Understanding the BPS Equation from SUSY Transformation Law

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SUMMARY

The BPS equation arises from the requirement that the fermion field, denoted as \(\psi\), satisfies the condition \(\delta \psi = 0\) within the context of supersymmetry (SUSY) transformation laws. This equation is linked to the BPS bound, which states that certain states, known as BPS states, maintain a specific energy-mass relationship when some supercharges are truncated by the introduction of a central charge term in the SUSY algebra. The BPS condition effectively indicates a breaking of supersymmetry, leading to a classification of states that preserve certain properties under transformations.

PREREQUISITES
  • Understanding of supersymmetry (SUSY) transformation laws
  • Familiarity with BPS states and the BPS bound
  • Knowledge of central charge terms in SUSY algebra
  • Basic concepts of fermion fields in quantum field theory
NEXT STEPS
  • Study the derivation of the BPS equation from SUSY transformation laws
  • Research the implications of the BPS bound on particle physics
  • Explore the role of central charges in extending SUSY algebras
  • Examine the properties of BPS states in various supersymmetric models
USEFUL FOR

The discussion is beneficial for theoretical physicists, particularly those specializing in supersymmetry, quantum field theory, and particle physics, as well as graduate students seeking to deepen their understanding of BPS states and their significance in SUSY frameworks.

ismaili
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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!
 
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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.
 

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