Linear Sigma Models With Strongly Coupled Phases -- One Parameter Models

TL;DR

The paper develops two families of 2D (2,2) GLSMs, labeled (A) and (S), whose strongly coupled phases feature unbroken gauge subgroups and yield rich Calabi–Yau/non-Calabi–Yau geometries. By leveraging recent localization techniques, it computes the two-sphere partition function to access the Kähler metric on the moduli space and the fundamental period, linking field-theoretic data to Picard–Fuchs structures. A key result is the emergence of equivalences of D-brane categories and, strikingly, an exact match of Kähler moduli spaces between two distinct SCFTs with different Hodge numbers, suggesting deep ties to homological projective duality and duality in the B-brane sector. The work extends the landscape of Calabi–Yau realizations via linear A(p) and S(p) data, provides novel hybrids and true hybrids, and demonstrates practical duality-based methods to access strongly coupled phases. Overall, the paper offers a systematic framework for constructing and analyzing strongly coupled GLSMs, with substantial implications for moduli-space geometry, mirror symmetry, and derived-category dualities.

Abstract

We systematically construct a class of two-dimensional $(2,2)$ supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken. We study some of their properties by employing a recently developed technique. The focus of the present work is on models with one Kähler parameter. The models include those corresponding to Calabi-Yau threefolds, extending three examples found earlier by a few more, as well as Calabi-Yau manifolds of other dimensions and non-Calabi-Yau manifolds. The construction leads to predictions of equivalences of D-brane categories, systematically extending earlier examples. There is another type of surprise. Two distinct superconformal field theories corresponding to Calabi-Yau threefolds with different Hodge numbers, $h^{2,1}=23$ versus $h^{2,1}=59$, have exactly the same quantum Kähler moduli space. The strong-weak duality plays a crucial rôle in confirming this, and also is useful in the actual computation of the metric on the moduli space.