28 research outputs found
Tinkertoys for the Twisted D-Series
We study 4D N=2 superconformal field theories that arise from the
compactification of 6D N=(2,0) theories of type D_N on a Riemann surface, in
the presence of punctures twisted by a Z_2 outer automorphism. Unlike the
untwisted case, the family of SCFTs is in general parametrized, not by M_{g,n},
but by a branched cover thereof. The classification of these SCFTs is carried
out explicitly in the case of the D_4 theory, in terms of three-punctured
spheres and cylinders, and we provide tables of properties of twisted punctures
for the D_5 and D_6 theories. We find realizations of Spin(8) and Spin(7) gauge
theories with matter in all combinations of vector and spinor representations
with vanishing beta-function, as well as Sp(3) gauge theories with matter in
the 3-index traceless antisymmetric representation.Comment: 75 pages, 270 figure
Tinkertoys for the Twisted Theory
We study superconformal field theories that arise as the
compactification of the six-dimensional theory of type on a
punctured Riemann surface in the presence of outer-automorphism
twists. We explicitly carry out the classification of these theories in terms
of three-punctured spheres and cylinders, and provide tables of properties of
the -twisted punctures. An expression is given for the
superconformal index of a fixture with twisted punctures of type , which
we use to check our identifications. Several of our fixtures have Higgs
branches which are isomorphic to instanton moduli spaces, and we find that
S-dualities involving these fixtures imply interesting isomorphisms between
hyperK\"ahler quotients of these spaces. Additionally, we find families of
fixtures for which the Sommers-Achar group, which was previously a Coulomb
branch concept, acts non-trivially on the Higgs branch operators.Comment: 52 pages, 56 figure
Seiberg-Witten for with Spinors
supersymmetric gauge theory admits hypermultiplets
in spinor representations of the gauge group, compatible with , for
. The theories with can be obtained as mass-deformations of
the theories, so it is of greatest interest to construct the
theories. In previous works, we discussed the theories.
Here, we turn to the cases. By compactifying the (2,0)
theory on a 4-punctured sphere, we find Seiberg-Witten solutions to almost all
of the remaining cases. There are five theories, however, which do not seem to
admit a realization from six dimensions.Comment: 28 pages, 54 figure
Tinkertoys for the E7 Theory
We classify the class theories of type . These are four-dimensional
superconformal field theories arising from the compactification
of the theory on a punctured Riemann surface, . The
classification is given by listing all 3-punctured spheres ("fixtures"), and
connecting cylinders, which can arise in a pants-decomposition of . We find
exactly 11,000 fixtures with three regular punctures, and an additional 48 with
one "irregular puncture" (in the sense used in our previous works). To organize
this large number of theories, we have created a web application at
https://golem.ph.utexas.edu/class-S/E7/ . Among these theories, we find 10 new
ones with a simple exceptional global symmetry group, as well as a new rank-2
SCFT and several new rank-3 SCFTs. As an application, we study the
strong-coupling limit of the gauge theory with 3 hypermultiplets in the
. Using our results, we also verify recent conjectures that the
compactification of certain theories can alternatively be realized
in class as fixtures in the or theories.Comment: Fixed one entry in table of interacting fixtures with an irregular
punctur
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