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      The star-triangle relation, lens partition function, and hypergeometric sum/integrals

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      Journal of High Energy Physics
      Springer Nature

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          Localization of gauge theory on a four-sphere and supersymmetric Wilson loops

          We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N=4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N=2 and the N=2* supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional N=2 superconformal gauge theory is treated similarly.
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            An Index for 4 dimensional Super Conformal Theories

            We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on \(S^3 \times \) time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the \(\mathcal{N}=4\) theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in \(AdS_5\times S^5\) and find perfect agreement at large \(N\) and small charges. Our index does not reproduce the entropy of supersymmetric black holes in \(AdS_5\), but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the \({\cal N}=4\) theory. We note that entropy for some small supersymmetric \(AdS_5\) black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the \(\mathcal{N}=4\) Yang Mills theory.
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              Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories

              N. Seiberg (1994)
              We demonstrate electric-magnetic duality in N=1 supersymmetric non-Abelian gauge theories in four dimensions by presenting two different gauge theories (different gauge groups and quark representations) leading to the same non-trivial long distance physics. The quarks and gluons of one theory can be interpreted as solitons (non-Abelian magnetic monopoles) of the elementary fields of the other theory. The weak coupling region of one theory is mapped to a strong coupling region of the other. When one of the theories is Higgsed by an expectation value of a squark, the other theory is confined. Massless glueballs, baryons and Abelian magnetic monopoles in the confining description are the weakly coupled elementary quarks (i.e.\ solitons of the confined quarks) in the dual Higgs description.
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                Author and article information

                Journal
                Journal of High Energy Physics
                J. High Energ. Phys.
                Springer Nature
                1029-8479
                February 2017
                February 8 2017
                February 2017
                : 2017
                : 2
                Article
                10.1007/JHEP02(2017)040
                ec50c54f-c0ab-4858-af89-bf4b89d14e87
                © 2017
                History

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