Constructive Holography
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913405602889728 |
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| author | Koch, Robert de Mello Van Zyl, Hendrik J. R. |
| author_facet | Koch, Robert de Mello Van Zyl, Hendrik J. R. |
| contents | We consider the collective field theory description of the singlet sector of a free and massless matrix field in $d$ dimensions. The $k$-local collective fields are functions of $(d-1)k+1$ coordinates. We provide a map between the collective fields and fields in the dual gravitational theory defined on AdS$_{d+1}$ spacetime. The coordinates of the collective field have a natural interpretation: the $k$-local collective field is a field defined on an AdS$_{d+1}\times$S$^{k-1}\times$S$^{(d-2)(k-2)}\times$S$^{d-3}$ spacetime. The modes of a harmonic expansion on the S$^{k-1}\times$S$^{(d-2)(k-2)}\times$S$^{d-3}$ portion of the spacetime leads to the spinning bulk fields of the dual gravity theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructive Holography Koch, Robert de Mello Van Zyl, Hendrik J. R. High Energy Physics - Theory We consider the collective field theory description of the singlet sector of a free and massless matrix field in $d$ dimensions. The $k$-local collective fields are functions of $(d-1)k+1$ coordinates. We provide a map between the collective fields and fields in the dual gravitational theory defined on AdS$_{d+1}$ spacetime. The coordinates of the collective field have a natural interpretation: the $k$-local collective field is a field defined on an AdS$_{d+1}\times$S$^{k-1}\times$S$^{(d-2)(k-2)}\times$S$^{d-3}$ spacetime. The modes of a harmonic expansion on the S$^{k-1}\times$S$^{(d-2)(k-2)}\times$S$^{d-3}$ portion of the spacetime leads to the spinning bulk fields of the dual gravity theory. |
| title | Constructive Holography |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.18248 |