JHEP08(2018)021
0 1 2 3 4 5 6 7
M: P M2 M5 KK6
IIA: D0 D2 D4 D6 D8
IIB: D1 D3 D5 D7
NS:
P F 1
5
0
2
5
1
2
0
(1,6)
4
1
6
4
5
2
2
5
3
2
IIB:
1
6
3
3
4
3
5
2
3
7
0
3
IIA:
0
7
3
2
5
3
4
3
3
6
1
3
IIB:
0
(1,7)
3
2
(1,5)
3
4
(1,3)
3
6
(1,1)
3
IIA:
1
(1,6)
3
3
(1,4)
3
5
(1,2)
3
7
(1,0)
3
IIA:
1
(4,3)
4
3
(2,3)
4
5
3
4
IIB:
0
(5,3)
4
2
(3,3)
4
4
(1,3)
4
M:
0
(1,7)
1
(1,1,6)
2
6
3
(2,4)
5
3
5
(1,3)
8
(1,0)
SL(5)
Figure 1. Branes of Type II theories whose tension is proportional to g
−α
s
with α ≤ 4 and the
relations between them and the M-theory branes (only some of the branes with α = 4 are shown).
The black, red and blue arrows respectively denote reduction/oxidation, T-duality and S-duality.
In subsection 2.2 we turn our attention to the SL(5) theory. We show which exotic
branes fit into which representations of the U-duality group and how the embedding ten-
sor decomposes. This lays the foundations for the study of the U-duality rotations in
subsequent sections.
2.1 g
−3
s
-branes from EFT
The generalised torsion of the E
7(7)
EFT has components transforming only in the 912 and
the 56 representations of E
7(7)
[20, 66–70]. These are decomposed under the embedding
E
7(7)
←- SO(6, 6) × SL(2) as follows:
912 −→ (12, 2) ⊕ (32, 3) ⊕ (220, 2) ⊕ (352, 1),
56 −→ (12, 2) ⊕ (32, 1).
(2.1)
The group SL(2) is the one that transforms the axio-dilaton, and hence by further decom-
posing SL(2) ←- R
+
to obtain the dilaton scaling and thus a relation to the g
s
power, we
– 6 –
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