# Understanding the BPS Equation from SUSY Transformation Law

• ismaili
In summary, the BPS equation is obtained by requiring that the SUSY transformation law for a fermion field, \psi, is equal to zero. This equation is named after the BPS bound, which is a bound on the states that satisfy this equation and are known as BPS states. The name "BPS" refers to the fact that this equation breaks some of the supersymmetry. This is due to the addition of a central charge term in the supersymmetry algebra, which effectively truncates the supermultiplets.

#### ismaili

Supposed we are given a set of SUSY transformation law, the way to get the BPS equation is by requiring that
$$\delta \psi = 0$$
where $$\psi$$ is a fermion field.

Could somebody explain why this is the BPS equation?
Thanks!

Thank You! Exactly this question I have, too!

I know vaguely, that the supersymmetry algebra can be extended by a central charge term, that effectively break some of the supercharges and thus truncate the supermultiplets. There is a bound, called the BPS bound and states that satisfy this bound are BPS states. Can't remember right now much about this bound. Anyways, I guess that the name BPS refers to the fact that you break some of the supersymmetry?

Let me know if you know more by now.

## What is the BPS equation?

The BPS equation is a mathematical equation that describes the relationship between the mass and charge of certain particles in a supersymmetric theory. It stands for Bogomol'nyi-Prasad-Sommerfield equation, named after the physicists who first proposed it.

## What is the SUSY transformation law?

The SUSY transformation law is a mathematical rule that describes how the properties of particles change under supersymmetry, a theoretical framework that extends the Standard Model of particle physics. It relates the fermionic (spin 1/2) and bosonic (integer spin) components of a supersymmetric particle.

## How does understanding the BPS equation from SUSY transformation law help in physics?

Understanding the BPS equation from the SUSY transformation law is crucial for physicists studying supersymmetric theories. It allows them to make predictions about the properties and behavior of particles in these theories, which can help to explain phenomena that cannot be explained by the Standard Model alone, such as dark matter.

## What is the significance of the BPS equation in supersymmetric theories?

The BPS equation is significant because it provides a way to study and understand the properties of supersymmetric particles. It also plays a key role in the search for a unified theory that can explain the fundamental forces of nature, as supersymmetry is a key aspect of many proposed theories of everything.

## Are there any practical applications of the BPS equation and SUSY transformation law?

While the BPS equation and SUSY transformation law are primarily used in theoretical physics, they have also found applications in other fields, such as mathematics and computer science. For example, the BPS equation has been used to study black holes and string theory, and the SUSY transformation law has been applied in machine learning algorithms.