# Obtaining BPS States in Interacting Field Theory

• arroy_0205
In summary, BPS states, or Bogomol'nyi-Prasad-Sommerfield states, are special states in a field theory that have zero energy and are annihilated by a subset of the supersymmetry generators. They can be obtained through solving BPS equations or studying the theory's spectrum and play a crucial role in understanding supersymmetric field theories. BPS states are only possible in theories with supersymmetry, but some theories without it may have similar states. While not directly observable, the existence of BPS states can impact the behavior and properties of other observable states.
arroy_0205
What is meant by BPS state in an interacting field theory? Suppose I have the action for some theory. Now how do I obtain the BPS states for the theory? I am looking for clear steps for calculations. Also I need to know what is special about these states. You may give reference to some review article or books.

You might try page 441 (and thereabouts) in The Quantum Theory of Fields II by Weinberg.

A BPS (Bogomol'nyi-Prasad-Sommerfield) state in an interacting field theory is a state that preserves a fraction of the supersymmetry of the theory. In other words, the state is annihilated by a subset of the supersymmetry generators. These states are special because they have a mass that is determined solely by the charges they carry, rather than the coupling constants of the theory.

To obtain the BPS states for a given theory, one must first determine the supersymmetry algebra of the theory. This algebra dictates the transformation rules for the supersymmetry generators and the fields of the theory. Then, one must identify the states that are annihilated by a subset of the supersymmetry generators, known as the BPS conditions. These conditions typically involve the momenta and charges of the states.

To find the BPS states, one can use the supersymmetry algebra to determine the transformation rules for the fields and then solve the BPS conditions for the states. This will result in a set of equations that determine the allowed values of the momenta and charges for the BPS states. The solutions to these equations will be the BPS states of the theory.

One reference that provides a detailed explanation of the process for obtaining BPS states in interacting field theories is the book "Supersymmetry and Supergravity" by Peter West. Chapter 12 of this book specifically discusses BPS states and their properties. Additionally, the review article "BPS States in Supersymmetric Field Theories" by Michael Dine and Nathan Seiberg provides a comprehensive overview of BPS states and their significance in various supersymmetric theories.

## 1. What are BPS states in interacting field theory?

BPS states, or Bogomol'nyi-Prasad-Sommerfield states, are special states in a field theory that preserve some amount of supersymmetry. They are characterized by having zero energy and being annihilated by a subset of the supersymmetry generators.

## 2. How are BPS states obtained in interacting field theory?

BPS states can be obtained through a variety of methods, such as by solving the BPS equations or by studying the spectrum of the theory. In general, they can be identified as states with zero energy and certain symmetries.

## 3. Why are BPS states important in field theory?

BPS states play a crucial role in understanding the behavior of supersymmetric field theories. They often have special properties that make them easier to study and can provide insight into the structure of the theory as a whole.

## 4. Can BPS states exist in theories without supersymmetry?

No, BPS states are a consequence of supersymmetry and cannot exist in theories without it. However, some theories without supersymmetry may have states that behave similarly to BPS states.

## 5. Are BPS states observable in experiments?

In general, BPS states are not directly observable in experiments. However, their existence can have important implications for the behavior of the theory and the properties of other observable states.

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