Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra

Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra We derive the generalization of the Knizhnik-Zamolodchikov equation (KZE) associated with the Ding-Iohara-Miki algebra Uq,t(gl^^1). We demonstrate that certain refined topological string amplitudes satisfy these equations and find that the braiding transformations are performed by the R matrix of Uq,t(gl^^1). The resulting system is the uplifting of the u^1 Wess-Zumino-Witten model. The solutions to the (q,t) KZE are identified with the (spectral dual of) building blocks of the Nekrasov partition function for five-dimensional linear quiver gauge theories. We also construct an elliptic version of the KZE and discuss its modular and monodromy properties, the latter being related to a dual version of the KZE. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra

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Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra

Abstract

We derive the generalization of the Knizhnik-Zamolodchikov equation (KZE) associated with the Ding-Iohara-Miki algebra Uq,t(gl^^1). We demonstrate that certain refined topological string amplitudes satisfy these equations and find that the braiding transformations are performed by the R matrix of Uq,t(gl^^1). The resulting system is the uplifting of the u^1 Wess-Zumino-Witten model. The solutions to the (q,t) KZE are identified with the (spectral dual of) building blocks of the Nekrasov partition function for five-dimensional linear quiver gauge theories. We also construct an elliptic version of the KZE and discuss its modular and monodromy properties, the latter being related to a dual version of the KZE.
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Publisher
American Physical Society (APS)
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.96.026021
Publisher site
See Article on Publisher Site

Abstract

We derive the generalization of the Knizhnik-Zamolodchikov equation (KZE) associated with the Ding-Iohara-Miki algebra Uq,t(gl^^1). We demonstrate that certain refined topological string amplitudes satisfy these equations and find that the braiding transformations are performed by the R matrix of Uq,t(gl^^1). The resulting system is the uplifting of the u^1 Wess-Zumino-Witten model. The solutions to the (q,t) KZE are identified with the (spectral dual of) building blocks of the Nekrasov partition function for five-dimensional linear quiver gauge theories. We also construct an elliptic version of the KZE and discuss its modular and monodromy properties, the latter being related to a dual version of the KZE.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Jul 15, 2017

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