GLSMs, joins, and nonperturbatively-realized geometries

Abstract

In this work we give a gauged linear sigma model (GLSM) realization of pairs of homologically projective dual Calabi-Yaus that have recently been constructed in the mathematics literature. Many of the geometries can be realized mathematically in terms of joins. We discuss how joins can be described in terms of GLSMs and how the associated Calabi-Yaus arise as phases in the GLSMs. Due to strong-coupling phenomena in the GLSM, the geometries are realized via a mix of perturbative and non-perturbative effects. We apply two-dimensional gauge dualities to construct dual GLSMs. Geometries that are realized perturbatively in one GLSM, are realized non-perturbatively in the dual, and vice versa.

Smoothing Calabi–Yau toric hypersurfaces using the Gross–Siebert algorithm

“…The differential operator is associated to the invariant part of the rank-three Calabi–Yau threefold (with ) obtained from the pair with respect to a subgroup of . This action is free, and the quotient of by this action is the rank-one Calabi–Yau threefold with obtained in [KS19, § ].…”

“…Knapp and Sharpe describe a family of (rank-one) Calabi-Yau threefolds in [KS19] corresponding to the Picard-Fuchs operator (14). We suggest the following conjecture, relating the family obtained in [KS19] to that described in Example 5.9…”

“…Consonant with this, we must verify a global condition (existence of a polarisation) before we are able to smooth all singularities of . In this language, we expect the join construction of Knapp and Sharpe [KS19, § ] to be related to the ‘simultaneous Jerry’ smoothing.…”

A toolkit for twisted chiral superfields

“…The last two are symmetric in their indices. Substituting the respective contributions of the previous expressions (18) and (20) in (24), the Lagrangian becomes…”

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

“…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.…”