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 generalizations of wellknown 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 generalized 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.

Crystal melting and black holes

“…Indeed, the ghost number of the corresponding vertex operators in the open topological B-model shows that such fields and thus the associated quiver theories are unphysical [23]. In the case of gauged quiver quantum mechanics, these exotic bosonic propagating degrees of freedom correspond to bifundamental 2 scalars with a wrong sign kinetic term.…”

“…These fields were interpreted in [22] as tachyons in a topological brane anti-brane system. In the physical string theory, such fields signal the presence of uncanceled ghosts [23,24].…”

Noncommutative Resolutions of ADE Fibered Calabi-Yau Threefolds

“…3 The multiplicities αi are uniquely determined via the condition i αi ch(Ei) = ch(OP ) (as asserted in Eq. (2.1) of [43]). and removes them leading to a path from the head of a to its tail.…”

Deformations and D-branes

“…The relation between Hochschild cohomology, deformations and string theory has been discussed from a different perspective in [38,39]. Noncommutative deformations of the moduli space of quiver gauge theories in the context of D-branes at a singularity have been examined in [14]. This paper is organized as follows.…”

“…While the physical import of this equivalence is not yet fully understood, it has many useful implications. It allows the easy identification of the fractional branes, an understanding of dibaryons [9], Seiberg duality [10], stability conditions [11], moduli spaces [12][13][14] and more. In addition, recent work [15] has connected this approach to the toric techniques pioneered in [16] and fully realized in [17,18].…”