Cost of holographic path integrals
We consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in $T\overline{T}$ deformed holographic CFTs. In Nielsen's geometric formulation cost is the length of a not-necessarily-geode...
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| Format: | Article |
| Language: | English |
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SciPost
2023-04-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.4.061 |
| _version_ | 1797851628465815552 |
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| author | Ammanamanchi Ramesh Chandra, Jan de Boer, Mario Flory, Michal P. Heller, Sergio Hörtner, Andrew Rolph |
| author_facet | Ammanamanchi Ramesh Chandra, Jan de Boer, Mario Flory, Michal P. Heller, Sergio Hörtner, Andrew Rolph |
| author_sort | Ammanamanchi Ramesh Chandra, Jan de Boer, Mario Flory, Michal P. Heller, Sergio Hörtner, Andrew Rolph |
| collection | DOAJ |
| description | We consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in $T\overline{T}$ deformed holographic CFTs. In Nielsen's geometric formulation cost is the length of a not-necessarily-geodesic path in a metric space of operators. Our cost proposals differ from holographic state complexity proposals in that (1) the boundary dual is cost, a quantity that can be 'optimised' to state complexity, (2) the set of proposals is large: all functions on all bulk subregions of any co-dimension which satisfy the physical properties of cost, and (3) the proposals are by construction UV-finite. The optimal path integral that prepares a given state is that with minimal cost, and cost proposals which reduce to the CV and CV2.0 complexity conjectures when the path integral is optimised are found, while bounded cost proposals based on gravitational action are not found. Related to our analysis of gravitational action-based proposals, we study bulk hypersurfaces with a constant intrinsic curvature of a specific value and give a Lorentzian version of the Gauss-Bonnet theorem valid in the presence of conical singularities. |
| first_indexed | 2024-04-09T19:19:47Z |
| format | Article |
| id | doaj.art-2681dc59a16c447393ae3f2327113b6f |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-09T19:19:47Z |
| publishDate | 2023-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-2681dc59a16c447393ae3f2327113b6f2023-04-05T14:45:47ZengSciPostSciPost Physics2542-46532023-04-0114406110.21468/SciPostPhys.14.4.061Cost of holographic path integralsAmmanamanchi Ramesh Chandra, Jan de Boer, Mario Flory, Michal P. Heller, Sergio Hörtner, Andrew RolphWe consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in $T\overline{T}$ deformed holographic CFTs. In Nielsen's geometric formulation cost is the length of a not-necessarily-geodesic path in a metric space of operators. Our cost proposals differ from holographic state complexity proposals in that (1) the boundary dual is cost, a quantity that can be 'optimised' to state complexity, (2) the set of proposals is large: all functions on all bulk subregions of any co-dimension which satisfy the physical properties of cost, and (3) the proposals are by construction UV-finite. The optimal path integral that prepares a given state is that with minimal cost, and cost proposals which reduce to the CV and CV2.0 complexity conjectures when the path integral is optimised are found, while bounded cost proposals based on gravitational action are not found. Related to our analysis of gravitational action-based proposals, we study bulk hypersurfaces with a constant intrinsic curvature of a specific value and give a Lorentzian version of the Gauss-Bonnet theorem valid in the presence of conical singularities.https://scipost.org/SciPostPhys.14.4.061 |
| spellingShingle | Ammanamanchi Ramesh Chandra, Jan de Boer, Mario Flory, Michal P. Heller, Sergio Hörtner, Andrew Rolph Cost of holographic path integrals SciPost Physics |
| title | Cost of holographic path integrals |
| title_full | Cost of holographic path integrals |
| title_fullStr | Cost of holographic path integrals |
| title_full_unstemmed | Cost of holographic path integrals |
| title_short | Cost of holographic path integrals |
| title_sort | cost of holographic path integrals |
| url | https://scipost.org/SciPostPhys.14.4.061 |
| work_keys_str_mv | AT ammanamanchirameshchandrajandeboermarioflorymichalphellersergiohortnerandrewrolph costofholographicpathintegrals |