Computing Entanglement Entropy of CFTs in the Large-c Limit

In summary, the conversation discusses the problem of computing the entanglement entropy of two CFTs in the thermofield double state on identical finite intervals in 1+1 dimensions. The Euclidean path integral is equivalent to computing the 2-point twist correlator on a torus. The question is whether there is a reference that computes this in the ##c\rightarrow \infty## limit without using holography, specifically without going to the thermal AdS saddle point and using Ryu-Takayanagi. One person mentions a paper that calculates it using Ryu-Takayanagi but it is not confirmed by another means. Another person is working on the holographic calculation but is interested in seeing if the CFT calculation is possible
  • #1
WannabeNewton
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Consider the problem of computing the entanglement entropy of two CFTs in the thermofield double state on identical finite intervals in 1+1 dimensions. The Euclidean path integral is then equivalent to computing the 2-point twist correlator on a torus. Given a central charge ##c##, does anyone know of a reference that computes this in the ##c\rightarrow \infty## limit without using holography i.e. without going to the thermal AdS saddle point (I think?) and using Ryu-Takayanagi?
 
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  • #2
What's the paper that calculates it using Ryu-Takayanagi? I guess they don't check the result by another means?
 
  • #3
I didn't have one in mind; I'm working on the holographic calculation but wanted to see if the CFT calculation was doable in the infinite central charge limit for a finite interval on a torus since the methods of Cardy et al (http://arxiv.org/pdf/0905.4013v2.pdf) to compute the 2-point twist correlations no longer apply to a torus as far as I can tell.
 
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FAQ: Computing Entanglement Entropy of CFTs in the Large-c Limit

1. What is the Large-c Limit in CFTs?

The Large-c Limit refers to a limit in which the central charge of a conformal field theory (CFT) becomes infinitely large. This limit is useful for studying CFTs because it simplifies the calculations and allows for the use of powerful analytical techniques.

2. What is Entanglement Entropy in CFTs?

Entanglement entropy measures the amount of entanglement between two regions in a quantum system. In CFTs, it is a measure of the correlations between two regions of space separated by a boundary. It is a useful tool for understanding the structure and properties of CFTs.

3. How is Entanglement Entropy computed in CFTs?

In CFTs, entanglement entropy can be computed using the replica trick, which involves taking multiple copies of the system and then analytically continuing the number of copies to a non-integer value. This allows for the calculation of entanglement entropy using well-established techniques from statistical mechanics.

4. What is the significance of Computing Entanglement Entropy in the Large-c Limit?

Computing entanglement entropy in the Large-c Limit allows for a better understanding of the behavior of CFTs in this simplified limit. It can also provide insights into the properties of quantum field theories in general, as CFTs are powerful tools for studying quantum systems.

5. Are there any applications of Computing Entanglement Entropy in the Large-c Limit?

Yes, there are several applications of computing entanglement entropy in the Large-c Limit. It can be used to study the dynamics of quantum systems, as well as to calculate the entanglement between different regions of space in various physical systems. It also has implications for quantum information and black hole physics.

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