Moving the CFT into the bulk with $T\bar T$ (1611.03470v2)

Abstract: Recent work by Zamolodchikov and others has uncovered a solvable irrelevant deformation of general 2D CFTs, defined by turning on the dimension 4 operator $T \bar T$, the product of the left- and right-moving stress tensor. We propose that in the holographic dual, this deformation represents a geometric cutoff that removes the asymptotic region of AdS and places the QFT on a Dirichlet wall at finite radial distance $r = r_c$ in the bulk. As a quantitative check of the proposed duality, we compute the signal propagation speed, energy spectrum, and thermodynamic relations on both sides. In all cases, we obtain a precise match. We derive an exact RG flow equation for the metric dependence of the effective action of the $T \bar T$ deformed theory, and find that it coincides with the Hamilton-Jacobi equation that governs the radial evolution of the classical gravity action in AdS.

• The paper establishes that T Tbar deformations in 2D CFT yield a holographic dual with a finite radial cutoff via Dirichlet boundary conditions.
• It demonstrates precise matching of signal speeds, energy spectra, and thermodynamic relations between the deformed CFT and bulk AdS gravity.
• The work reveals that the corresponding RG flow and numerical analyses indicate a UV cutoff, offering new insights into effective non-UV complete field theories.

An Analysis of $T\bar{T}$ Deformations in AdS/CFT Correspondence

This essay evaluates the paper "Moving the CFT into the bulk with $T\bar{T}$," which explores the implications of $T\bar{T}$ deformations in the context of the AdS/CFT correspondence, focusing on two-dimensional conformal field theories (CFTs) and their dual gravitational descriptions. The authors, Lauren McGough, Mark Mezei, and Herman Verlinde, address recent developments in understanding how irrelevant deformations, specifically the $T\bar{T}$ deformation, can be manifested in holographic dualities by incorporating a geometric cutoff in Anti-de Sitter (AdS) space. This deformation introduces a finite radial distance, effectively imposing Dirichlet boundary conditions, and challenges traditional interpretations of UV completions within effective quantum field theories (QFTs).

$T\bar{T}$ Deformation and Its Holographic Dual

In their investigation, the authors revisit the $T\bar{T}$ operator, defined by the product of the left-moving and right-moving components of the stress tensor in a 2D CFT. The introduction of this dimension 4 operator is reminiscent of a high energy 'irrelevant' coupling that disrupts the UV fixed point structure typically preserved in CFTs. The paper posits that, from a holographic perspective, the $T\bar{T}$ deformation implicates a cutoff that eliminates the asymptotic region of the AdS spacetime. This suggests that instead of terminating at infinity, the CFT now exists on a Dirichlet boundary within the bulk at finite radial distance $r = r_c$.

Analytical Checks and Matching of Physical Quantities

To substantiate this proposed duality, the authors conduct calculations demonstrating a precise match in several key physical quantities both in the deformed CFT and the bulk AdS theory. Specifically, they compute propagation speeds of signals, examine the energy spectrum, and analyze thermodynamic relations. These computations, according to their results, align quantitatively across both descriptions. A significant mathematical aspect is the introduction of a renormalization group (RG) flow equation, which coincides with the Hamilton-Jacobi equation governing radial evolution in AdS gravity. This congruence affords a novel perspective on how potentially non-UV complete field theories can manifest within a holographic paradigm.

Numerical Results and Implications

Numerically, the paper provides detailed analyses of the flow of energy states under the $T\bar{T}$ deformation as a function of the coupling parameter $\mu$. One of the pivotal observations is how the spectrum's behavior indicates the presence of a UV cutoff, established by the singularities at specific energy thresholds. Such thresholds give insights into finite effective theories, enhancing our understanding of field theories beyond conventional UV-completeness paradigms.

The authors' analyses extend further to explore consistent unitary models established by the $T\bar{T}$ deformation. These models demonstrate an equivalence to the worldsheet theories of critical string theory, specifically when the CFT has a central charge of $c=24$. This equivalence suggests that analogous formulations might expose consistent physical systems even when deeply nonlocal interactions, such as those typified by gravitational shockwave models, are inherent to the system.

Future Directions and Impact in AI

Speculatively, implications of this work might extend to further holographic dualities and nonperturbative insights that can be engineered using machine learning approaches in artificial intelligence, such as the application of neural networks in understanding complex QFT and string theory landscapes. The synthesis of exact numerical methods and theoretical models could explore the parameter spaces of quantum gravity contexts, potentially yielding algorithms and AI systems that can navigate multi-scale QFT phenomena or string vacua efficiently.

In summary, the work by McGough, Mezei, and Verlinde significantly advances the understanding of $T\bar{T}$ deformations by reconciling them with holographic principles. This research provides a robust framework through which traditional concepts of QFT can be extended, challenging and enriching the existing boundaries of theoretical physics. Future developments might explore broader implications of this duality, invigorating the ongoing discourse on effective field theories and their nonperturbative completions in the landscape of modern physics.