Gravitational formulation of stress-tensor deformed field theories
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912955696676864 |
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| author | Xie, Yunfei Li, Yun-Ze Xu, Lixin He, Song |
| author_facet | Xie, Yunfei Li, Yun-Ze Xu, Lixin He, Song |
| contents | Stress-tensor deformations suggest a geometric origin of emergent gravity but are typically non-local for $d>2$. We couple a seed QFT to Einstein gravity with deformation parameter $λ$ and evaluate the gravitational path integral at the metric saddle. Around a fixed reference background, the leading deformation is universal: a bilocal term quadratic in the stress tensor with kernel set by the graviton Green's function, plus a systematic higher-order expansion. Expressed on the saddle-point (deformed) metric, the flow becomes local. We then provide two constructive completions on deformed backgrounds--Palatini $f(R)$ gravity and an eigenvalue method for general Ricci-based theories--and apply them to scalar generalized Nambu-Goto and $\det T$ deformations (arbitrary $d$), two-dimensional multi-scalar ModMax and Born-Infeld models, and four-dimensional root-$T\bar T$ and $T\bar T$ flows of Maxwell theory yielding ModMax and Born-Infeld electrodynamics. In free field theory, an off-shell analysis further shows that the leading quantum correction generates an Einstein-Hilbert term with controlled higher-derivative terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08481 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gravitational formulation of stress-tensor deformed field theories Xie, Yunfei Li, Yun-Ze Xu, Lixin He, Song High Energy Physics - Theory General Relativity and Quantum Cosmology Stress-tensor deformations suggest a geometric origin of emergent gravity but are typically non-local for $d>2$. We couple a seed QFT to Einstein gravity with deformation parameter $λ$ and evaluate the gravitational path integral at the metric saddle. Around a fixed reference background, the leading deformation is universal: a bilocal term quadratic in the stress tensor with kernel set by the graviton Green's function, plus a systematic higher-order expansion. Expressed on the saddle-point (deformed) metric, the flow becomes local. We then provide two constructive completions on deformed backgrounds--Palatini $f(R)$ gravity and an eigenvalue method for general Ricci-based theories--and apply them to scalar generalized Nambu-Goto and $\det T$ deformations (arbitrary $d$), two-dimensional multi-scalar ModMax and Born-Infeld models, and four-dimensional root-$T\bar T$ and $T\bar T$ flows of Maxwell theory yielding ModMax and Born-Infeld electrodynamics. In free field theory, an off-shell analysis further shows that the leading quantum correction generates an Einstein-Hilbert term with controlled higher-derivative terms. |
| title | Gravitational formulation of stress-tensor deformed field theories |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.08481 |