Abstract
We study the interplay between mass deformations and unoriented projections of super-conformal quiver gauge theories resulting from D3-branes at (toric) Calabi-Yau singularities. We focus on simple orbifold cases (ℂ3/ℤ3 and ℂ3/ℤ4) and their non-orbifold descendants. This allows us to generalize the construction rules and clarify points that have been previously overlooked. In particular we spell out the conditions of anomaly cancellations as well as super-conformal invariance that typically require the introduction of flavour branes, which in turn may spoil toric symmetry. Finally, we discuss duality cascades in this context and the interplay between Seiberg/toric duality and unoriented projection with (or without) mass deformations.
Highlights
Introduction and motivationsOpen and unoriented strings, whose systematic construction was addressed long ago [1, 2],1 have proven to be an unprecedented tool in the exploration of gauge field dynamics after the introduction of D-branes [5,6,7] and even more so after the advent of the holographic AdS/CFT correspondence [8,9,10,11]
We study the interplay between mass deformations and unoriented projections of super-conformal quiver gauge theories resulting from D3-branes at Calabi-Yau singularities
In particular we spell out the conditions of anomaly cancellations as well as super-conformal invariance that typically require the introduction of flavour branes, which in turn may spoil toric symmetry
Summary
Open and unoriented strings, whose systematic construction was addressed long ago [1, 2],1 have proven to be an unprecedented tool in the exploration of gauge field dynamics after the introduction of D-branes [5,6,7] and even more so after the advent of the holographic AdS/CFT correspondence [8,9,10,11]. Our analysis crucially relies on mass-deformations of orbifold models: we extend the validity of the consistency conditions to non-orbifold models when the latter can be obtained by mass-deformations [48] and/or (Un-)Higgsing [29, 30] of orbifold theories With these results, we recover a convenient Quiver description of unoriented singularities which, starting from simple orbifolds cases, can enlighten the relation between Orientifold charges, used in the context of Quiver diagrams, and T-parities, which are widely used in the context of Dimer models. Several interesting non-perturbative unoriented models without flavour branes, found in [25, 26], are beyond the reach of our present approach It should be noted, that non-compact D7-branes can backreact on the local geometry and spoil the previously-existing toric symmetry. We review the role of Higgsing in appendix A and of Seiberg duality [53, 54] in the above context in appendix B
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