In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...
, the Fayet–Iliopoulos D-term (introduced by Pierre Fayet and
John Iliopoulos
John (Jean) Iliopoulos (Greek language, Greek: Ιωάννης Ηλιόπουλος; 1940) is a Greeks, Greek physicist. He is the first person to present the Standard Model of particle physics in a single report. He is best known for his predictio ...
) is a
D-term
In theoretical physics, the D-term is the final term in the expansion of a vector superfield over fermionic coordinates. A superfield is a field that depends on all coordinates of the superspace, which is the coordinate space of a theory exhibitin ...
in a
supersymmetric
Supersymmetry is a theoretical framework in physics that suggests the existence of a symmetry between particles with integer spin (''bosons'') and particles with half-integer spin (''fermions''). It proposes that for every known particle, there ...
theory obtained from a
vector superfield
In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion.
Gauge theory
A gauge theory is a field theory with gauge symmetry. Rough ...
''V'' simply by an integral over all of
superspace
Superspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions ''x'', ''y'', ''z'', ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann num ...
:
:
Because a natural trace must be a part of the expression, the action only exists for U(1) vector superfields.
In terms of the components, it is proportional simply to the last auxiliary D-term of the superfield ''V''. It means that the corresponding ''D'' that appears in D-flatness conditions (and whose square enters the ordinary potential) is additively shifted by
, the coefficient.
References
*
Supersymmetric quantum field theory
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