Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Expanding the landscape of $\mathcal{N}$=2 rank 1 SCFTs

Philip C. Argyres, Matteo Lotito, Yongchao Lü, Mario Martone

TL;DR

The paper broadens the rank-1 ${\mathcal N}=2$ SCFT landscape by allowing discrete flavor factors and refining CB-geometry constraints, showing that four recently discussed rank-1 theories, including novel ${\mathcal N}=3$ cases, fit within the updated framework. RG-flow consistency then necessitates the existence of at least four more rank-1 SCFTs, nearly doubling the known spectrum. Through detailed checks of curve discriminants, central charges, and ECB fibers, the authors map flavor identifications (including outer-automorphism actions) and classify flows into good, ugly, or bad, providing a structured view of which flavor assignments yield consistent IR physics. The results unify ${\mathcal N}=3$ rank-1 theories with their ${\mathcal N}=2$ CB geometries, compute flavor-central charges for nonabelian factors, and offer a robust methodology for expanding the rank-1 SCFT landscape via RG-flow constraints and discrete symmetry considerations.

Abstract

We refine our previous proposal for systematically classifying 4d rank-1 $\mathcal N=2$ SCFTs by constructing their possible Coulomb branch geometries. Four new recently discussed rank-1 theories, including novel $\mathcal{N}=3$ SCFTs, sit beautifully in our refined classification framework. By arguing for the consistency of their RG flows we can make a strong case for the existence of at least four additional rank-1 SCFTs, nearly doubling the number of known rank-1 SCFTs. The refinement consists of relaxing the assumption that the flavor symmetries of the SCFTs have no discrete factors. This results in an enlarged (but finite) set of possible rank-1 SCFTs. Their existence can be further constrained using consistency of their central charges and RG flows.

Expanding the landscape of $\mathcal{N}$=2 rank 1 SCFTs

TL;DR

The paper broadens the rank-1 SCFT landscape by allowing discrete flavor factors and refining CB-geometry constraints, showing that four recently discussed rank-1 theories, including novel cases, fit within the updated framework. RG-flow consistency then necessitates the existence of at least four more rank-1 SCFTs, nearly doubling the known spectrum. Through detailed checks of curve discriminants, central charges, and ECB fibers, the authors map flavor identifications (including outer-automorphism actions) and classify flows into good, ugly, or bad, providing a structured view of which flavor assignments yield consistent IR physics. The results unify rank-1 theories with their CB geometries, compute flavor-central charges for nonabelian factors, and offer a robust methodology for expanding the rank-1 SCFT landscape via RG-flow constraints and discrete symmetry considerations.

Abstract

We refine our previous proposal for systematically classifying 4d rank-1 SCFTs by constructing their possible Coulomb branch geometries. Four new recently discussed rank-1 theories, including novel SCFTs, sit beautifully in our refined classification framework. By arguing for the consistency of their RG flows we can make a strong case for the existence of at least four additional rank-1 SCFTs, nearly doubling the number of known rank-1 SCFTs. The refinement consists of relaxing the assumption that the flavor symmetries of the SCFTs have no discrete factors. This results in an enlarged (but finite) set of possible rank-1 SCFTs. Their existence can be further constrained using consistency of their central charges and RG flows.

Paper Structure

This paper contains 12 sections, 48 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Discrete parts of flavor symmetries
  3. CB geometries of new SCFTs
  4. The ${\mathfrak f}=A_3$ theory with ${\Delta}(u)=6$
  5. The ${\mathfrak f}=\mathop{\rm u}(1)$ ${\mathcal{N}}=3$ theories with ${\Delta}(u) = 6 ,4, 3$
  6. Some checks
  7. Curve discriminants
  8. RG flows
  9. Central charges
  10. ECB fibers
  11. RG flow constraints for all flavor assignments
  12. Conclusion

Figures (4)

  • Figure 1: Green, blue and red arrows label matching, compatible and unphysical RG flows, while green and blue backgrounds indicate "good" and "ugly" theories, respectively. There are flows of all theories with ${\mathfrak f}=A_1^p\oplus\mathop{\rm u}(1)^q$ to an $[I_4,A_3\oplus\mathop{\rm u}(1)]$ theory, with an ${\mathfrak f}\supset A_3$ factor to an $[I_2^*,C_3/A_1^3]$ theory, and the flow $[II^*,D_5\rtimes\mathbb{Z}_2] \to [I_3^*,A_3A_1/A_1^2]$ which render all these theories ugly.
  • Figure 2: Green, blue and red arrows label matching, compatible and unphysical RG flows, while green, blue and red backgrounds indicate "good", "ugly" and "bad" theories, respectively. For the $I_1$ series there is always a compatible flow of any theory with ${\mathfrak f}=\mathop{\rm u}(1)^p$ to an $[I_5, A_4\oplus\mathop{\rm u}(1)]$ singularity, rendering them ugly. For the $I_1^*$ series there are unphysical flows $[II^*,BC_3]\to[I_3^*,A_1^2]$ and $[III^*,A_1^2]\to[I_2^*,\mathop{\rm u}(1)]$, rendering them "bad" theories. The flows of $[II^*,A_1^3\rtimes\mathbb{Z}_2]$ and $[II^*,\mathop{\rm u}(1)^3\rtimes{\Gamma}_{\!BC_3}]$ to $[I_3,A_2\oplus\mathop{\rm u}(1)]$ and from $[III^*,(\mathop{\rm u}(1)\rtimes\mathbb{Z}_2)^2]$ to $[I_2,A_1\oplus\mathop{\rm u}(1)]$ are instead only compatible, rendering these theories "ugly".
  • Figure 3: Green and red arrows label matching and unphysical RG flows, while green and red backgrounds indicate "good" and "bad" theories, respectively.
  • Figure 4: Green, blue and red arrows label matching, compatible and unphysical RG flows, while green and blue backgrounds indicate "good" and "ugly" theories respectively. There is a $[II^*,\mathop{\rm u}(1)\rtimes{\Gamma}_{\!G_2}]\to[I_2,A_1\oplus\mathop{\rm u}(1)]$ flow which is necessarily only compatible, making the theory ugly.