[Paper Review] Quantum Local Quench, AdS/BCFT and Yo-Yo String

Amin Faraji Astaneh, Amir Esmaeil Mosaffa|arXiv (Cornell University)|May 21, 2014

Black Holes and Theoretical Physics31 references4 citations

TL;DR

This paper proposes a holographic model for quantum local quench in 1+1D CFTs using AdS/BCFT and the tensionless Yo-Yo string solution. When two identical CFTs on semi-infinite lines are joined, their boundary surfaces detach into a folded closed string in AdS₃ governed by the Yo-Yo solution, with the string tip falling along a null geodesic. The resulting light-cone deformation of Ryu-Takayanagi surfaces yields time-dependent entanglement entropy that fully matches field theory results in the zero boundary entropy limit.

ABSTRACT

We propose a holographic model for local quench in 1+1 dimensional Conformal Field Theory (CFT). The local quench is produced by joining two identical CFT's on semi-infinite lines. When these theories have a zero boundary entropy, we use the AdS/Boundary CFT proposal to describe this process in terms of bulk physics. Boundaries of the original CFT's are extended in AdS as dynamical surfaces. In our holographic picture these surfaces detach from the boundary and form a closed folded string which can propagate in the bulk. The dynamics of this string is governed by the tensionless Yo-Yo string solution and its subsequent evolution determines the time dependence after quench. We use this model to calculate holographic Entanglement Entropy (EE) of an interval as a function of time. We propose how the falling string deforms Ryu-Takayanagi's curves. Using the deformed curves we calculate EE and find complete agreement with field theory results.

Motivation & Objective

• To develop a holographic description of quantum local quench in 1+1D CFTs using AdS/BCFT.
• To model the time evolution after joining two CFTs on semi-infinite lines via dynamical boundary surfaces in AdS₃.
• To show that the resulting folded string dynamics, governed by the tensionless Yo-Yo solution, reproduces the correct time-dependent entanglement entropy.
• To establish a geometric correspondence between the light-cone of the falling string tip and the propagation of quasi-particles in the field theory.
• To validate the holographic entanglement entropy calculation against exact field theory results in the zero boundary entropy case.

Proposed method

• Use the AdS/BCFT correspondence to describe each CFT on a half-line via a co-dimension two dynamical surface (Q) in AdS₃.
• Model the local quench as the detachment of two such surfaces from the boundary and their joining into a single folded closed string in the bulk.
• Apply the tensionless limit of the Polyakov action to describe the string dynamics, leading to the Yo-Yo string solution.
• Identify the tip of the folded string as moving along a null geodesic in AdS₃, generating a light-cone that propagates causally through the bulk.
• Deform Ryu-Takayanagi curves by the light-cone front to compute time-dependent entanglement entropy holographically.
• Use geodesic lengths in AdS₃ to compute entanglement entropy, with the radial cutoff representing the field theory short-distance regulator.

Experimental results

Research questions

• RQ1 How can the local quench process in 1+1D CFTs be described holographically using AdS/BCFT?
• RQ2 What is the bulk realization of the time evolution after joining two CFTs on semi-infinite lines?
• RQ3 How does the tensionless Yo-Yo string solution describe the dynamics of the joined boundary surfaces?
• RQ4 How does the light-cone from the falling string tip deform Ryu-Takayanagi surfaces to yield time-dependent entanglement entropy?
• RQ5 To what extent does the holographic entanglement entropy match the exact field theory result in the zero boundary entropy limit?

Key findings

• The holographic model successfully reproduces the exact time-dependent entanglement entropy of the local quench as derived in the field theory via conformal symmetry.
• The falling tip of the folded Yo-Yo string moves along a null geodesic in AdS₃, forming a light-cone that propagates causally and geometrically encodes the quasi-particle propagation in the field theory.
• The deformation of Ryu-Takayanagi curves by the light-cone front leads to a precise geometric prescription for computing entanglement entropy at any time after the quench.
• In the zero boundary entropy limit, the boundary surfaces become tensionless open strings that detach and form a closed folded string, consistent with the Yo-Yo solution.
• The radial cutoff in the bulk corresponds to the short-distance regulator in the field theory, establishing a direct geometric interpretation of the regulator.
• The model shows no backreaction on the geometry due to the tensionless limit, allowing the time evolution to be purely causal and geometrically encoded in the string dynamics.