Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
We revisit the correspondence between Calabi-Yau (CY) threefoldisolated singularities \mathbf{X} 𝐗 and five-dimensional superconformal field theories (SCFTs), which ariseat low energy in M-theory on the space-time transverse to \mathbf{X} 𝐗 .Focussing on the case of toric CY singularities, we analyze the“gauge-theory phases” of the SCFT by exploiting fiberwise M-theory/typeIIA duality. In this setup, the low-energy gauge group simply arises onstacks of coincident D6-branes wrapping 2-cycles in some ALE space oftype A_{M-1} A M − 1 fibered over a real line, and the map between the Kähler parameters of \mathbf{X} 𝐗 and the Coulomb branch parameters of the field theory (masses and VEVs)can be read off systematically. Different type IIA “reductions” giverise to different gauge theory phases, whose existence depends on theparticular (partial) resolutions of the isolated singularity \mathbf{X} 𝐗 .We also comment on the case of non-isolated toric singularities.Incidentally, we propose a slightly modified expression for theCoulomb-branch prepotential of 5d \mathcal{N}=1 𝒩 = 1 gauge theories.
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10165541
Journal Name:
SciPost Physics
Volume:
6
Issue:
5
ISSN:
2542-4653
4. A bstract We study 4 d $$\mathcal{N}$$ N = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.