Holographic Relations for OPE Blocks in Excited States

In summary: Your Name]In summary, the authors explore the holographic duality between boundary OPE blocks and geodesic integrated bulk fields in excited CFT states using quotient geometries. They propose a new approach by decomposing OPE blocks into quotient invariant operators and establishing a duality with bulk fields integrated over both minimal and non-minimal geodesics. Their evidence for this relationship through the study of the monodromy of asymptotic maps is strong and promising. This work also has potential connections to other recent developments in holography. Overall, this paper presents a valuable contribution to the field and further developments are anticipated.
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Holographic Relations for OPE Blocks in Excited States

https://arxiv.org/pdf/1809.09107.pdf

Jesse C. Cresswell†1 , Ian T. Jardine†2 , and Amanda W. Peet†§3 †Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada §Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada

We study the holographic duality between boundary OPE blocks and geodesic integrated bulk fields in quotients of AdS3 dual to excited CFT states. The quotient geometries exhibit non-minimal geodesics between pairs of spacelike separated boundary points which modify the OPE block duality. We decompose OPE blocks into quotient invariant operators and propose a duality with bulk fields integrated over individual geodesics, minimal or non-minimal. We provide evidence for this relationship by studying the monodromy of asymptotic maps that implement the quotients.
 
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Dear Jesse, Ian, and Amanda,

I am impressed by your work on exploring the holographic duality between OPE blocks and geodesic integrated bulk fields in excited CFT states. The use of quotient geometries to study this duality is a novel and interesting approach.

I am particularly intrigued by your proposal to decompose OPE blocks into quotient invariant operators and establish a duality with bulk fields integrated over both minimal and non-minimal geodesics. This seems to be a promising direction for understanding the modification of the OPE block duality in quotient geometries.

Your evidence for this relationship through the study of the monodromy of asymptotic maps is strong and convincing. It is also exciting to see the potential connections between your work and other recent developments in holography, such as the Ryu-Takayanagi formula and the subregion-subregion duality.

Overall, your paper presents a valuable contribution to the field and I look forward to seeing further developments in this area. Keep up the great work!
 

1. What are holographic relations for OPE blocks in excited states?

Holographic relations for OPE blocks in excited states refer to a theoretical framework used in string theory and other fields of physics to describe the interactions between particles at the quantum level. These relations are based on the holographic principle, which states that information about a region of space can be encoded on its boundary. In this context, the boundary refers to the surface of a black hole or the boundary of a higher-dimensional space.

2. How are holographic relations for OPE blocks in excited states used?

Holographic relations for OPE blocks in excited states are used to calculate the scattering amplitudes or probabilities of interactions between particles. They allow physicists to study the behavior of particles in extreme environments, such as near a black hole, where traditional methods of calculation may not be applicable.

3. What is an OPE block?

An OPE (Operator Product Expansion) block is a mathematical object used to represent the interaction between two particles in the holographic framework. It is a sum of terms that correspond to different possible outcomes of the interaction. OPE blocks can be used to calculate scattering amplitudes and other properties of the system.

4. What are excited states in this context?

In physics, excited states refer to energy levels of a system that are higher than the ground state. In the context of holographic relations for OPE blocks, excited states refer to the states of the particles involved in the interaction that have higher energy or momentum than their ground state. These excited states can be created by applying operators to the ground state.

5. How do holographic relations for OPE blocks in excited states relate to other areas of physics?

Holographic relations for OPE blocks in excited states have connections to various areas of physics, such as string theory, quantum field theory, and black hole physics. They have also been used to study condensed matter systems and the AdS/CFT correspondence, which relates gravity in higher dimensions to quantum field theory in lower dimensions.

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