214 research outputs found
On the 6d origin of discrete additional data of 4d gauge theories
Starting with a choice of gauge algebras, specification of a 4d gauge theory
involves additional data, namely the gauge groups and the discrete theta
angles. Equivalently, one needs to specify the set of charges of allowed line
operators. In this note, we study how these additional data are represented in
6d, when the 4d theory in question is an N=4 super Yang-Mills theory or an N=2
class S theory. We will see that the Z_N symmetry of the so-called T_N theory
plays an important role. As a byproduct, we will find that the superconformal
index of class S theories can be refined so that it can give 2d q-deformed
Yang-Mills theory with different gauge groups associated to the same gauge
algebra.Comment: 18 pages; v2: minor correction
On W-algebras and the symmetries of defects of 6d N=(2,0) theory
We consider 6d N=(2,0) theory on N M5-branes, together with a 4d defect
labeled by a Young diagram Y specifying its global symmetry G_Y. A recent
conjecture states that a compactification of this system leads to a 2d theory
with W-algebra symmetry depending on Y. We provide a check of the conjecture by
reproducing the level of the current subalgebra \hat{G}_Y of this W-algebra
from the property of the 4d defect.Comment: 16 pages; v2: Corrections to Sec. 2, conclusions unchanged.
Additional reference
Derivation of the linearity principle of Intriligator-Leigh-Seiberg
Utilizing the techniques recently developed for N=1 super Yang-Mills theories
by Dijkgraaf, Vafa and collaborators, we derive the linearity principle of
Intriligator, Leigh and Seiberg, for the confinement phase of the theories with
semi-simple gauge groups and matters in a non-chiral representation which
satisfies a further technical assumption.Comment: 7 pages, no figures; v2: a few clarifications and references adde
Magnetic discrete gauge field in the confining vacua and the supersymmetric index
It has recently been argued that the confining vacua of Yang-Mills theory in
the far infrared can have topological degrees of freedom given by magnetic
gauge field, both in the non-supersymmetric case and in the N=1
supersymmetric case. In this short note we give another piece of evidence by
computing and matching the supersymmetric index of the pure super Yang-Mills
theory both in the ultraviolet and in the infrared.Comment: 12 page
Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d N=2 supersymmetric theories
The worldvolume theory of D3-branes probing four D7-branes and an O7-plane on
is given by a supersymmetric USp x USp gauge
theory. We demonstrate that, at least for a particular choice of the holonomy
at infinity, we can go to a dual description of the gauge theory, where we can
add a Fayet-Iliopoulos term describing the blowing-up of the orbifold to the
smooth ALE space. This allows us to express the moduli space of SO(8)
instantons on the smooth ALE space as a hyperk\"ahler quotient of a flat space
times the Higgs branch of a class S theory. We also discuss a generalization to
, and speculate how to extend the analysis to
bigger SO groups and to ALE spaces of other types.Comment: 18 pages, 10 figures; v2: additional references and minor changes;
published versio
Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
Supersymmetric gauge theories in five dimensions often exhibit less symmetry
than the ultraviolet fixed points from which they flow. The fixed points might
have larger flavor symmetry or they might even be secretly six-dimensional
theories on S^1. Here we provide a simple criterion when such symmetry
enhancement in the ultraviolet should occur, by a direct study of the fermionic
zero modes around one-instanton operators.Comment: v3: 20 pages; an error in Sec. 4.2 corrected, overall conclusion
unchanged. published versio
- …