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The deformed Hermitian-Yang-Mills equation in geometry and physics

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arxiv 1712.00893 v1 pith:RFQYHQOL submitted 2017-12-04 math.DG hep-thmath.AG

Tristan C. Collins , Dan Xie , Shing-Tung Yau This is my paper · ORCID
classification math.DGhep-thmath.AG
keywords equationdeformeddiscusshermitian-yang-millsphysicsalgebraicchernconditions
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We provide an introduction to the mathematics and physics of the deformed Hermitian-Yang-Mills equation, a fully nonlinear geometric PDE on Kahler manifolds which plays an important role in mirror symmetry. We discuss the physical origin of the equation, and some recent progress towards its solution. In dimension 3 we prove a new Chern number inequality and discuss the relationship with algebraic stability conditions.

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  1. Deformed Hermitian-Yang-Mills equation on the manifold of full flags

    math.DG 2026-07 accept novelty 7.0 of 10

    First irreducible rank-2 dHYM connections are constructed on the full flag manifold F₂, and rank-1 solutions outside the supercritical regime disprove conjectured stability conditions.

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