Relation between large dimension operators and oscillator algebra of Young diagrams
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2014
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910346994778112 |
|---|---|
| author | Lin, Hai |
| author_facet | Lin, Hai |
| contents | The operators with large scaling dimensions can be labelled by Young diagrams. Among other bases, the operators using restricted Schur polynomials have been known to have a large $N$ but nonplanar limit under which they map to states of a system of harmonic oscillators. We analyze the oscillator algebra acting on pairs of long rows or long columns in the Young diagrams of the operators. The oscillator algebra can be reached by a Inonu-Wigner contraction of the $u(2)$ algebra inside of the $u(p)$ algebra of $p$ giant gravitons. We present evidences that integrability in this case can persist at higher loops due to the presence of the oscillator algebra which is expected to be robust under loop corrections in the nonplanar large $N$ limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1407_7815 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Relation between large dimension operators and oscillator algebra of Young diagrams Lin, Hai High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics The operators with large scaling dimensions can be labelled by Young diagrams. Among other bases, the operators using restricted Schur polynomials have been known to have a large $N$ but nonplanar limit under which they map to states of a system of harmonic oscillators. We analyze the oscillator algebra acting on pairs of long rows or long columns in the Young diagrams of the operators. The oscillator algebra can be reached by a Inonu-Wigner contraction of the $u(2)$ algebra inside of the $u(p)$ algebra of $p$ giant gravitons. We present evidences that integrability in this case can persist at higher loops due to the presence of the oscillator algebra which is expected to be robust under loop corrections in the nonplanar large $N$ limit. |
| title | Relation between large dimension operators and oscillator algebra of Young diagrams |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/1407.7815 |