Abstract
In this paper we study a class of mathcal{N}=2 SCFTs with ADE global symmetry defined via Type IIB compactification on a class of hypersurfaces in ℂ3 × ℂ*. These can also be constructed by compactifying the 6d (2,0) theory of type ADE on a sphere with an irregular and a full punctures. When we couple to the ADE moment map a chiral multiplet in the adjoint representation and turn on a (principal) nilpotent vev for it, all the theories in this family display enhancement of supersymmetry in the infrared. We observe that all known examples of theories which flow, upon the same type of deformation, to strongly coupled mathcal{N}=2 theories fit naturally in our framework, thus providing a new perspective on this topic. We propose an infrared equivalence between this RG flow and a manifestly mathcal{N}=2 preserving one and, as a byproduct, we extract a precise prescription to relate the SW curves describing the UV and IR fixed points for all theories with A or D global symmetry. We also find, for a certain subclass, a simple relation between UV and IR theories at the level of chiral algebras.
Highlights
Nonlagrangian theories were found and more recently the class S construction [7] provided a general framework to study a vast landscape of nonlagrangian theories
In this paper we study a class of N = 2 SCFTs with ADE global symmetry defined via Type IIB compactification on a class of hypersurfaces in C3 × C∗
In [8,9,10] it was realized that the nonlagrangian class of N = 2 theories is smaller than what we thought, if we relax the assumption that the gauge theory description has manifest extended supersymmetry: the authors noticed that if we consider an N = 2 lagrangian SCFT with a global symmetry G, couple a chiral multiplet transforming in the adjoint representation to the G moment map and turn on for it a nilpotent vev, sometimes supersymmetry enhances in the IR
Summary
We have all the ingredients we need to state the main claim of this note: starting from any Dkb (J) theory (for every choice of J, b and k > 0), the susy enhancing RG flow triggered by a principal nilpotent vev for the symmetry group J leads to supersymmetry enhancement in the infrared and the IR fixed point is the Jk(b) theory, which can be obtained, as explained above, by closing the J full puncture of Dkb+b(J). We find that the number of operators which violate the unitarity bound and should be flipped is always equal to r(J) Combining this with the fact that the “candidate” CB operators of the IR SCFT are either CB operators of the Dkb (J) theory or the singlets Mi (and we always have r(J) of them), we conclude that the UV and IR SCFT’s always have the same rank. This conclusion follows by comparing the Milnor numbers of the two theories (2.9), (2.14) and exploiting the fact that the rank of the global symmetry group of Dkb (J) is equal to that of Jb(k) plus r(J) (see the appendix). More general nilpotent vevs and linear quivers ending with a SO gauge group coupled to fundamentals can be analyzed in the same way with identical conclusions
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