Quantum Higgs branches of isolated N=2 superconformal field theories

We study the Higgs branches of the superconformal points of four-dimensional N=2 super Yang-Mills (SYM) which appear due to the occurrence of mutually local monopoles having appropriate charges. We show, for example, that the maximal superconformal point of SU(2n) SYM has a Higgs branch of the form C^2/Z_n. These Higgs branches are intrinsic to the superconformal field theory (SCFT) at the superconformal point, but do not appear in the SYM theory in which it is embedded. This is because the embedding is a UV extension of the SCFT in which some global symmetry acting on the Higgs branch is gauged irrelevantly. Higgs branches deduced from earlier direct studies of these isolated SCFTs using BPS wall-crossing or 3-d mirror symmetry agree with the ones we find here using just the Seiberg-Witten data for the SYM theories.Comment: 18 page

Singular points in N=2 SQCD

We revisit the study of singular points in N=2 SQCD with classical gauge groups. Using a technique proposed recently by Gaiotto, Seiberg and Tachikawa we find that the low-energy physics at the maximally singular point involves two superconformal sectors coupled to an infrared free SU(2) gauge group. When one softly breaks extended supersymmetry to N=1 adding a mass term for the chiral multiplet in the adjoint representation, a finite number of vacua remain and the theory becomes confining. Our analysis allows to identify the low-energy physics at these distinguished points in the moduli space. In some cases, which we will describe in detail, two sectors coupled to an infrared free SU(2) gauge group emerge as before. For USp and SO gauge groups one of these sectors is always free, contrary to the SU case.Comment: 22 pages, 2 figure

Comments on scaling limits of 4d N=2 theories

We revisit the study of the maximally singular point in the Coulomb branch of 4d N=2 SU(N) gauge theory with N_f=2n flavors for N_f= 2, we find that the low-energy physics is described by two non-trivial superconformal field theories coupled to a magnetic SU(2) gauge group which is infrared free. (In the special case n=2, one of these theories is a theory of free hypermultiplets.) This observation removes a possible counter example to a conjectured a-theorem.Comment: 13 page

Tinkertoys for Gaiotto Duality

We describe a procedure for classifying N=2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A_{N-1} SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N=5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian N=2 SCFTs.Comment: 61 pages, 136 figures (a veritable comic book). V2: Grotty bitmapped figures replaced with PDF versions; a couple of references fixe

On 4d rank-one N=3 superconformal field theories

We study the properties of 4d N=3 superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form C^3/Z_k for k=1,2,3,4,6, and that the supersymmetry automatically enhances to N=4 for k=1,2. In addition, we determine the central charges a and c in terms of k, and construct the associated 2d chiral algebras, which turn out to be exotic N=2 supersymmetric W-algebras.Comment: 24 page

Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups

N=2 Seiberg-Witten theories allow an interesting interplay between the Argyres-Douglas loci, singularity structures and wall-crossing formulae. In this paper we investigate this connection by first studying the singularity structures of hyper-elliptic Seiberg-Witten curves for pure N=2 gauge theories with SU(r+1) and Sp(2r) gauge groups, and propose new methods to locate the Argyres-Douglas loci in the moduli space, where multiple mutually non-local BPS states become massless. In a region of the moduli space, we compute dyon charges for all 2r+2 and 2r+1 massless dyons for SU(r+1) and Sp(2r) gauge groups respectively for rank r>1. From here we elucidate the connection to the wall-crossing phenomena for pure Sp(4) Seiberg-Witten theory near the Argyres-Douglas loci, despite our emphasis being only at the massless sector of the BPS spectra. We also present 2r-1 candidates for the maximal Argyres-Douglas points for pure SO(2r+1) Seiberg-Witten theory.Comment: 81 pages, 41 figures, LaTeX; v2: Minor cosmetic changes and correction of a typographical error in acknowledgement. Final version to appear in JHE

Argyres-Douglas theories and S-duality

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are creditedM.B. and T.N. are partly supported by the U.S. Department of Energy under grants DOE-SC0010008, DOE-ARRA-SC0003883, and DOE-DE-SC0007897. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. S.G. is partially supported by the ERC Advanced Grant “SyDuGraM”, by FNRS-Belgium (convention FRFC PDR T.1025.14 and convention IISN 4.4514.08) and by the “Communaut´e Francaise de Belgique” through the ARC progra

More Three Dimensional Mirror Pairs

We found a lot of new three dimensional N = 4 mirror pairs generalizing previous considerations on three dimensional generalized quiver gauge theories. We recovered almost all previous discovered mirror pairs with these constructions. One side of these mirror pairs are always the conventional quiver gauge theories. One of our result can also be used to determine the matter content and weakly coupled gauge groups of four dimensional N = 2 generalized quiver gauge theories derived from six dimensional A_N and D_N theory, therefore we explicitly constructed four dimensional S-duality pairs.Comment: 33 pages, 18 figures version2 minor correction

Constraints on chiral operators in N=2 SCFTs

Open Access, © The Authors. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

General Argyres-Douglas Theory

We construct a large class of Argyres-Douglas type theories by compactifying six dimensional (2,0) A_N theory on a Riemann surface with irregular singularities. We give a complete classification for the choices of Riemann surface and the singularities. The Seiberg-Witten curve and scaling dimensions of the operator spectrum are worked out. Three dimensional mirror theory and the central charges a and c are also calculated for some subsets, etc. Our results greatly enlarge the landscape of N=2 superconformal field theory and in fact also include previous theories constructed using regular singularity on the sphere.Comment: 55 pages, 20 figures, minor revision and typos correcte