Quantum integrability and supersymmetric vacua
Citation:
Samson L. Shatashvili (with Nikita Nekrasov), Quantum integrability and supersymmetric vacua, Prog.Theor.Phys.Suppl., 177, 2009, 105 - 119Download Item:
0901.4748.pdf (Published (author's copy) - Peer Reviewed) 201.2Kb
Abstract:
Supersymmetric 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. Examples include: t
he Heisenberg
SU
(2)
XXX
spin chain
which is mapped to the two dimensional
U
(
N
) theory with fundamental hypermultiplets, the
XXZ
spin chain which is mapped to the analogous three dimensiona
l super-Yang-Mills theory
compactified on a circle, the
XYZ
spin chain and eight-vertex model which are related to the fo
ur
dimensional theory compactified on
T
2
. A consequence of our correspondence is the isomorphism
of the quantum cohomology ring of various quiver varieties,
such as
T
?
Gr(
N,L
) and the ring
of quantum integrals of motion of various spin chains. The co
rrespondence extends to any spin
group, representations, boundary conditions, and inhomog
eneity, it includes Sinh-Gordon and
non-linear Schr ?odinger models as well as the dynamical spi
n chains like Hubbard model. We give
the gauge-theoretic interpretation of Drinfeld polynomia
ls and Baxter operators. The two-sphere
compactifications of the four dimensional
N
= 2 theories lead to the instanton corrected Bethe
equations. We suggest the Yangian, quantum affine, and ellipt
ic algebras are a completely novel
kind of symmetry of the (collections of the) interacting qua
ntum field theories
Author's Homepage:
http://people.tcd.ie/shatassDescription:
PUBLISHED
Author: SHATASHVILI, SAMSON
Type of material:
Journal ArticleSeries/Report no:
Prog.Theor.Phys.Suppl.;177;
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