It was first constructed in 1984 by a dimensional reduction of eleven-dimensional supergravity on a circle.
In 1986 a deformation of the theory was discovered which gives mass to one of the fields and is known as massive type IIA supergravity.
[4] Type IIA supergravity plays a very important role in string theory as it is the low-energy limit of type IIA string theory.
[5] Using this technique, type IIA supergravity was first constructed in 1984 by three different groups, by F. Giani and M. Pernici,[1] by I.C.G.
[3] In 1986 it was noticed by L. Romans that there exists a massive deformation of the theory.
[nb 1] Since the smallest spinorial representations in ten dimensions are Majorana–Weyl spinors, the supercharges come in two types
theory formed using two supercharges of opposite chiralities is denoted by
supersymmetry is given by[10] where all terms on the right-hand side besides the first one are the central charges allowed by the theory.
[7]: 47–48 Going only up to five-index matrices, since the rest are equivalent up to Poincare duality, yields the set of central charges described by the above algebra.
The various central charges in the algebra correspond to different BPS states allowed by the theory.
The type IIA supergravity action is given up to four-fermion terms by[11] Here
The last line contains the cubic interaction terms between two fermions and a boson.
The supersymmetry variations that leave the action invariant are given up to three-fermion terms by[11][14]: 665 [nb 7] They are useful for constructing the Killing spinor equations and finding the supersymmetric ground states of the theory since these require that the fermionic variations vanish.
[12]: 115 Such a field therefore has no propagating degrees of freedom, but does have an energy density associated to it.
is equivalent to the original type IIA supergravity up to the replacement of
Often one integrates out this field strength tensor resulting in an action where
Unlike in the regular type IIA theory, which has a vanishing scalar potential
, massive type IIA has a nonvanishing scalar potential.
supersymmetry transformations appear to be realised, they are actually formally broken since the theory corresponds to a D8-brane background.
It is acquired by a compactification of eleven-dimensional MM theory on a circle.
Compactification of eleven-dimensional supergravity on a circle and keeping only the zero Fourier modes that are independent of the compact coordinates results in type IIA supergravity.
For eleven-dimensional supergravity with the graviton, gravitino, and a 3-form gauge field denoted by
Dimensional reduction of the fermions must generally be done in terms of the flat coordinates
,[9]: 268 [nb 10] although the exact identification is given by[14]: 664 where this is chosen to make the supersymmetry transformations simpler.
[nb 11] The ten-dimensional supersymmetry variations can also be directly acquired from the eleven-dimensional ones by setting
[15]: 187 The fields correspond to the different massless excitations of the string, with the metric, 2-form
, and dilaton being NSNS states that are found in all string theories, while the 3-form and 1-form fields correspond to the RR states of type IIA string theory.
[15]: 321–324 Such corrections often play an important role in type IIA string phenomenology.
theory in four dimensions, while reduction on a Calabi–Yau orientifold further breaks the symmetry down to give the phenomenologically viable four-dimensional
[13]: 356–357 Type IIA supergravity is automatically anomaly free since it is a non-chiral theory.