Supersymmetric vacua and Bethe ansatz
Citation:
Samson L. Shatashvili (with Nikita Nekrasov), Supersymmetric vacua and Bethe ansatz, Nucl.Phys.Proc.Suppl., 192-193, 2009, 91 - 112Download Item:
0901.4744v2.pdf (Published (author's copy) - Peer Reviewed) 310.1Kb
Abstract:
This note is a short announcement of some results of a longer p
aper where the supersymmet-
ric vacua of two dimensional
N
= 4 gauge theories with matter, softly broken by the twisted
masses down to
N
= 2, are shown to be in one-to-one correspondence with the eig
enstates of
integrable spin chain Hamiltonians. The Heisenberg
SU
(2)
XXX
spin chain is mapped to the
two dimensional
U
(
N
) theory with fundamental hypermultiplets, the
XXZ
spin chain is mapped
to the analogous three dimensional super-Yang-Mills theor
y compactified on a circle, the
XY Z
spin chain and eight-vertex model are related to the four dim
ensional theory compactified on
T
2
.
The correspondence extends to any spin group, representati
ons, boundary conditions, and inho-
mogeneity, it includes Sinh-Gordon and non-linear Schr ?od
inger models as well as the dynamical
spin chains such as the Hubbard model. Compactifications of f
our dimensional
N
= 2 theories
on a two-sphere lead to the instanton-corrected Bethe equat
ions. We propose a completely novel
way for the Yangian, quantum affine, and elliptic algebras to a
ct as a symmetry of a union of
quantum field theories
Author's Homepage:
http://people.tcd.ie/shatassDescription:
PUBLISHED
Author: SHATASHVILI, SAMSON
Type of material:
Journal ArticleSeries/Report no:
Nucl.Phys.Proc.Suppl.;192-193;
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