First, one works with the bosonic truncation . The background, in Cartesian coordinates,
involves the metric
Half-BPS branes should correspond to vacuum configurations in these field theories describing infinite
branes breaking the isometry group to
and preserving half of
the supersymmetries. Geometrically, these configurations are specified by the brane location. This is
equivalent to first splitting the scalar fields
into longitudinal
and transverse
directions,
setting the latter to constant values
(the transverse brane location). Second, one identifies the
world volume directions with the longitudinal directions,
. The latter can also be viewed as fixing
the world volume diffeomorphisms to the static gauge. This information can be encoded as an array
It is easy to check that the above is an on-shell configuration given the structure of the Euler–Lagrange
equations and the absence of non-trivial couplings except for the induced world volume metric , which
equals
in this case.
To analyse the supersymmetry preserved, one must solve Eq. (214). Notice that in the
static gauge and in the absence of any further excitations, the induced gamma matrices equal
BPS state |
Projector |
M2-brane |
|
M5-brane |
|
IIA D2n-brane |
|
IIB D2n-1-brane |
|
All these configurations have an energy density equaling the brane tension since the Hamiltonian
constraint is always solved by
http://www.livingreviews.org/lrr-2012-3 |
Living Rev. Relativity 15, (2012), 3
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