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Notes on GLSMs for Supermanifolds and Their Mirrors

Hao Zou

Abstract

In this paper, we revisit the A-twisted gauged linear sigma models (GLSMs) whose geometric phases are complex Kähler supermanifolds. For abelian models without superpotentials we propose an explicit orbifold description of the non-geometric (Landau-Ginzburg) point, and give a systematic rule for the nontrivial R-charge assignments at that point. We then study topological super Landau-Ginzburg models, derive chiral ring relations and genus-$g$ correlation functions, and use these formulas to test a Hori-Vafa-type mirror proposal for supermanifolds.

Notes on GLSMs for Supermanifolds and Their Mirrors

Abstract

In this paper, we revisit the A-twisted gauged linear sigma models (GLSMs) whose geometric phases are complex Kähler supermanifolds. For abelian models without superpotentials we propose an explicit orbifold description of the non-geometric (Landau-Ginzburg) point, and give a systematic rule for the nontrivial R-charge assignments at that point. We then study topological super Landau-Ginzburg models, derive chiral ring relations and genus- correlation functions, and use these formulas to test a Hori-Vafa-type mirror proposal for supermanifolds.

Paper Structure

This paper contains 17 sections, 50 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The LG Point of GLSM for Supermanifolds
  3. GLSM for TEXT revisited
  4. R-charges
  5. Examples beyond TEXT
  6. Super weighted projective spaces
  7. Multiple Grassmann-odd directions
  8. Product of superspaces
  9. Mirror Symmetry
  10. Topological Super Landau-Ginzburg Model
  11. Correlation functions
  12. Verification of mirror proposal
  13. Chiral ring relations.
  14. Correlation functions.
  15. Outlook
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Relations between different phases of A-twisted GLSMs.
  • Figure 2: Relations between GLSM for a supermanifold and for the corresponding hypersurface and their mirrors.