Built on

W. Gu, H. Parsian and E. Sharpe, “More non-Abelian mirrors and some two-dimensional dualities,” Int. J. Mod. Phys. A 34
Original
1907
Earlier work this paper cites.
W. Gu, J. Guo and E. Sharpe, “A proposal for nonabelian (0,2) mirrors,” arXiv:1908.06036
Original
1908
Earlier work this paper cites.
E. Sharpe, “Undoing decomposition,” Int. J. Mod. Phys. A 34
Original
1911
Earlier work this paper cites.
J. Ang, K. Roumpedakis and S. Seifnashri, “Line operators of gauge theories on non-Spin manifolds,” JHEP 04
Original
1911
Earlier work this paper cites.
Y. Tanizaki and M. Ünsal, “Modified instanton sum in QCD and higher-groups,” JHEP 03
Original
1912
Earlier work this paper cites.
E. Witten, “ θ \theta vacua in two-dimensional quantum chromodynamics,” Nuovo Cim. A 51
1979
Earlier work this paper cites.
T. Bröcker, T. tom Dieck, Representations of compact Lie groups
1985
Earlier work this paper cites.
W. Fulton, J. Harris, Representation theory: a first course
1991
Earlier work this paper cites.
K. Hori, “Global aspects of gauged Wess-Zumino-Witten models,” Commun. Math. Phys. 182
1996
Earlier work this paper cites.
H. Georgi, Lie algebras in particle physics
1999
Earlier work this paper cites.

Similar

W. Gu, “Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities,” arXiv:2001.10562
Original
2001
Cited alongside, same era.
T. Pantev and E. Sharpe, “GLSM’s for gerbes (and other toric stacks),” Adv. Theor. Math. Phys. 10
2006
Cited alongside, same era.
S. Hellerman, A. Henriques, T. Pantev, E. Sharpe and M. Ando, “Cluster decomposition, T-duality, and gerby CFT’s,” Adv. Theor. Math. Phys. 11
2007
Cited alongside, same era.
K. Rietsch, “A mirror symmetry construction for q H T ∗ ( G / P ) q qH^{*}_{T}(G/P)_{q} ,” Adv. Math. 217
2008
Cited alongside, same era.
A. Caldararu, J. Distler, S. Hellerman, T. Pantev and E. Sharpe, “Non-birational twisted derived equivalences in abelian GLSMs,” Commun. Math. Phys. 294
Original
2010
Cited alongside, same era.

Then

J. Halverson, V. Kumar and D. R. Morrison, “New methods for characterizing phases of 2D supersymmetric gauge theories,” JHEP 1309
Original
2013
Later among the works it cites.
E. Sharpe, “Decomposition in diverse dimensions,” Phys. Rev. D 90
Original
2014
Later among the works it cites.
N. A. Nekrasov and S. L. Shatashvili, “Bethe/Gauge correspondence on curved spaces,” JHEP 1501
Original
2015
Later among the works it cites.
C. Closset, S. Cremonesi and D. S. Park, “The equivariant A-twist and gauged linear sigma models on the two-sphere,” JHEP 1506
Original
2015
Later among the works it cites.
O. Aharony, S. S. Razamat, N. Seiberg and B. Willett, “The long flow to freedom,” JHEP 1702

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2020

Notes on two-dimensional pure supersymmetric gauge theories

Gu, W., Sharpe, E., Zou, H.

Understand

In this note we study IR limits of pure two-dimensional supersymmetric gauge theories with semisimple non-simply-connected gauge groups including SU(k)/Z_k, SO(2k)/Z_2, Sp(2k)/Z_2, E_6/Z_3, and E_7/Z_2 for various discrete theta angles, both directly in the gauge theory and also in nonabelian mirrors, extending a classification begun in previous work.

We find in each case that there are supersymmetric vacua for precisely one value of the discrete theta angle, and no supersymmetric vacua for other values, hence supersymmetry is broken in the IR for most discrete theta angles.
Furthermore, for the one distinguished value of the discrete theta angle for which supersymmetry is unbroken, the theory has as many twisted chiral multiplet degrees of freedom in the IR as the rank.
We take this opportunity to further develop the technology of nonabelian mirrors to discuss how the mirror to a G gauge theory differs from the mirror to a G/K gauge theory for K a subgroup of the center of G.

Built on

W. Gu, H. Parsian and E. Sharpe, “More non-Abelian mirrors and some two-dimensional dualities,” Int. J. Mod. Phys. A 34
Original
1907
Earlier work this paper cites.
W. Gu, J. Guo and E. Sharpe, “A proposal for nonabelian (0,2) mirrors,” arXiv:1908.06036
Original
1908
Earlier work this paper cites.
E. Sharpe, “Undoing decomposition,” Int. J. Mod. Phys. A 34
Original
1911
Earlier work this paper cites.
J. Ang, K. Roumpedakis and S. Seifnashri, “Line operators of gauge theories on non-Spin manifolds,” JHEP 04
Original
1911
Earlier work this paper cites.
Y. Tanizaki and M. Ünsal, “Modified instanton sum in QCD and higher-groups,” JHEP 03
Original
1912
Earlier work this paper cites.
E. Witten, “ θ \theta vacua in two-dimensional quantum chromodynamics,” Nuovo Cim. A 51
1979
Earlier work this paper cites.
T. Bröcker, T. tom Dieck, Representations of compact Lie groups
1985
Earlier work this paper cites.
W. Fulton, J. Harris, Representation theory: a first course
1991
Earlier work this paper cites.
K. Hori, “Global aspects of gauged Wess-Zumino-Witten models,” Commun. Math. Phys. 182
1996
Earlier work this paper cites.
H. Georgi, Lie algebras in particle physics
1999
Earlier work this paper cites.

Similar

W. Gu, “Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities,” arXiv:2001.10562
Original
2001
Cited alongside, same era.
T. Pantev and E. Sharpe, “GLSM’s for gerbes (and other toric stacks),” Adv. Theor. Math. Phys. 10
2006
Cited alongside, same era.
S. Hellerman, A. Henriques, T. Pantev, E. Sharpe and M. Ando, “Cluster decomposition, T-duality, and gerby CFT’s,” Adv. Theor. Math. Phys. 11
2007
Cited alongside, same era.
K. Rietsch, “A mirror symmetry construction for q H T ∗ ( G / P ) q qH^{*}_{T}(G/P)_{q} ,” Adv. Math. 217
2008
Cited alongside, same era.
A. Caldararu, J. Distler, S. Hellerman, T. Pantev and E. Sharpe, “Non-birational twisted derived equivalences in abelian GLSMs,” Commun. Math. Phys. 294
Original
2010
Cited alongside, same era.