Built on

E. Lerman, S. Tolman, “Symplectic Toric Orbifolds,” Trans. Amer. Math. Soc., 349
1997
Earlier work this paper cites.
M. Nishizawa, “An elliptic analogue of the multiple gamma function,” J. Phys. A 34 no. 36, (2001) 7411
2001
Earlier work this paper cites.
C. Romelsberger, “Counting chiral primaries in N = 1, d=4 superconformal field theories,” Nucl. Phys. B 747
2006
Earlier work this paper cites.
J. P. Gauntlett, D. Martelli, J. Sparks and S. T. Yau, “Obstructions to the existence of Sasaki-Einstein metrics,” Commun. Math. Phys. 273
2007
Earlier work this paper cites.
D. Martelli, J. Sparks and S. T. Yau, “Sasaki-Einstein manifolds and volume minimisation,” Commun. Math. Phys. 280
2008
Earlier work this paper cites.
M. Spreafico, “On the Barnes double zeta and Gamma functions,” Journal of Number Theory 129 (2009)
2009
Earlier work this paper cites.
V. Pestun, “Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” Commun. Math. Phys. 313
Original
2012
Earlier work this paper cites.
C. Klare, A. Tomasiello and A. Zaffaroni, “Supersymmetry on Curved Spaces and Holography,” JHEP 1208
Original
2012
Earlier work this paper cites.
T. T. Dumitrescu, G. Festuccia and N. Seiberg, “Exploring Curved Superspace,” JHEP 1208
Original
2012
Earlier work this paper cites.
F. Benini, T. Nishioka and M. Yamazaki, “4d Index to 3d Index and 2d TQFT,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.

Similar

L. F. Alday, M. Fluder and J. Sparks, “The Large N limit of M2-branes on Lens spaces,” JHEP 1210
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2012
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Then

E. Gerchkovitz, “Constraints on the R-charges of free bound states from the Römelsberger index,” JHEP 1407
Original
2014
Later among the works it cites.
B. Assel, D. Cassani and D. Martelli, “Supersymmetric counterterms from new minimal supergravity,” JHEP 1411
Original
2014
Later among the works it cites.
V. P. Spiridonov, “Modified elliptic gamma functions and 6d superconformal indices,” Lett. Math. Phys. 104
Original
2014
Later among the works it cites.
D. Cassani and D. Martelli, “The gravity dual of supersymmetric gauge theories on a squashed S 1 × S 3 S^{1}\times S^{3} ,” JHEP 1408
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2014
Later among the works it cites.
J. Lorenzen and D. Martelli, “Comments on the Casimir energy in supersymmetric field theories,” JHEP 1507

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2015

The character of the supersymmetric Casimir energy

Martelli, Dario, Sparks, James

Understand

We study the supersymmetric Casimir energy $E_\mathrm{susy}$ of $\mathcal{N}=1$ field theories with an R-symmetry, defined on rigid supersymmetric backgrounds $S^1\times M_3$, using a Hamiltonian formalism.

These backgrounds admit an ambi-Hermitian geometry, and we show that the net contributions to $E_\mathrm{susy}$ arise from certain twisted holomorphic modes on $\mathbb{R}\times M_3$, with respect to both complex structures.
The supersymmetric Casimir energy may then be identified as a limit of an index-character that counts these modes.
In particular this explains a recent observation relating $E_\mathrm{susy}$ on $S^1\times S^3$ to the anomaly polynomial.

Built on

E. Lerman, S. Tolman, “Symplectic Toric Orbifolds,” Trans. Amer. Math. Soc., 349
1997
Earlier work this paper cites.
M. Nishizawa, “An elliptic analogue of the multiple gamma function,” J. Phys. A 34 no. 36, (2001) 7411
2001
Earlier work this paper cites.
C. Romelsberger, “Counting chiral primaries in N = 1, d=4 superconformal field theories,” Nucl. Phys. B 747
2006
Earlier work this paper cites.
J. P. Gauntlett, D. Martelli, J. Sparks and S. T. Yau, “Obstructions to the existence of Sasaki-Einstein metrics,” Commun. Math. Phys. 273
2007
Earlier work this paper cites.
D. Martelli, J. Sparks and S. T. Yau, “Sasaki-Einstein manifolds and volume minimisation,” Commun. Math. Phys. 280
2008
Earlier work this paper cites.
M. Spreafico, “On the Barnes double zeta and Gamma functions,” Journal of Number Theory 129 (2009)
2009
Earlier work this paper cites.
V. Pestun, “Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” Commun. Math. Phys. 313
Original
2012
Earlier work this paper cites.
C. Klare, A. Tomasiello and A. Zaffaroni, “Supersymmetry on Curved Spaces and Holography,” JHEP 1208
Original
2012
Earlier work this paper cites.
T. T. Dumitrescu, G. Festuccia and N. Seiberg, “Exploring Curved Superspace,” JHEP 1208
Original
2012
Earlier work this paper cites.
F. Benini, T. Nishioka and M. Yamazaki, “4d Index to 3d Index and 2d TQFT,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.