Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities

Gu, Wei

doi:10.1007/jhep12(2020)180

Cited by 2 publications

(1 citation statement)

References 44 publications

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“…For connected gauge groups, the Weyl group orbifold acts freely on the critical locus, so as we only consider connected gauge groups in this paper, we shall largely ignore the orbifold, except to take Weyl-invariant combinations of fields. (Mirrors to gauge theories whose gauge groups have multiple components were discussed in [30,31]. )…”

Section: Jhep04(2021)261mentioning

confidence: 99%

Notes on two-dimensional pure supersymmetric gauge theories

Sharpe

Zou

2021

J. High Energ. Phys.

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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.

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Section: Jhep04(2021)261mentioning

confidence: 99%

Notes on two-dimensional pure supersymmetric gauge theories

Sharpe

Zou

2021

J. High Energ. Phys.

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Non-Abelian T-dualities in two dimensional (0, 2) gauged linear sigma models

Bizet,

Díaz-Correa,

García-Compeán

2024

J. High Energ. Phys.

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We consider two dimensional (2D) gauged linear sigma models (GLSMs) with (0, 2) supersymmetry and U(1) gauge group which posses global symmetries. We distinguish between two cases: one obtained as a reduction from the (2, 2) supersymmetric GLSM and another not coming from a reduction. In the first case we find the Abelian T-dual, comparing with previous studies. Then, the Abelian T-dual model of the second case is found. Instanton corrections are also discussed in both situations. We explore the vacua for the scalar potential and we analyse the target space geometry of the dual model. An example with gauge symmetry U(1) × U(1) is discussed, which posses non-Abelian global symmetry. Non-Abelian T-dualization of U(1) (0, 2) 2D GLSMs is implemented for models that arise as a reduction from the (2, 2) case; we study a model with U(1) gauge symmetry and SU(2) global symmetry. It is shown that for a positive definite scalar potential, the dual vacua to $${\mathbb{P}}^{1}$$ constitutes a disk. Instanton corrections to the superpotential are obtained and are shown to be encoded in a shift of the holomorphic function E. We conclude by analyzing an example with SU(2) × SU(2) global symmetry, obtaining that the space of dual vacua to $${\mathbb{P}}^{1}$$ × $${\mathbb{P}}^{1}$$ consists of two copies of the disk, also for the case of positive definite potential. Here we are able to fully integrate the equations of motion of non-Abelian T-duality, improving the analysis with respect to the studies in (2, 2) models.

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Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities

Cited by 2 publications

References 44 publications

Notes on two-dimensional pure supersymmetric gauge theories

Notes on two-dimensional pure supersymmetric gauge theories

Non-Abelian T-dualities in two dimensional (0, 2) gauged linear sigma models

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