# Question about dilaton monopole interaction derivation

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• user1139
In summary, the authors of "Black holes and membranes in higher-dimensional theories with dilaton fields" introduce the dilaton monopole interaction by defining a dilaton kinetic term with a coefficient of 1. They derive this by considering the coefficient of (∇φ)2 in equation 2.1, which is minus the square of the field redefinition factor. To obtain ##\Sigma##, they consider the asymptotic behavior of ##\Psi## and define ##\Sigma## accordingly. This reasoning is analogous to the derivation of electric charge and electrostatic potential in equations 4.5 and 4.4.
user1139
TL;DR Summary
I am trying to understand how one derives the dilaton monopole interaction. In "Black holes and membranes in higher-dimensional theories with dilaton fields", Gibbons and Maeda mentioned that one could obtain the dilaton monopole interaction as such:

where the action is given by

However, I do not understand their reasoning for introducing ##\Psi## to define ##\Sigma## in order to derive Eq. (4.8). Could someone explain it?

If you look at the coefficient of (∇φ)2 in their equation 2.1, you'll see it's minus the square of the field redefinition factor. So they must be aiming for a dilaton kinetic term with a coefficient of 1.

mitchell porter said:
If you look at the coefficient of (∇φ)2 in their equation 2.1, you'll see it's minus the square of the field redefinition factor. So they must be aiming for a dilaton kinetic term with a coefficient of 1.
Still, how do they get ##\Sigma## from ##\Psi##? Did they just consider the asymptotic behaviour of ##\Psi## and define ##\Sigma## as such?

4.7, 4.8 are the same form as 4.5, 4.4, which describe electric charge and electrostatic potential. The reasoning would appear to be exactly analogous.

## What is a dilaton monopole interaction?

A dilaton monopole interaction refers to the theoretical interaction between a dilaton, which is a hypothetical scalar field that appears in various theories of gravity and string theory, and a magnetic monopole, which is a hypothetical particle that carries a single magnetic charge. This interaction is studied to understand the coupling between scalar fields and topological defects in field theories.

## Why is the dilaton monopole interaction important in theoretical physics?

The dilaton monopole interaction is important because it provides insights into the behavior of scalar fields in the presence of topological defects like monopoles. This has implications for understanding fundamental forces, symmetry breaking, and the unification of forces in theoretical physics. It also offers potential connections to string theory and cosmology.

## How is the dilaton monopole interaction derived?

The derivation of the dilaton monopole interaction typically involves starting with the action that includes both the dilaton field and the monopole field. The interaction term is derived by considering the coupling between these fields, often through a Lagrangian that includes kinetic and potential terms. The equations of motion are then obtained by varying the action with respect to the fields, leading to the interaction terms.

## What mathematical tools are used in the derivation of the dilaton monopole interaction?

The derivation of the dilaton monopole interaction employs several mathematical tools, including differential geometry, variational calculus, and field theory techniques. Specifically, the use of Lagrangians, Euler-Lagrange equations, and symmetry considerations are crucial. Additionally, concepts from gauge theory and general relativity may be used depending on the complexity of the model.

## What are the potential implications of understanding dilaton monopole interactions?

Understanding dilaton monopole interactions could have several implications. It may provide deeper insights into the nature of scalar fields and their role in the early universe, contribute to the development of unified theories of fundamental forces, and offer new perspectives on dark matter and dark energy. Additionally, it could lead to new predictions that can be tested in high-energy physics experiments or cosmological observations.

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