An Explicit Categorical Construction of Instanton Density in Lattice Yang-Mills Theory
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911017536061440 |
|---|---|
| author | Zhang, Peng Chen, Jing-Yuan |
| author_facet | Zhang, Peng Chen, Jing-Yuan |
| contents | Since the inception of lattice QCD, a natural definition for the Yang-Mills instanton on lattice has been long sought for. In a recent work, one of authors showed the natural solution has to be organized in terms of bundle gerbes in higher homotopy theory / higher category theory, and introduced the principles for such a categorical construction. To pave the way towards actual numerical implementation in the near future, nonetheless, an explicit construction is necessary. In this paper we provide such an explicit construction for $SU(2)$ gauge theory, with technical aspects inspired by Lüscher's 1982 geometrical construction. We will see how the latter is in a suitable sense a saddle point approximation to the full categorical construction. The generalization to $SU(N)$ will be discussed. The construction also allows for a natural definition of lattice Chern-Simons-Yang-Mills theory in three spacetime dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Explicit Categorical Construction of Instanton Density in Lattice Yang-Mills Theory Zhang, Peng Chen, Jing-Yuan High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics Since the inception of lattice QCD, a natural definition for the Yang-Mills instanton on lattice has been long sought for. In a recent work, one of authors showed the natural solution has to be organized in terms of bundle gerbes in higher homotopy theory / higher category theory, and introduced the principles for such a categorical construction. To pave the way towards actual numerical implementation in the near future, nonetheless, an explicit construction is necessary. In this paper we provide such an explicit construction for $SU(2)$ gauge theory, with technical aspects inspired by Lüscher's 1982 geometrical construction. We will see how the latter is in a suitable sense a saddle point approximation to the full categorical construction. The generalization to $SU(N)$ will be discussed. The construction also allows for a natural definition of lattice Chern-Simons-Yang-Mills theory in three spacetime dimensions. |
| title | An Explicit Categorical Construction of Instanton Density in Lattice Yang-Mills Theory |
| topic | High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2411.07195 |