Built on

E. Witten, “Constraints on Supersymmetry Breaking,” Nucl. Phys. B 202
1982
Earlier work this paper cites.
J. Chidambaraswamy and R. Sitaramachandrarao, “Asymptotic Results for a Class of Arithmetical Functions,” Mh. Math. 99
1985
Earlier work this paper cites.
D. Collingwood and W. McGovern, “Nilpotent Orbits In Semisimple Lie Algebra,” (1993), CRC Press
1993
Earlier work this paper cites.
R. Donagi and E. Witten, “Supersymmetric Yang-Mills theory and integrable systems,” Nucl. Phys. B 460
1996
Earlier work this paper cites.
E. Witten, “Toroidal compactification without vector structure,” JHEP 9802
1998
Earlier work this paper cites.
A. Keurentjes, A. Rosly and A. V. Smilga, “Isolated vacua in supersymmetric Yang-Mills theories,” Phys. Rev. D 58
1998
Earlier work this paper cites.
A. Keurentjes, “Non-trivial flat connections on the 3-torus I: G(2) and the orthogonal groups,” JHEP 9905
1999
Earlier work this paper cites.

Similar

A. Keurentjes, “Non-trivial flat connections on the 3-torus II. The Exceptional groups F4 and E6, E7, E8,” JHEP 9905
1999
Cited alongside, same era.
N. Dorey, “An Elliptic superpotential for softly broken N=4 supersymmetric Yang-Mills theory,” JHEP 9907
1999
Cited alongside, same era.
O. Aharony, N. Dorey and S. P. Kumar, “New modular invariance in the N=1* theory, operator mixings and supergravity singularities,” JHEP 0006
2000
Cited alongside, same era.
A. Hanany and J. Troost, “Orientifold planes, affine algebras and magnetic monopoles,” JHEP 0108
2001
Cited alongside, same era.
A. Borel, R. Friedman, J. Morgan, “Almost Commuting Elements in Compact Lie Groups,” Memoirs of the American Mathematical Society, Volume 157, Issue 747, AMS 2002
2002
Cited alongside, same era.

Then

O. Aharony, N. Seiberg and Y. Tachikawa, “Reading between the lines of four-dimensional gauge theories,” JHEP 1308
Original
2013
Later among the works it cites.
O. Aharony, S. S. Razamat, N. Seiberg and B. Willett, “3 d d dualities from 4 d d dualities for orthogonal groups,” JHEP 1308
Original
2013
Later among the works it cites.
M. M. Anber and E. Poppitz, “On the global structure of deformed Yang-Mills theory and QCD(adj) on ℝ 3 × 𝕊 1 {\mathrm{\mathbb{R}}}^{3}\times{\mathbb{S}}^{1} ,” JHEP 1510
Original
2015
Later among the works it cites.
A. Bourget and J. Troost, “Counting the Massive Vacua of N=1* Super Yang-Mills Theory,” JHEP 1508
Original
2015
Later among the works it cites.
A. Bourget and J. Troost, “Duality and modularity in elliptic integrable systems and vacua of 𝒩 = 1 ∗ \mathcal{N}={1}^{\ast} gauge theories,” JHEP 1504

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2016

The Arithmetic of Supersymmetric Vacua

Bourget, Antoine, Troost, Jan

Understand

We provide explicit formulas for the number of vacua of four-dimensional pure N=1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators.

These form a key ingredient in the semi-classical calculation of the number of massive vacua of N=1* gauge theories with gauge algebra su(n) compactified on a circle.
Using arithmetic, we express that number in an SL(2,Z) duality invariant manner.
We confirm our tally of massive vacua of the N=1* theories by a count of inequivalent extrema of the exact superpotential.

Built on

E. Witten, “Constraints on Supersymmetry Breaking,” Nucl. Phys. B 202
1982
Earlier work this paper cites.
J. Chidambaraswamy and R. Sitaramachandrarao, “Asymptotic Results for a Class of Arithmetical Functions,” Mh. Math. 99
1985
Earlier work this paper cites.
D. Collingwood and W. McGovern, “Nilpotent Orbits In Semisimple Lie Algebra,” (1993), CRC Press
1993
Earlier work this paper cites.
R. Donagi and E. Witten, “Supersymmetric Yang-Mills theory and integrable systems,” Nucl. Phys. B 460
1996
Earlier work this paper cites.
E. Witten, “Toroidal compactification without vector structure,” JHEP 9802
1998
Earlier work this paper cites.
A. Keurentjes, A. Rosly and A. V. Smilga, “Isolated vacua in supersymmetric Yang-Mills theories,” Phys. Rev. D 58
1998
Earlier work this paper cites.
A. Keurentjes, “Non-trivial flat connections on the 3-torus I: G(2) and the orthogonal groups,” JHEP 9905
1999
Earlier work this paper cites.

Similar

A. Keurentjes, “Non-trivial flat connections on the 3-torus II. The Exceptional groups F4 and E6, E7, E8,” JHEP 9905
1999
Cited alongside, same era.
N. Dorey, “An Elliptic superpotential for softly broken N=4 supersymmetric Yang-Mills theory,” JHEP 9907
1999
Cited alongside, same era.
O. Aharony, N. Dorey and S. P. Kumar, “New modular invariance in the N=1* theory, operator mixings and supergravity singularities,” JHEP 0006
2000
Cited alongside, same era.
A. Hanany and J. Troost, “Orientifold planes, affine algebras and magnetic monopoles,” JHEP 0108
2001
Cited alongside, same era.
A. Borel, R. Friedman, J. Morgan, “Almost Commuting Elements in Compact Lie Groups,” Memoirs of the American Mathematical Society, Volume 157, Issue 747, AMS 2002
2002
Cited alongside, same era.

Then

O. Aharony, N. Seiberg and Y. Tachikawa, “Reading between the lines of four-dimensional gauge theories,” JHEP 1308
Original
2013
Later among the works it cites.
O. Aharony, S. S. Razamat, N. Seiberg and B. Willett, “3 d d dualities from 4 d d dualities for orthogonal groups,” JHEP 1308
Original
2013
Later among the works it cites.
M. M. Anber and E. Poppitz, “On the global structure of deformed Yang-Mills theory and QCD(adj) on ℝ 3 × 𝕊 1 {\mathrm{\mathbb{R}}}^{3}\times{\mathbb{S}}^{1} ,” JHEP 1510
Original
2015
Later among the works it cites.
A. Bourget and J. Troost, “Counting the Massive Vacua of N=1* Super Yang-Mills Theory,” JHEP 1508
Original
2015
Later among the works it cites.
A. Bourget and J. Troost, “Duality and modularity in elliptic integrable systems and vacua of 𝒩 = 1 ∗ \mathcal{N}={1}^{\ast} gauge theories,” JHEP 1504

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

E. Witten, “Supersymmetric index in four-dimensional gauge theories,” Adv. Theor. Math. Phys. 5

2002

Cited alongside, same era.

S. Kim, K. M. Lee, H. U. Yee and P. Yi, “The N = 1* theories on R**(1+2) x S1 with twisted boundary conditions,” JHEP 0408

2004

Cited alongside, same era.

V. G. Kac and A. V. Smilga, “Vacuum structure in supersymmetric Yang-Mills theories with any gauge group,” In *Shifman, M.A. (ed.): The many faces of the superworld* 185-234 [hep-th/9902029]

Cited in the paper.

Original

2015

Later among the works it cites.

A. Bourget and J. Troost, “On the 𝒩 = 1 ∗ \mathcal{N}={1}^{\ast} gauge theory on a circle and elliptic integrable systems,” JHEP 1601

Original

2016

Closest in time.