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Gauge Theories and Macdonald Polynomials

Gadde, Abhijit and Rastelli, Leonardo and Razamat, Shlomo S. and Yan, Wenbin (2013) Gauge Theories and Macdonald Polynomials. Communications in Mathematical Physics, 319 (1). pp. 147-193. ISSN 0010-3616. doi:10.1007/s00220-012-1607-8.

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We study the N = 2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class S , which in general do not have one. We test our proposals against several expected dualities. The index can always be interpreted as a correlator in a two-dimensional topological theory, which we identify in each limit as a certain deformation of two-dimensional Yang-Mills theory. The structure constants of the topological algebra are diagonal in the basis of Macdonald polynomials of the holonomies.

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Additional Information:© 2012 Springer-Verlag Berlin Heidelberg. Received: 9 December 2011; Accepted: 27 May 2012. Communicated by N. A. Nekrasov. We would like to thank M. Aganagic, C. Beem, F. van de Bult, T. Dimofte, D. Gaiotto, S. Gukov, D. Jafferis, A. Kirillov Jr, J. Maldacena, Y. Nakayama, N. Nekrasov, A. Okounkov, H. Ooguri, E. Rains, B. van Rees, Y. Tachikawa, and E. Witten for very useful discussions. The research of SSR was supported in part by NSF grant PHY-0969448 and he would like to thank the Aspen Center for Physics, where part of this work was conducted with the support of the National Science Foundation under Grant No. 1066293. LR thanks the Galileo Galilei Institute for hospitality and the INFN for partial support during the completion of this work. AG would like to thank the Tata Institute for Fundamental Research for hospitality during the final stages of this project. This work was supported in part by NSF grant PHY-0969739.
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Istituto Nazionale di Fisica Nucleare (INFN)UNSPECIFIED
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Record Number:CaltechAUTHORS:20130425-081111172
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Official Citation:Gadde, A., L. Rastelli, et al. (2013). "Gauge Theories and Macdonald Polynomials." Communications in Mathematical Physics 319(1): 147-193.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38109
Deposited By: Tony Diaz
Deposited On:25 Apr 2013 23:14
Last Modified:09 Nov 2021 23:33

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