-cycles over the geometry, and find that in some cases they can undergo flops in going from the IR to the UV When this happens, descriptions in terms of different brane/anti-brane configurations are more natural at different energy scales, and one can smoothly interpolate between them.
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