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Register a new userClassification of 5d N=1 gauge theories
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We classify 5d N=1 gauge theories carrying a simple gauge group that can arise by mass-deforming 5d SCFTs and 6d SCFTs (compactified on a circle, possibly with a twist). For theories having a 6d UV completion, we determine the tensor branch data of the 6d SCFT and capture the twist in terms of the tensor branch data. We also determine the dualities between these 5d gauge theories, thus determining the sets of gauge theories having a common UV completion.
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We propose 5-brane webs for 5d $mathcal{N}=1$ $G_2$ gauge theories. From a Higgsing of the $SO(7)$ gauge theory with a hypermultiplet in the spinor representation, we construct two types of 5-brane web configurations for the pure $G_2$ gauge theory using an O5-plane or an $widetilde{text{O5}}$-plane. Adding flavors to the 5-brane web for the pure $G_2$ gauge theory is also discussed. Based on the obtained 5-brane webs, we compute the partition functions for the 5d $G_2$ gauge theories using the recently suggested topological vertex formulation with an O5-plane, and we find agreement with known results.
We discuss fractional D3-branes on the orbifold C^3/Z_2*Z_2. We study the open and the closed string spectrum on this orbifold. The corresponding N=1 theory on the brane has, generically, a U(N_1)*U(N_2)*U(N_3)*U(N_4) gauge group with matter in the bifundamental. In particular, when only one type of brane is present, one obtains pure N=1 Yang-Mills. We study the coupling of the branes to the bulk fields and present the corresponding supergravity solution, valid at large distances. By using a probe analysis, we are able to obtain the Wilsonian beta-function for those gauge theories that possess some chiral multiplet. Although, due to the lack of moduli, the probe technique is not directly applicable to the case of pure N=1 Yang-Mills, we point out that the same formula gives the correct result also for this case.
The full moduli space M of a class of N=1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X, M is a combination of the mesonic and baryonic branches, the former being the symmetric product of X. In consonance with the mathematical literature, the single brane moduli space is called the master space F. Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode ``hidden global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for arbitrary number of branes.
For any 5d ${cal N}=1$ superconformal field theory, we propose a complete prepotential which reduces to the perturbative prepotential for any of its possible gauge theory realizations, manifests its global symmetry when written in terms of the invariant Coulomb branch parameters, and is valid for the whole parameter region. As concrete examples, we consider $SU(2)$ gauge theories with up to 7 flavors, $Sp(2)$ gauge theories with up to 9 flavors, and $Sp(2)$ gauge theories with 1 antisymmetric tensor and up to 7 flavors, as well as their dual gauge theories.
We study weak coupling perturbative series in 4d N=2 and 5d N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in zero instanton sector are Borel summable for various observables. Our result for 4d $mathcal{N}=2$ case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely Borel summable. We also prove that the perturbative series in arbitrary number of instanton sector are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations in each number of instanton sector.
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