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The Gauge-Bethe Correspondence and Geometric Representation Theory · Around

2010

The Gauge-Bethe Correspondence and Geometric Representation Theory

Orlando, Domenico, Reffert, Susanne

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The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories.

Up to now, this correspondence has been an observation; the underlying reason for its existence remaining elusive.
We argue here that geometrical representation theory is the mathematical foundation of the Gauge/Bethe correspondence, and it provides a framework to study families of gauge theories in a unified way.

Built on

A. N. Kirillov and N. Y. Reshetikhin, The Bethe ansatz and the combinatorics of Young tableaux
1986
Earlier work this paper cites.
hep-th/9605187
L. D. Faddeev, How algebraic Bethe ansatz works for integrable model · 1998
Earlier work this paper cites.
H. Nakajima, Quiver varieties and Kac-Moody algebras
1998
Earlier work this paper cites.

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N. A. Nekrasov and S. L. Shatashvili, Supersymmetric vacua and Bethe ansatz
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2009
Cited alongside, same era.
N. A. Nekrasov and S. L. Shatashvili, Quantization of Integrable Systems and Four Dimensional Gauge Theories
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Cited in the paper.

Then

N. A. Nekrasov and S. L. Shatashvili, Quantum integrability and supersymmetric vacua
Original
2009
Later among the works it cites.
D. Orlando and S. Reffert, Relating Gauge Theories via Gauge/Bethe Correspondence
Original
2010
Closest in time.
Birkhäuser Boston, 2010
N. Chriss and V. Ginzburg, Representation Theory and Complex Geometry · 2010
Closest in time.

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