A quiver of many runaways

Abstract

We study the quantum corrections to the moduli space of the quiver gauge theory corresponding to regular and fractional D3-branes at the dP 1 singularity. We find that besides the known runaway behavior at the lowest step of the duality cascade, there is a runaway direction along a mesonic branch at every higher step of the cascade. Moreover, the algebra of the chiral operators which obtain the large expectation values is such that we reproduce Altmann's first order deformation of the dP 1 cone.

Transmutation of \mathbf{{\cal N}=2} fractional D3 branes into twisted sector fluxes

“…Instead, our exact solution (3.1) involves twisted fields only, with no need of smeared tensionless fractional brane sources. Indeed, the solution for γ is holomorphic everywhere along the ring, except at the 2M branch points of the square root 6 , and the discontinuity of the D5 brane charge is simply provided by the M disjoint branch cuts joining them, along with the M branch cuts lying between one branch point in each pair and the point at infinity. Therefore, we see that at nonvanishing string coupling those fractional D3 branes, rather than becoming tensionless and uniformly smeared along the ring, completely dissolve into twisted fluxes.…”

“…In the past few years the attention has been mainly drawn to D5 branes wrapped on rigid collapsed 2-cycles, the best known examples of which are fractional D3 branes at the tip of the conifold [1] and of the complex cone over the first Del Pezzo surface [2]: there the gauge theories have N = 1 supersymmetry, the cascade is an infinite sequence of Seiberg dualities [3], and the low energy confining dynamics drives either chiral symmetry breaking [1] or a runaway [4,5,6].…”

The mesonic branch of the deformed conifold

“…The baryonic branch allows also for solutions that break the Z 2 symmetry [10]. The corresponding supergravity duals based on the so-called resolved warped deformed conifold were constructed in [9] (see also [10,11]).…”

The Octagon at large M

“…More technically, the F-term equations of certain baryonic operators set the parameter of the complex structure deformation to be proportional to Λ # /X, with X a gauge invariant operator. However, since the complex structure deformation is obstructed this implies that the parameter has to vanish, and the F-term equation can be satisfied only at X → ∞ (see [29] for a detailed discussion for the prototype CY where this happens, namely the complex cone over the first del Pezzo surface).…”