Laurent polynomial Landau-Ginzburg models for cominuscule homogeneous spaces

Abstract

In this article we construct Laurent polynomial Landau-Ginzburg models for cominuscule homogeneous spaces. These Laurent polynomial potentials are defined on a particular algebraic torus inside the Lie-theoretic mirror model constructed for arbitrary homogeneous spaces in [Rie08]. The Laurent polynomial takes a similar shape to the one given in [Giv96] for projective complete intersections, i.e. it is the sum of the toric coordinates plus a quantum term. We also give a general enumeration method for the summands in the quantum term of the potential in terms of the quiver introduced in [CMP08], associated to the Langlands dual homogeneous space. This enumeration method generalizes the use of Young diagrams for Grassmannians and Lagrangian Grassmannians and can be defined typeindependently. The obtained Laurent polynomials coincide with the results obtained so far in [PRW16] and [PR13] for quadrics and Lagrangian Grassmannians. We also obtain new Laurent polynomial Landau-Ginzburg models for orthogonal Grassmannians, the Cayley plane and the Freudenthal variety.

GLSMs for exotic Grassmannians

“…In this section we will briefly discuss mirrors to these nonabelian GLSMs, following the nonabelian mirror ansatz discussed in [10]. (It should be noted that other notions of mirrors exist, with different UV presentations but apparently equivalent IR physics, see [6][7][8][9]28,29]. )…”