Two-dimensional supersymmetric gauge theories with exceptional gauge groups

Chen, Zhuo; Gu, Wei; Parsian, Hadi; Sharpe, Eric

doi:10.4310/atmp.2020.v24.n1.a3

Cited by 11 publications

(27 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Two-dimensional pure (2,2) supersymmetric gauge theories with gauge group SU(k) were studied in [1], which argued that the theory flows in the IR to a free theory of k − 1 twisted chiral multiplets. In our previous work [2,3], we looked at the nonabelian mirrors [2] of these theories, confirming the prediction of [1], and also extending to other gauge theories. Specifically, [2] looked at two-dimensional pure SU(k), SO(k), and Sp(2k) gauge theories, and [3] looked at pure G 2 , F 4 , and E 6,7,8 gauge theories.…”

Section: Introductionsupporting

confidence: 78%

“…In our previous work [2,3], we looked at the nonabelian mirrors [2] of these theories, confirming the prediction of [1], and also extending to other gauge theories. Specifically, [2] looked at two-dimensional pure SU(k), SO(k), and Sp(2k) gauge theories, and [3] looked at pure G 2 , F 4 , and E 6,7,8 gauge theories. In each case, computations in the mirror suggested that the mirror flows in the IR to a theory of twisted chiral multiplets,…”

Section: Introductionsupporting

confidence: 78%

“…To be completely clear, the nonabelian mirror analysis of [2,3] can explicitly determine for which discrete theta angles supersymmetric vacua exist, and the number of degrees of freedom remaining in the IR in those discrete theta angles. However, the nonabelian mirror analysis of [2,3] did not explicitly exclude all possible interactions -it can count the number of degrees of freedom, and for the same reasons as in [1] one may expect that those degrees of freedom are free, but the mirror construction does not explicitly demonstrate that the result is necessarily a free theory, a limitation shared by the current work.…”

Section: Jhep04(2021)261mentioning

confidence: 99%

“…In any event, the analyses of [1][2][3] still left a few groups unanalyzed, namely further quotients of theories above in cases in which the gauge group has a nontrivial center. These analyses require a deeper understanding of the difference between the mirror to a G gauge theory and a G/K gauge theory, for K a subgroup of the center of G, and also an understanding of the mirrors of more intricate discrete theta angles than described in [2], which is the reason they were not previously discussed.…”

Section: Jhep04(2021)261mentioning

confidence: 99%

See 3 more Smart Citations

Notes on two-dimensional pure supersymmetric gauge theories

Sharpe

Zou

2021

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

In this note we study IR limits of pure two-dimensional supersymmetric gauge theories with semisimple non-simply-connected gauge groups including SU(k)/ℤk, SO(2k)/ℤ2, Sp(2k)/ℤ2, E6/ℤ3, and E7/ℤ2 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. In particular, the discrete theta angles in these cases are considerably more intricate than those of the pure gauge theories studied in previous papers, so we discuss the realization of these more complex discrete theta angles in the mirror construction. We find that discrete theta angles, both in the original gauge theory and their mirrors, are intimately related to the description of centers of universal covering groups as quotients of weight lattices by root sublattices. We perform numerous consistency checks, comparing results against basic group-theoretic relations as well as with decomposition, which describes how two-dimensional theories with one-form symmetries (such as pure gauge theories with nontrivial centers) decompose into disjoint unions, in this case of pure gauge theories with quotiented gauge groups and discrete theta angles.

show abstract

Section: Introductionsupporting

confidence: 78%

Section: Introductionsupporting

confidence: 78%

Section: Jhep04(2021)261mentioning

confidence: 99%

Section: Jhep04(2021)261mentioning

confidence: 99%

See 2 more Smart Citations

Notes on two-dimensional pure supersymmetric gauge theories

Sharpe

Zou

2021

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…After that, two follow-up works were aimed to do more consistency checks to the mirror proposal as well as other physical results in the gauge theories. One is the mirrors of pure gauge theories of exceptional groups studied in [25] and the other is about the consistency check of Hori-Seiberg dual [11,12] in the mirror LGs [26]. See also [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] for some related works on these directions.…”

Section: Introductionmentioning

confidence: 99%