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2014-01-26T11:58:02Z

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In [[theoretical physics]], one often analyzes theories with [[supersymmetry]] in which '''chiral superfields''' play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using the notion of [[superspace]]. Superspace contains the usual space-time coordinates <math>x^{\mu}</math>, <math>\mu=0,\ldots,3</math>, and four extra fermionic coordinates <math>\theta^1,\theta^2,\bar\theta^1,\bar\theta^2</math>, transforming as a two-component (Weyl) [[spinor]] and its conjugate.

In N=1 [[supersymmetry]] in 3+1D, a '''chiral superfield''' is a function over '''chiral superspace'''. There exists a projection from the (full) superspace to chiral superspace. So, a function over chiral
superspace can be [[Differential geometry|pulled back]] to the full superspace. Such a function satisfies the covariant constraint <math>\overline{D}f=0</math>. Similarly, we also have an '''antichiral superspace''' which is the complex conjugate of chiral superspace and '''antichiral superfields'''.

Superspace is the [[homogeneous space]] of the SUSY supergroup with the [[Lorentz group]] as the stabilizer. Chiral superspace is the homogeneous space with the supergroup generated by the Lorentz
transformations and <math>\overline{Q}</math> as the stabilizer. Clearly, there is a [[projection (mathematics)|projection]] from the former to the latter.

Every superfield—i.e. a field that depends on all coordinates of the superspace—may be expanded with respect to the fermionic coordinates. There exists a special kind of superfields, the so-called '''chiral superfields''', that, in the chiral representation of supersymmetry, depend only on the variables <math>\theta</math> but not their conjugates. See also [[F-term]]s.

Chiral superfields satisfy the relation <math>\overline{D}_{\dot{\alpha}}f=0</math>. They can also be expressed as fields over '''chiral superspace'''.

==See also==
* [[vector superfield]]
* [[current superfield]]
* [[F-term]]
* [[superpotential]]

{{DEFAULTSORT:Chiral Superfield}}
[[Category:Supersymmetry]]

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