Abstract
We compute the supersymmetric partition function on \({L(r,1)\times \mathbb{S}^1}\) , the lens space index, for 4d gauge theories related by supersymmetric dualities and involving non simply-connected groups. This computation is sensitive to the global properties of the underlying gauge group and to discrete theta angle parameters and thus distinguishes versions of dualities differing by such. We explicitly discuss \({\mathcal{N}=1}\) so(N c ) Seiberg dualities and \({\mathcal{N}=4\,su(N_c)}\) S-dualities.
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Benini, F., Nishioka, T., Yamazaki, M.: 4d index to 3d index and 2d TQFT. Phys. Rev. D 86, 065015 (2012). arXiv:1109.0283 [hep-th]
Romelsberger, C.: Counting chiral primaries in N = 1, d =4 superconformal field theories. Nucl. Phys. B 747, 329 (2006). [hep-th/0510060]
Kinney, J., Maldacena, J.M., Minwalla, S., Raju, S.: An index for 4 dimensional super conformal theories. Commun. Math. Phys. 275, 209 (2007). [hep-th/0510251]
Gadde, A., Rastelli, L., Razamat, S.S., Yan, W.: Gauge theories and macdonald polynomials. Commun. Math. Phys. 319, 147 (2013). arXiv:1110.3740 [hep-th]
Gaiotto, D., Rastelli, L., Razamat, S.S.: Bootstrapping the superconformal index with surface defects. J. High Energy Phys. 2013, 22 (2013). arXiv:1207.3577 [hep-th]
Festuccia, G., Seiberg, N.: Rigid supersymmetric theories in curved superspace. JHEP 1106, 114 (2011). arXiv:1105.0689 [hep-th]
Seiberg, N.: Electric–magnetic duality in supersymmetric nonabelian gauge theories. Nucl. Phys. B 435, 129 (1995). [hep-th/9411149]
Dolan, F.A., Osborn, H.: Applications of the superconformal index for protected operators and q-hypergeometric identities to N =1 dual theories. Nucl. Phys. B 818, 137 (2009). arXiv:0801.4947 [hep-th]
Spiridonov, V.P., Vartanov, G.S.: Elliptic hypergeometry of supersymmetric dualities. Commun. Math. Phys. 304, 797 (2011). arXiv:0910.5944 [hep-th]
Gaiotto, D.: N = 2 dualities. JHEP 1208, 034 (2012). arXiv:0904.2715 [hep-th]
Gadde, A., Pomoni, E., Rastelli, L., Razamat, S.S.: S-duality and 2d topological QFT. JHEP 1003, 032 (2010). arXiv:0910.2225 [hep-th]
Gadde, A., Rastelli, L., Razamat, S.S., Yan, W.: The superconformal index of the E 6 SCFT. JHEP 1008 107 (2010). arXiv:1003.4244 [hep-th]
Spiridonov, V.P., Vartanov, G.S.: Superconformal indices of \({\mathcal{N}=4}\) SYM field theories. Lett. Math. Phys. 100, 97 (2012). arXiv:1005.4196 [hep-th]
Nakayama, Y.: Index for supergravity on AdS(5) x T**1,1 and conifold gauge theory. Nucl. Phys. B 755, 295 (2006). [hep-th/0602284]
Gadde, A., Rastelli, L., Razamat, S.S., Yan, W.: On the superconformal index of N = 1 IR fixed points: a holographic check. JHEP 1103, 041 (2011). arXiv:1011.5278 [hep-th]
Eager, R., Schmude, J., Tachikawa, Y.: Superconformal indices, Sasaki–Einstein manifolds, and cyclic homologies. arXiv:1207.0573 [hep-th]
Aharony, O., Seiberg, N., Tachikawa, Y.: Reading between the lines of four-dimensional gauge theories. J. High Energy Phys. 2013, 115 (2013). arXiv:1305.0318 [hep-th]
Gaiotto, D., Moore, G.W., Neitzke, A.: Framed BPS states. arXiv:1006.0146 [hep-th]
Aharony, O., Razamat, S.S., Seiberg, N., Willett, B.: 3d dualities from 4d dualities for orthogonal groups. J. High Energy Phys. 99 (2013). arXiv:1307.0511 [hep-th]
Pasquetti, S.: Factorisation of N = 2 theories on the squashed 3-sphere. JHEP 1204, 120 (2012). arXiv:1111.6905 [hep-th]
Beem, C., Dimofte, T., Pasquetti, S.: Holomorphic blocks in three dimensions. arXiv:1211.1986 [hep-th]
Krattenthaler, C., Spiridonov, V.P., Vartanov, G.S.: Superconformal indices of three-dimensional theories related by mirror symmetry. JHEP 1106, 008 (2011). arXiv:1103.4075 [hep-th]
Witten, E.: Supersymmetric index in four-dimensional gauge theories. Adv. Theor. Math. Phys. 5, 841 (2002). [hep-th/0006010]
Borel, A., Friedman, R., Morgan, J.W.: Almost commuting elements in compact Lie groups. Memoirs of the American Mathematical Society, Vol. 157. American Mathematical Society, Prividence, RI (2002). arXiv:math/9907007
Schweigert, C.: On moduli spaces of flat connections with nonsimply connected structure group. Nucl. Phys. B 492, 743 (1997). [hep-th/9611092]
Intriligator, K.A., Seiberg, N.: Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO(N(c)) gauge theories. Nucl. Phys. B 444, 125 (1995). [hep-th/9503179]
Vafa, C., Witten, E.: A Strong coupling test of S duality. Nucl. Phys. B 431, 3 (1994). [hep-th/9408074]
Freed, D.S., Moore, G.W., Segal, G.: The uncertainty of fluxes. Commun. Math. Phys. 271, 247 (2007). [hep-th/0605198]
Witten, E.: AdS/CFT correspondence and topological field theory. JHEP 9812, 012 (1998). [hep-th/9812012]
Alday, L.F., Bullimore, M., Fluder, M.: On S-duality of the superconformal index on lens spaces and 2d TQFT. JHEP 1305, 122 (2013). arXiv:1301.7486 [hep-th]
Razamat, S.S., Yamazaki, M.: S-duality and the N = 2 lens space index. J. High Energy Phys. 2013, 48 (2013). arXiv:1306.1543 [hep-th]
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Communicated by N. A. Nekrasov
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Razamat, S.S., Willett, B. Global Properties of Supersymmetric Theories and the Lens Space. Commun. Math. Phys. 334, 661–696 (2015). https://doi.org/10.1007/s00220-014-2111-0
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DOI: https://doi.org/10.1007/s00220-014-2111-0