8 research outputs found
Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra
We study the basic features of BPS quiver mutations in 4D
supersymmetric quantum field theory with gauge symmetries.\ We show,
for these gauge symmetries, that there is an isotropy group
associated to a set of quiver mutations capturing
information about the BPS spectra. In the strong coupling limit, it is shown
that BPS chambers correspond to finite and closed groupoid orbits with an
isotropy symmetry group isomorphic to the discrete
dihedral groups contained in Coxeter with the
Coxeter number of G. These isotropy symmetries allow to determine the BPS
spectrum of the strong coupling chamber; and give another way to count the
total number of BPS and anti-BPS states of gauge theories. We
also build the matrix realization of these mutation groups from which we read directly the electric-magnetic
charges of the BPS and anti-BPS states of QFT as well as
their matrix intersections. We study as well the quiver mutation symmetries in
the weak coupling limit and give their links with infinite Coxeter groups. We
show amongst others that is contained in
; and isomorphic to the infinite Coxeter
. Other issues such as building
and are also
studied.Comment: LaTeX, 98 pages, 18 figures, Appendix I on groupoids adde
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