Parameter Space of Quiver Gauge Theories

Abstract

Placing a set of branes at a Calabi-Yau singularity leads to an N=1 quiver gauge theory. We analyze F-term deformations of such gauge theories. A generic deformation can be obtained by making the Calabi-Yau non-commutative. We discuss non-commutative generalisations of well-known singularities such as the Del Pezzo singularities and the conifold. We also introduce new techniques for deriving superpotentials, based on quivers with ghosts and a notion of generalised Seiberg duality. The curious gauge structure of quivers with ghosts is most naturally described using the BV formalism. Finally we suggest a new approach to Seiberg duality by adding fields and ghost-fields whose effects cancel each other.

Figures (14)

• Figure 1: Ghost number zero operators can be used to relate disk amplitudes.
• Figure 2: A braiding operation on the collection of fractional branes. These pictures can be interpreted in terms of D6 branes wrapped on Lagrangian cycles in the mirror Hori:2000ck.
• Figure 3: (A): Organising the nodes before appkying a Seiberg duality. (B): The quarks $Q$ are replaced by the dual quarks $q$ and the mesons $M = Q \tilde{Q}$, and the gauge group is changed from $SU(N_c)$ to $SU(N_f - N_c)$.
• Figure 4: (A) Quiver diagram associated to the exceptional collection (\ref{['P2standard']}). (B) Dual quiver diagram, obtained from (A) by Seiberg duality on node (3).
• Figure 5: (A): Quiver associated with the collection (\ref{['P1xP1exc']}). (B): Quiver obtained from (A) by Seiberg duality on node 2.