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A. D. Shapere and Y. Tachikawa, “Central charges of N=2 superconformal field theories in four dimensions,” JHEP
Original
1957
Earlier work this paper cites.
N. Arkani-Hamed, A. G. Cohen, and H. Georgi, “(De)constructing dimensions,” Phys.Rev.Lett
2001
Earlier work this paper cites.
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas, and M. Van Raamsdonk, “The Hagedorn / Deconfinement Phase Transition in Weakly Coupled Large N N Gauge Theories,” Adv. Theor. Math. Phys
2004
Earlier work this paper cites.
C. Romelsberger, “Counting Chiral Primaries in 𝒩 = 1 {\mathcal{N}}\!=1 , d = 4 d=4 Superconformal Field Theories,” Nucl. Phys
2006
Earlier work this paper cites.
H. Lin and J. M. Maldacena, “Fivebranes from Gauge Theory,” Phys. Rev
2006
Earlier work this paper cites.
Y. Hikida, “Phase Transitions of Large N N Orbifold Gauge Theories,” JHEP
2006
Earlier work this paper cites.
S. Matsuura and K. Ohta, “Localization on the D-Brane, Two-Dimensional Gauge Theory and Matrix Models,” Phys. Rev
2006
Earlier work this paper cites.
J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, “An Index for 4 Dimensional Super Conformal Theories,” Commun. Math. Phys
2007
Earlier work this paper cites.
J. Bhattacharya, S. Bhattacharyya, S. Minwalla, and S. Raju, “Indices for Superconformal Field Theories in 3,5 and 6 Dimensions,” JHEP
Original
2008
Earlier work this paper cites.

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2011

Benini, Francesco, Nishioka, Tatsuma, Yamazaki, Masahito

We compute the 4d superconformal index for N=1,2 gauge theories on S^1 x L(p,1), where L(p,1) is a lens space.

We find that the 4d N=1,2 index on S^1 x L(p,1) reduces to a 3d N=2,4 index on S^1 x S^2 in the large p limit, and to a 3d partition function on a squashed L(p,1) when the size of temporal S^1 shrinks to zero.
As an application of our index, we study 4d N=2 superconformal field theories arising from the 6d N=(2,0) A_1 theory on a punctured Riemann surface, and conjecture the existence of a 2d Topological Quantum Field Theory on the Riemann surface whose correlation function coincides with the 4d N=2 index on S^1 x L(p,1).

A. D. Shapere and Y. Tachikawa, “Central charges of N=2 superconformal field theories in four dimensions,” JHEP
Original
1957
Earlier work this paper cites.
N. Arkani-Hamed, A. G. Cohen, and H. Georgi, “(De)constructing dimensions,” Phys.Rev.Lett
2001
Earlier work this paper cites.
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas, and M. Van Raamsdonk, “The Hagedorn / Deconfinement Phase Transition in Weakly Coupled Large N N Gauge Theories,” Adv. Theor. Math. Phys
2004
Earlier work this paper cites.
C. Romelsberger, “Counting Chiral Primaries in 𝒩 = 1 {\mathcal{N}}\!=1 , d = 4 d=4 Superconformal Field Theories,” Nucl. Phys
2006
Earlier work this paper cites.
H. Lin and J. M. Maldacena, “Fivebranes from Gauge Theory,” Phys. Rev
2006
Earlier work this paper cites.
Y. Hikida, “Phase Transitions of Large N N Orbifold Gauge Theories,” JHEP
2006
Earlier work this paper cites.
S. Matsuura and K. Ohta, “Localization on the D-Brane, Two-Dimensional Gauge Theory and Matrix Models,” Phys. Rev
2006
Earlier work this paper cites.
J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, “An Index for 4 Dimensional Super Conformal Theories,” Commun. Math. Phys
2007
Earlier work this paper cites.
J. Bhattacharya, S. Bhattacharyya, S. Minwalla, and S. Raju, “Indices for Superconformal Field Theories in 3,5 and 6 Dimensions,” JHEP
Original
2008
Earlier work this paper cites.