Emergent gravitational action from non-local T T-like deformations

2026/08/06 by Yun-Ze Li, Bo-Rui Li, Yu-Xiao Liu +1
Physics and Astronomy · #hep-th #gr-qc

paper · pdf

43 pages, no figures

arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

We study the gravitational effective action induced, at first order in the deformation parameter, by non-local T T-like deformations of quantum field theories. Using a heat-kernel formulation, we extract the local geometric terms generated by stress-tensor two-point functions, and apply the construction to free fermions, massive Maxwell theory, and second-order Yang-Mills theory. While the resulting coefficients are generally model dependent, conformal field theories contain a universal sector fixed by the central charge C_T. After regularization and renormalization, this sector yields finite, scheme-independent contributions organized into a finite set of curvature invariants. We further analyze trace-trace deformations, for which the relevant contact terms are determined by the Weyl anomaly, and derive the corresponding finite gravitational action for a general class of minimal non-local kernels. These results provide a quantum effective-action realization of induced gravity in which universal conformal data determine calculable contributions to the emergent geometric response.

Citations

• Emergent classical gravity as stress-tensor deformed field theories
• Null energy constraints on two-dimensional RG flows
• Averaged Null Energy and the Renormalization Group
• On the global Hadamard parametrix in QFT and the signed squared geodesic distance defined in domains larger than convex normal neighbourhoods
• TT deformations in general dimensions
• Anomalous elasticity, fluctuations and disorder in elastic membranes
• On space of integrable quantum field theories
• Quantum gravity of Kerr-Schild spacetimes and the logarithmic correction to Schwarzschild black hole entropy
• The Necessity of the Hadamard Condition
• The operator product expansion for perturbative quantum field theory in curved spacetime
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• Expectation value of composite field T T in two-dimensional quantum field theory
• Heat kernel expansion: user's manual
• The motion of point particles in curved spacetime
• The motion of point particles in curved spacetime
• Sakharov's induced gravity: a modern perspective
• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Comments on the Stress-Energy Tensor Operator in Curved Spacetime
• MICROLOCAL SPECTRUM CONDITION AND HADAMARD FORM FOR VECTOR-VALUED QUANTUM FIELDS IN CURVED SPACETIME
• The Holographic Weyl anomaly
• Anti De Sitter Space And Holography
• Gauge Theory Correlators from Non-Critical String Theory
• The Large-N Limit of Superconformal Field Theories and Supergravity
• Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
• Twenty years of the Weyl anomaly
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation
• Limits on massless particles
• On Gauge Invariance and Vacuum Polarization