Chien‐Hao Liu

activity

19952025

most citedTarget Space Duality between Simple Compact Lie Groups and Lie Algebras under the Hamiltonian Formalism: I. Remnants of Duality at the Classical Level

22 citations · 221 across the 45 of their papers we have counts for

collaborators

45 papers

math.AG2025

A D-brane fantasy on noncommutative mirror symmetry, prelude: Noncommutative ringed spaces from local noncommutative crepant resolutions of a singular Calabi-Yau space, dynamical D-branes thereupon, and questions beyond

Chien-Hao Liu, Shing-Tung Yau

In contrast to the world-sheet of a fundamental string, the world-volume of stacked D-branes carries an Azumaya noncommutative structure ([L-Y1: Sec.\ 2] (D(1))), allowing it to di…

math.AG2022

Soft noncommutative flag schemes

Chien-Hao Liu, Shing-Tung Yau

The construction of soft noncommutative schemes via toric geometry in arXiv:2108.05328 [math.AG] (D(15.1), NCS(1)) can be generalized and applied to a commutative scheme with a dis…

math.AG2021

Soft noncommutative schemes via toric geometry and morphisms from an Azumaya scheme with a fundamental module thereto -- (Dynamical, complex algebraic) D-branes on a soft noncommutative space

Chien-Hao Liu, Shing-Tung Yau

A class of noncommutative spaces, named `soft noncommutative schemes via toric geometry', are constructed and the mathematical model for (dynamical/nonsolitonic, complex algebraic)…

math.AG2020★ 2 cited

Grothendieck meeting [Wess & Bagger]: [Supersymmetry and supergravity: IV, V, VI, VII, XXII] (2nd ed.) reconstructed in complexified $Z /2$ -graded $C^{\infty}$ -Algebraic Geometry, I. Construction under trivialization of spinor bundle

Chien-Hao Liu, Shing-Tung Yau

Forty-six years after the birth of supersymmetry in 1973 from works of Julius Wess and Bruno Zumino, the standard quantum-field-theorists and particle physicists' language of `supe…

hep-th2019

Physicists' $d = 3 + 1$ , $N = 1$ superspace-time and supersymmetric QFTs from a tower construction in complexified $Z /2$ -graded $C^{\infty}$ -Algebraic Geometry and a purge-evaluation/index-contracting map

Chien-Hao Liu, Shing-Tung Yau

The complexified $Z /2$ -graded $C^{\infty}$ -Algebraic Geometry aspect of a superspace(-time) $X$ in Sec.\,1 of D(14.1) (arXiv:1808.05011 [math.DG]) together with the…

math.DG2018★ 1 cited

$N = 1$ fermionic D3-branes in RNS formulation I. $C^{\infty}$ -Algebrogeometric foundations of $d = 4$ , $N = 1$ supersymmetry, SUSY-rep compatible hybrid connections, and $D$ -chiral maps from a $d = 4$ $N = 1$ Azumaya/matrix superspace

Chien-Hao Liu, Shing-Tung Yau

As the necessary background to construct from the aspect of Grothendieck's Algebraic Geometry dynamical fermionic D3-branes along the line of Ramond-Neveu-Schwarz superstrings in s…

A D-brane fantasy on noncommutative mirror symmetry, prelude: Noncommutative ringed spaces from local noncommutative crepant resolutions of a singular Calabi-Yau space, dynamical D-branes thereupon, and questions beyond

Soft noncommutative flag schemes

Soft noncommutative schemes via toric geometry and morphisms from an Azumaya scheme with a fundamental module thereto -- (Dynamical, complex algebraic) D-branes on a soft noncommutative space

Grothendieck meeting [Wess & Bagger]: [Supersymmetry and supergravity: IV, V, VI, VII, XXII] (2nd ed.) reconstructed in complexified Z/2-graded C∞-Algebraic Geometry, I. Construction under trivialization of spinor bundle

Physicists' d=3+1, N=1 superspace-time and supersymmetric QFTs from a tower construction in complexified Z/2-graded C∞-Algebraic Geometry and a purge-evaluation/index-contracting map

N=1 fermionic D3-branes in RNS formulation I. C∞-Algebrogeometric foundations of d=4, N=1 supersymmetry, SUSY-rep compatible hybrid connections, and D-chiral maps from a d=4 N=1 Azumaya/matrix superspace

Grothendieck meeting [Wess & Bagger]: [Supersymmetry and supergravity: IV, V, VI, VII, XXII] (2nd ed.) reconstructed in complexified $Z /2$ -graded $C^{\infty}$ -Algebraic Geometry, I. Construction under trivialization of spinor bundle

Physicists' $d = 3 + 1$ , $N = 1$ superspace-time and supersymmetric QFTs from a tower construction in complexified $Z /2$ -graded $C^{\infty}$ -Algebraic Geometry and a purge-evaluation/index-contracting map

$N = 1$ fermionic D3-branes in RNS formulation I. $C^{\infty}$ -Algebrogeometric foundations of $d = 4$ , $N = 1$ supersymmetry, SUSY-rep compatible hybrid connections, and $D$ -chiral maps from a $d = 4$ $N = 1$ Azumaya/matrix superspace