arXiv subjects

Yun-Ze Li

Publications and source records attributed to Yun-Ze Li.

9 recordsLinked to original sources

arXiv2026

Emergent gravitational action from non-local $T\bar T$-like deformations

We study the gravitational effective action induced, at first order in the deformation parameter, by non-local $T\bar T$-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.

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arXiv2026

Gravitational formulation of stress-tensor deformed field theories

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 $\lambda$ 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.

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arXiv2025

Geometric realization of stress-tensor deformed field theory

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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arXiv2025

Holographic Correlators of Boundary/Crosscap CFTs in Two Dimensions

This work explores holographic correlators within the frameworks of two-dimensional Boundary Conformal Field Theory (BCFT) and Crosscap Conformal Field Theory (XCFT). Utilizing the AdS/CFT correspondence, we compute stress tensor correlators in BCFT, considering both tensionless and tensionful end-of-the-world (EOW) brane scenarios. We derive recurrence relations for two-point and three-point correlators and examine the impact of non-zero brane tension on correlators. Extending these results, we investigate the holographic duals of XCFTs, presenting explicit scalar and stress tensor correlator computations on projective geometries such as $\mathbb{RP}^2$. Additionally, we analyze stress tensor correlators at a finite cutoff, uncovering deformations to one-point and two-point functions induced by the cutoff. Our findings provide novel insights into the holographic structures of BCFT and XCFT while laying the groundwork for future research into higher-dimensional extensions.

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arXiv2024

Holographic stress tensor correlators on higher genus Riemann surfaces

In this work, we present a comprehensive study of holographic stress tensor correlators on general Riemann surfaces, extending beyond the previously well-studied torus cases to explore higher genus conformal field theories (CFTs) within the framework of the Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We develop a methodological approach to compute holographic stress tensor correlators, employing the Schottky uniformization technique to address the handlebody solutions for higher genus Riemann surfaces. Through rigorous calculations, we derive four-point stress tensor correlators, alongside recurrence relations for higher-point correlators, within the $\mathrm{AdS}_3/\mathrm{CFT}_2$ context. Additionally, our research delves into the holography of cutoff $\mathrm{AdS}_3$ spaces, offering novel insights into the lower-point correlators of the $T\bar{T}$-deformed theories on higher genus Riemann surfaces up to the first deformation order.

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arXiv2024

Note on holographic torus stress tensor correlators in $AdS_3$ gravity

In the AdS$_3$/CFT$_2$ framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/$T\bar{T}$-deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system's dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.

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arXiv2023

Holographic torus correlators in $\text{AdS}_3$ gravity coupled to scalar field

This paper investigates holographic torus correlators of generic operators at conformal infinity and a finite cutoff within AdS$_3$ gravity coupled with a free scalar field. Using a near-boundary analysis and solving the gravitational boundary value problem, we solve Einstein's equation and calculate mixed correlators for massless and massive coupled scalar fields. The conformal ward identity on the torus has been reproduced holographically, which can be regarded as a consistency check. Further, recurrence relations for a specific class of higher-point correlators are derived, validating AdS$_3$/CFT$_2$ with non-trivial boundary topology. While the two-point scalar correlator is accurately computed on the thermal AdS$_3$ saddle, the higher-point correlators associated with scalar and stress tensor operators are explored.

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arXiv2023

Genus Two Correlation Functions in CFTs with $T\bar{T}$ Deformation

Since the definition of $T\bar{T}$ deformation in the curved Riemann surface is obstructive in the literature, we propose a way to do the deformation in the genus two Riemann surfaces by sewing prescription. We construct the correlation functions of conformal field theories (CFTs) on genus two Riemann surfaces with the $T\bar{T}$ deformation in terms of the perturbative CFT approach. Thanks to sewing construction to form higher genus Riemann surfaces from lower genus ones and conformal symmetry, we systematically obtain the first order $T\bar{T}$ correction to the genus two correlation functions in the $T\bar{T}$ deformed CFTs, e.g., partition function and one/higher-point correlation functions.

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arXiv2023

Holographic torus correlators of stress tensor in $AdS_3/CFT_2$

In the context of $\rm AdS_3/CFT_2$, we investigate holographic correlators of the stress tensor of a conformal field theory (CFT) on a torus in this work. To calculate the correlators of the stress tensor, we employ the Einstein-Hilbert theory of gravity and perturbatively solve Einstein's equation in the bulk. We offer an explicit prescription to develop a recurrence relation that makes it simple to compute higher point correlators. The correlators and the recurrence relation are found to be consistent with what is known in CFTs. Following the spirit of the proposed cutoff $\rm AdS$/$T\bar{T}$ CFT holography, we then expand our computation program to investigate holographic torus correlators at a finite cutoff in the $\rm AdS_3$. A parallel recurrence relation associated with higher point correlators can be obtained.

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