Motivic GUT Part I: Grand Unified Theory of Topological Order
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908902585532416 |
|---|---|
| author | Yamada, Masahiko G. |
| author_facet | Yamada, Masahiko G. |
| contents | In the series of papers Motivic GUT Part I: Grand Unified Theory of Topological Order, Motivic GUT Part II: Grand Unified Theory of Symmetry-Protected Topological Order, and Motivic GUT Part III: Grand Unified Theory of Symmetry-Enriched Topological Order, we propose a unified framework for gapped topological phases based on the Grothendieck-Kitaev-Lurie motivic yoga. In the spirit of Grothendieck's rising sea, we argue that the classification problem can only be properly addressed after identifying the correct higher-categorical ambient space in which its full richness appears. In this first part, we propose a unified definition of gapped topological order in spatial dimension $d$ in terms of unitary fusion $(\infty,d)$-categorical data, considered up to Morita equivalence. For $d=2$, this framework recovers unitary modular tensor categories. For $d>2$, it naturally leads to genuinely higher-categorical structures. This suggests a Copernican turn in the theory of topological phases: many existing classification schemes should be reinterpreted as lower-categorical shadow realizations of intrinsically $\infty$-categorical objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15361 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Motivic GUT Part I: Grand Unified Theory of Topological Order Yamada, Masahiko G. Strongly Correlated Electrons In the series of papers Motivic GUT Part I: Grand Unified Theory of Topological Order, Motivic GUT Part II: Grand Unified Theory of Symmetry-Protected Topological Order, and Motivic GUT Part III: Grand Unified Theory of Symmetry-Enriched Topological Order, we propose a unified framework for gapped topological phases based on the Grothendieck-Kitaev-Lurie motivic yoga. In the spirit of Grothendieck's rising sea, we argue that the classification problem can only be properly addressed after identifying the correct higher-categorical ambient space in which its full richness appears. In this first part, we propose a unified definition of gapped topological order in spatial dimension $d$ in terms of unitary fusion $(\infty,d)$-categorical data, considered up to Morita equivalence. For $d=2$, this framework recovers unitary modular tensor categories. For $d>2$, it naturally leads to genuinely higher-categorical structures. This suggests a Copernican turn in the theory of topological phases: many existing classification schemes should be reinterpreted as lower-categorical shadow realizations of intrinsically $\infty$-categorical objects. |
| title | Motivic GUT Part I: Grand Unified Theory of Topological Order |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2603.15361 |