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arXiv · 2508.15461

Geometric realization of stress-tensor deformed field theory

Yun-Ze Li·Yunfei Xie·Song He
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Abstract

We present a semiclassical framework in which stress-tensor deformations of a quantum field theory (QFT) reorganize into a gravitational action evaluated at a metric saddle. The deformed partition function can be written as a gravitational path integral evaluated at the saddle, establishing a direct link between stress-tensor flows and gravitational dynamics. Two complementary routes arise: (i) from gravitational actions such as Einstein and Palatini, which map to stress-tensor deformations of a seed QFT; and (ii) from deformed QFTs such as generalized Nambu-Goto and $T\bar{T}$-like deformed models, which reconstruct the corresponding gravitational actions. Finally, in a free, massive scalar theory, we show that the one-loop effective action of the nonlocal deformation contains a local curvature term; its coefficient defines an induced Newton constant at a chosen renormalization scale, thereby demonstrating a bidirectional link between stress-tensor flows and classical gravity.

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Yun-Ze Li, Yunfei Xie, Song He. 2025-08-21. Geometric realization of stress-tensor deformed field theory. https://doi.org/10.1103/ch45-fbmp

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