Bethe Ansatz and supersymmetric vacua

Journal Article · Thu May 14 00:00:00 EDT 2009 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3149487· OSTI ID:21304863

Nekrasov, Nikita ^[1]; Shatashvili, Samson ^[2]

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1. Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette (France)
2. Hamilton Mathematical Institute, Trinity College, Dublin 2 (Ireland)

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 eigenstates of integrable spin chain Hamiltonians. Examples include: the 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 dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T{sup 2}. A consequence of our correspondence is the isomorphism of the quantum cohomology ring of various quiver varieties, such as cotangent bundles to (partial) flag varieties and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. Compactifications of four dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equations.

• OSTI ID: 21304863
• Journal Information: AIP Conference Proceedings, Vol. 1134, Issue 1; Conference: Landau memorial conference on advances in theoretical physics, Chernogolovka (Russian Federation), 22-26 Jun 2008; Other Information: DOI: 10.1063/1.3149487; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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COMPACTIFICATION
EIGENSTATES
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONAL ANALYSIS
GAUGE INVARIANCE
HAMILTONIANS
HUBBARD MODEL
INTEGRAL EQUATIONS
NONLINEAR PROBLEMS
QUANTUM FIELD THEORY
SINE-GORDON EQUATION
SPIN
SUPERSYMMETRY
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
U GROUPS
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