# Q: Scalar Boundary Condition & U(1) Isometry - Lewkowycz & Maldacena

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• craigthone
In summary, scalar boundary conditions are conditions imposed on a scalar field at the boundary of a space or system, while U(1) isometry is a type of symmetry where the system remains unchanged under a rotation by an angle of 2π around a specific axis. These two concepts are related because U(1) isometry can be used to impose scalar boundary conditions on a system. The work of Lewkowycz and Maldacena on these concepts is significant because it provides a framework for studying scalar fields in holographic systems with boundaries, with implications for understanding black holes and quantum gravity. There are also practical applications of these concepts in fields such as string theory, quantum field theory, and quantum technologies.

#### craigthone

I have a simple question about Lewkowycz and Maldacena's paper [PLAIN]http://arxiv.org/abs/1304.4926v2[/PLAIN] [Broken]
http://arxiv.org/abs/1304.4926v2

In section 2, they consider the scalar field in BTZ background ground and require boundary condition of the scalar field,

$\phi \sim e^{i\tau}$ . This boudary condition breaks the U(1) isomentry of BTZ background. My question is what kinds of boudary condition will respect the U(1) isometry? $\phi$does not depend on $\tau$?

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The answer is YES. Respecting U(1) symmetry of phi means independence of tau coordinate.

## What is a scalar boundary condition?

A scalar boundary condition is a condition imposed on a scalar field at the boundary of a space or system, which determines the behavior of the scalar field at that boundary.

## What is U(1) isometry?

U(1) isometry is a type of symmetry where the system remains unchanged under a rotation by an angle of 2π around a specific axis. In other words, the system has a continuous rotational symmetry around that axis.

## How are scalar boundary conditions and U(1) isometry related?

Scalar boundary conditions and U(1) isometry are related because U(1) isometry can be used to impose scalar boundary conditions on a system. This means that the scalar field must remain unchanged under a U(1) isometry transformation at the boundary.

## What is the significance of Lewkowycz & Maldacena's work on Scalar Boundary Condition & U(1) Isometry?

Lewkowycz and Maldacena's work on Scalar Boundary Condition & U(1) Isometry is significant because it provides a framework for studying the behavior of scalar fields in holographic systems with boundaries. This has implications for understanding the physics of black holes and quantum gravity.

## Are there any practical applications of the concepts of Scalar Boundary Condition & U(1) Isometry?

Yes, the concepts of Scalar Boundary Condition & U(1) Isometry have practical applications in fields such as string theory, quantum field theory, and black hole physics. They also have potential applications in the development of quantum technologies such as quantum computing and quantum communication.