Journal article 916 views
Quantization of integrable systems and a 2d/4d duality
Journal of High Energy Physics, Volume: 2011, Issue: 10, Start page: 077
Swansea University Author:
Timothy Hollowood
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DOI (Published version): 10.1007/JHEP10(2011)077
Abstract
We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two dimensi...
| Published in: | Journal of High Energy Physics |
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| ISSN: | 1029-8479 |
| Published: |
Springer
2011
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa7245 |
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| Abstract: |
We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two dimensions. On the four dimensional side, our main example is N=2 SQCD with gauge group SU(L) and 2L fundamental flavours. Using ideas of Nekrasov and Shatashvili, we argue that the Coulomb branch of this theory provides a quantization of the classical Heisenberg SL(2) spin chain. Agreement with the standard quantization via the Algebraic Bethe Ansatz implies the existence of an isomorphism between the chiral ring of the 4d theory and that of a certain two-dimensional theory. The latter can be understood as the worldvolume theory on a surface operator/vortex string probing the Higgs branch of the same 4d theory. We check the proposed duality by explicit calculation at low orders in the instanton expansion. One striking consequence is that the Seiberg-Witten solution of the 4d theory is captured by a one-loop computation in two dimensions. The duality also has interesting connections with the AGT conjecture, matrix models and topological string theory where it corresponds to a refined version of the geometric transition. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
10 |
| Start Page: |
077 |