JHEP02(2016)168
type IIB string theory [15] whose dynamics is governed by the N = (1, 1) vector mul-
tiplet in six dimensions. On the other hand, the type IIA 5
2
2
-brane contains the 2-form
field in the N = (2, 0) tensor multiplet. We de r i ved the effective action of the type IIA
5
2
2
-brane [
14] from the type IIA NS5-brane whose M-theory origin is th e M5-brane in
eleven-dimensions [
16].
We know that the BPS extended objects in type IIA string t heor y have their eleven-
dimensional M-theory origin. The D0-brane is obtained from the M-wave. The F-string
and the D2-brane come from the M2-b r ane while the NS5-brane and the D4-brane come
from the M5-brane. The type IIA KK5-brane and the D6-brane are obtained by the
double/direct dimensional reductions of the KK6-brane, respectively. The D8-brane and
also the KK8-brane is expected to come f r om a nine-di men si onal object in eleven dimen-
sions [
17, 18]. It is also important to study M -t he or y origins of exotic branes in string
theories. Indeed, there is an exotic five-brane known as the 5
3
-brane [
4, 5, 19] in eleven-
dimensional M-theory. We call th i s t he M 5
3
-brane in this paper. The M5
3
-brane has
isometries along thr ee transverse directions to its world-vol ume . The tension of the M5
3
-
brane is proportional to the volume of the torus T
3
realized i n the isometry directions. This
is just a generalized KK monopole in eleven dim en si ons [20]. The supergravity solution
associated with the M5
3
-brane exhibits non-geome tr i c nature whose monodromy is given
by the U-duality group SL(3, Z) ×SL(2, Z) in eight dimensi ons. The direct/double dimen-
sional reductions of the M5
3
-brane to ten dimensions provide the exotic 5
2
2
-brane/4
3
3
-brane
in type IIA string theory. The re for e the M5
3
-brane is the higher dimensional origin of the
type IIA exotic branes. In this paper we study the world-volume effective action of the
exotic M5
3
-brane in eleven dimensions.
The organization of this paper is as follows. In the nex t sect i on, we introduce the world-
volume effective action of the exotic 5
2
2
-brane in type IIA string theory. In section
3, we
propose the world-volume effective action of the M5
3
-brane. We wil l show that the action
correctly reproduces the action of the type IIA 5
2
2
-brane in ten dimensions. In section
4,
we will show th at the actions of the 5
2
2
-brane and M5
3
-brane give the source terms of thes e
five-brane geometries. Section
5 is devoted to the conclusion and discussions.
2 Effective action of type IIA 5
2
2
-brane
In this section we introduce the world-volume effective action of the exotic 5
2
2
-brane in type
IIA string theory. The background geometry of the 5
2
2
-brane is a 1/2-BPS solution to the
type IIA supergravity and th e world-volume theory has 16 conserved supercharges. The
geometry of the 5
2
2
-brane exhibits the monodromy given by the SO(2, 2) T-duality group
and this is a T-fold.
The world-volume action of the 5
2
2
-brane is obtained from that of the typ e IIA NS5-
brane by repeated T-duality transformations. The type IIA NS5-brane is obtained by the
direct dimensional reduction of the M5-brane in eleven di me ns i ons. We start from the
effective action of the M5-brane whi ch has been established in [
16]. The supermultiplet
of the six-dimensional world-volume theory on the M5-brane is the N = (2, 0) tensor
multiplet. This consists of a 2-form field A
ab
, five scalar fi el ds X
ˆ
M
(
ˆ
M = 1, . . . , 5) and
– 2 –
