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TMF, 2013, Volume 174, Number 1, Pages 177–192 (Mi tmf8357)  

This article is cited in 7 scientific papers (total in 7 papers)

Four-dimensional superconformal index reloaded

M. Yamazaki


Abstract: We consider the four-dimensional $\mathcal N\ge 1$ superconformal index and its generalization to the lens space. We discuss reductions of the latter to the three-dimensional $\mathcal N\ge 2$ sphere partition function, the three-dimensional $\mathcal N\ge 2$ superconformal index, and the two-dimensional $\mathcal{N}\ge(2,2)$ sphere partition function. We apply these reductions to a class of four-dimensional $\mathcal N=1$ superconformal field theories dual to toric Calabi–Yau manifolds, and we find surprising connections with integrable spin chains and hyperbolic geometry. We comment on the problem of classifying infrared fixed points of four-dimensional and three-dimensional supersymmetric gauge theories.

Keywords: superconformal index, elliptic gamma function, sphere partition function, dimensional reduction

DOI: https://doi.org/10.4213/tmf8357

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English version:
Theoretical and Mathematical Physics, 2013, 174:1, 154–166

Bibliographic databases:


Citation: M. Yamazaki, “Four-dimensional superconformal index reloaded”, TMF, 174:1 (2013), 177–192; Theoret. and Math. Phys., 174:1 (2013), 154–166

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8357
  • http://mi.mathnet.ru/eng/tmf/v174/i1/p177

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sh. S. Razamat, M. Yamazaki, “S-duality and the $\mathscr N=2$ lens space index”, J. High Energy Phys., 2013, no. 10, 048  crossref  mathscinet  zmath  isi  scopus
    2. M. Yamazaki, “New integrable models from the gauge/YBE correspondence”, J. Stat. Phys., 154:3 (2014), 895–911  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. A. P. Kels, “New solutions of the star-triangle relation with discrete and continuous spin variables”, J. Phys. A-Math. Theor., 48:43 (2015), 435201  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. I. Gahramanov, H. Rosengren, “Basic hypergeometry of supersymmetric dualities”, Nucl. Phys. B, 913 (2016), 747–768  crossref  zmath  isi  elib  scopus
    5. I. Gahramanov, A. P. Kels, “The star-triangle relation, lens partition function, and hypergeometric sum/integrals”, J. High Energy Phys., 2017, no. 2, 040  crossref  mathscinet  isi  scopus
    6. F. Benini, B. Le Floch, “Supersymmetric localization in two dimensions”, J. Phys. A-Math. Theor., 50:44 (2017), 443003  crossref  mathscinet  zmath  isi  scopus
    7. I. Gahramanov, Sh. Jafarzade, “Integrable lattice spin models from supersymmetric dualities”, Phys. Part. Nuclei Lett., 15:6 (2018), 650–667  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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