Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

More on the N=2 superconformal systems of type $D_p(G)$

Sergio Cecotti, Michele Del Zotto, Simone Giacomelli

Abstract

A large family of 4d N=2 SCFT's was introduced in arXiv:1210.2886. Its elements $D_p(G)$ are labelled by a positive integer p\in N and a simply-laced Lie group G; their flavor symmetry is at least G. In the present paper we study their physics in detail. We also analyze the properties of the theories obtained by gauging the diagonal symmetry of a collection of $D_{p_i}(G)$ models. In all cases the computation of the physical quantities reduces to simple Lie-theoretical questions. To make the analysis more functorial, we replace the notion of the BPS-quiver of the N=2 QFT by the more intrinsic concept of its META-quiver. In particular: 1) We compute the SCFT central charges a, c, k, and flavor group F for all $D_p(G)$ models. 2) We identify the subclass of $D_p(G)$ theories which correspond to previously known SCFT's (linear SU and SO-USp quiver theories, Argyres-Douglas models, superconformal gaugings of Minahan-Nemeshanski E_r models, etc.), as well as to non-trivial IR fixed points of known theories. The $D_p(E_r)$ SCFT's with $p\geq 3$ cannot be constructed by any traditional method. 3) We investigate the finite BPS chambers of some of the models. 4) As a by product, we prove three conjectures by Xie and Zhao, and provide new checks of the Argyres-Seiberg duality.

More on the N=2 superconformal systems of type $D_p(G)$

Abstract

A large family of 4d N=2 SCFT's was introduced in arXiv:1210.2886. Its elements are labelled by a positive integer p\in N and a simply-laced Lie group G; their flavor symmetry is at least G. In the present paper we study their physics in detail. We also analyze the properties of the theories obtained by gauging the diagonal symmetry of a collection of models. In all cases the computation of the physical quantities reduces to simple Lie-theoretical questions. To make the analysis more functorial, we replace the notion of the BPS-quiver of the N=2 QFT by the more intrinsic concept of its META-quiver. In particular: 1) We compute the SCFT central charges a, c, k, and flavor group F for all models. 2) We identify the subclass of theories which correspond to previously known SCFT's (linear SU and SO-USp quiver theories, Argyres-Douglas models, superconformal gaugings of Minahan-Nemeshanski E_r models, etc.), as well as to non-trivial IR fixed points of known theories. The SCFT's with cannot be constructed by any traditional method. 3) We investigate the finite BPS chambers of some of the models. 4) As a by product, we prove three conjectures by Xie and Zhao, and provide new checks of the Argyres-Seiberg duality.

Paper Structure

This paper contains 46 sections, 282 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. A quick review of the 2d/4d correspondence
  3. $\widehat{A}(p,1)\boxtimes G$ models
  4. The old viewpoint (quivers)
  5. Light subcategory of the $\widehat{A}(p,1)\boxtimes G$ model
  6. The new viewpoint: META--quivers
  7. The META--quiver for the light category of the $\widehat{A}(p,1)\boxtimes G$ model
  8. The SYM sector
  9. Non--perturbative completion
  10. The product $\circledast$
  11. The $D_p(G)$ category
  12. Deformed preprojective META--algebras vs. $D_p(G)$ SCFT's
  13. Quantum monodromies, beta function, and flavor charges
  14. Several $D_p(G)$ matter subsectors
  15. The BPS spectrum of $\widehat{H}\boxtimes G$ models at strong coupling
  16. ...and 31 more sections

Figures (8)

  • Figure 1: The tensor product quiver of $\widehat{A}(p,1)$ and $G=A_n$.
  • Figure 2: The reduced quiver $Q_{p,A_n}$ of the light subcategory of the model $\widehat{A}(p,1)\boxtimes A_n$. The dashed arrows represents the relations inherited from the triangular tensor product.
  • Figure 3: The DWZ--reduced quivers ${\cal D}(G)$ for the $D_2(G)$ SCFT's.
  • Figure 4: Element in the quiver mutation class of $D_2(SO(10))$ describing the $S$-duality frame of Argyres--Seiberg argyresseiberg. The full subquiver of type $A(1,1)$ on the nodes $\{ \, 1 , 6 \, \}$ represents the $SU(2)$ SYM subsector, and the node 2 represents the gauged $SU(2)$ flavor symmetry of $E_7$ MN.
  • Figure 5: An element in the mutation-class of the quiver of the model $D_2(E_6)$. This quiver clearly represents an $S$-duality frame in which we have an explicit $SU(3)$ SYM sector coupled to the $E_8$ MN theory. The $SU(3)$ SYM full subquiver is on the nodes $\{ 2, 3, 5, 11 \}$. The node 8 represents the gauged $SU(3)$ flavor symmetry of $E_8$ MN.
  • ...and 3 more figures