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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2306.07442 |
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| _version_ | 1866916248322834432 |
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| author | Dharanipragada, Pavan Sathiapalan, B. |
| author_facet | Dharanipragada, Pavan Sathiapalan, B. |
| contents | In earlier papers it was shown that the correct kinetic term for scalar, vector gauge field and the spin two field in $AdS_{D+1}$ space is obtained starting from the ERG equation for a $CFT_D$ perturbed by scalar composite, conserved vector current and conserved traceless energy momentum tensor respectively. In this paper interactions are studied and it is shown that a flipped version of Polchinski ERG equation that evolves towards the UV can be written down and is useful for making contact with the usual AdS/CFT prescriptions for correlation function calculations. The scalar-scalar-spin-2 interaction in the bulk is derived from the ERG equation in the large $N$ semiclasical approximation.
It is also shown that after mapping to AdS the interaction is local on a scale of the bare cutoff rather than the moving cutoff (which would have corresponded to the AdS scale). The map to $AdS_{D+1}$ plays a crucial role in this locality. The local nature of the coupling ensures that this interaction term in the bulk action is obtained by gauge fixing a general coordinate invariant scalar kinetic term in the bulk action. A wave function renormalization of the scalar field is found to be required for a mutually consistent map of the two fields to $AdS_{D+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07442 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Holographic RG from ERG: Locality and General Coordinate Invariance in the Bulk Dharanipragada, Pavan Sathiapalan, B. High Energy Physics - Theory In earlier papers it was shown that the correct kinetic term for scalar, vector gauge field and the spin two field in $AdS_{D+1}$ space is obtained starting from the ERG equation for a $CFT_D$ perturbed by scalar composite, conserved vector current and conserved traceless energy momentum tensor respectively. In this paper interactions are studied and it is shown that a flipped version of Polchinski ERG equation that evolves towards the UV can be written down and is useful for making contact with the usual AdS/CFT prescriptions for correlation function calculations. The scalar-scalar-spin-2 interaction in the bulk is derived from the ERG equation in the large $N$ semiclasical approximation. It is also shown that after mapping to AdS the interaction is local on a scale of the bare cutoff rather than the moving cutoff (which would have corresponded to the AdS scale). The map to $AdS_{D+1}$ plays a crucial role in this locality. The local nature of the coupling ensures that this interaction term in the bulk action is obtained by gauge fixing a general coordinate invariant scalar kinetic term in the bulk action. A wave function renormalization of the scalar field is found to be required for a mutually consistent map of the two fields to $AdS_{D+1}$. |
| title | Holographic RG from ERG: Locality and General Coordinate Invariance in the Bulk |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2306.07442 |