Mendel Nguyen
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View article: Phases of Theories with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> 1-Form Symmetry, and the Roles of Center Vortices and Magnetic Monopoles
Phases of Theories with 1-Form Symmetry, and the Roles of Center Vortices and Magnetic Monopoles Open
We analyze the phases of theories having a microscopic ZN 1-form symmetry, starting with a topological theory and deforming it so that only the microscopic symmetry is preserved. These theories have a well-defined notion of confinement, pr…
View article: Refined instanton analysis of the 2D CPN−1 model: mass gap, theta dependence, and mirror symmetry
Refined instanton analysis of the 2D CPN−1 model: mass gap, theta dependence, and mirror symmetry Open
A bstract We address nonperturbative dynamics of the two-dimensional bosonic and supersymmetric CP N −1 models for general N by developing new tools directly on R 2 . The analysis starts with a new formulation of instantons that is consist…
View article: Fractionalization of flux tubes in 3d and screening by emergent electric charges in 2d
Fractionalization of flux tubes in 3d and screening by emergent electric charges in 2d Open
We consider a class of 3d theories with a $\mathbb Z_n$ magnetic symmetry in which confinement is generated by charge $n$ clusters of monopoles. Such theories naturally arise in quantum antiferromagnets in 2+1, QCD-like theories on $\mathb…
View article: Chiral symmetry and Atiyah-Patodi-Singer index theorem for staggered fermions
Chiral symmetry and Atiyah-Patodi-Singer index theorem for staggered fermions Open
We consider the Atiyah-Patodi-Singer (APS) index theorem corresponding to the chiral symmetry of a continuum formulation of staggered fermions called Kähler-Dirac fermions, which have been recently investigated as an ingredient in lattice …
View article: Phases of theories with $\mathbb{Z}_N$ 1-form symmetry and the roles of center vortices and magnetic monopoles
Phases of theories with $\mathbb{Z}_N$ 1-form symmetry and the roles of center vortices and magnetic monopoles Open
We analyze the phases of theories which only have a microscopic $\mathbb{Z}_N$ 1-form symmetry, starting with a topological BF theory and deforming it in accordance with microscopic symmetry. These theories have a well-defined notion of co…
View article: Refined instanton analysis of the 2D $\mathbb{C}P^{N-1}$ model: mass gap, theta dependence, and mirror symmetry
Refined instanton analysis of the 2D $\mathbb{C}P^{N-1}$ model: mass gap, theta dependence, and mirror symmetry Open
We address nonperturbative dynamics of the two-dimensional bosonic and supersymmetric $\mathbb{C}P^{N-1}$ models for general $N$ by developing new tools directly on $\mathbb{R}^2$. The analysis starts with a new formulation of instantons t…
View article: Study of gapped phases of 4d gauge theories using temporal gauging of the $\mathbb{Z}_N$ 1-form symmetry
Study of gapped phases of 4d gauge theories using temporal gauging of the $\mathbb{Z}_N$ 1-form symmetry Open
To study gapped phases of $4$d gauge theories, we introduce the temporal gauging of $\mathbb{Z}_N$ $1$-form symmetry in $4$d quantum field theories (QFTs), thereby defining effective $3$d QFTs with $\widetilde{\mathbb{Z}}_N\times \mathbb{Z…
View article: Lattice regularizations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>θ</mml:mi></mml:math> vacua: Anomalies and qubit models
Lattice regularizations of vacua: Anomalies and qubit models Open
Anomalies are a powerful way to gain insight into possible lattice regularizations of a quantum field theory. In this work, we argue that the continuum anomaly for a given symmetry can be matched by a manifestly symmetric, local, lattice r…
View article: Lattice regularizations of $θ$ vacua: Anomalies and qubit models
Lattice regularizations of $θ$ vacua: Anomalies and qubit models Open
Anomalies are a powerful way to gain insight into possible lattice regularizations of a quantum field theory. In this work, we argue that the continuum anomaly for a given symmetry can be matched by a manifestly-symmetric, local, lattice r…
View article: Winding theta and destructive interference of instantons
Winding theta and destructive interference of instantons Open
While the $θ$ dependence of field theories is $2π$ periodic, the ground-state wavefunctions at $θ$ and $θ+2π$ often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the $θ$…
View article: Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory
Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory Open
Pure Yang-Mills theory in two spacetime dimensions shows exact Casimir scaling. Thus, there are infinitely many string tensions, and this has been understood as a result of nonpropagating gluons in two dimensions. From ordinary symmetry co…