Author:
Nuchino Patharadanai,Karndumri Parinya
Abstract
AbstractWe continue our study of gaugings the maximal $$N=(2,2)$$
N
=
(
2
,
2
)
supergravity in six dimensions with gauge groups obtained from decomposing the embedding tensor under $${\mathbb {R}}^+\times SO(4,4)$$
R
+
×
S
O
(
4
,
4
)
subgroup of the global symmetry SO(5, 5). Supersymmetry requires the embedding tensor to transform in $${\textbf{144}}_c$$
144
c
representation of SO(5, 5). Under $${\mathbb {R}}^+\times SO(4,4)$$
R
+
×
S
O
(
4
,
4
)
subgroup, this leads to the embedding tensor in $$({\textbf{8}}^{\pm 3},$$
(
8
±
3
,
$${\textbf{8}}^{\pm 1},{\textbf{56}}^{\pm 1})$$
8
±
1
,
56
±
1
)
representations. Gaugings in $${\textbf{8}}^{\pm 3}$$
8
±
3
representations lead to a translational gauge group $${\mathbb {R}}^8$$
R
8
while gaugings in $${\textbf{8}}^{\pm 1}$$
8
±
1
representations give rise to gauge groups related to the scaling symmetry $${\mathbb {R}}^+.$$
R
+
.
On the other hand, the embedding tensor in $${\textbf{56}}^{\pm 1}$$
56
±
1
representations gives $$CSO(4-p,p,1)\sim SO(4-p,p) < imes {\mathbb {R}}^4\subset SO(4,4)$$
C
S
O
(
4
-
p
,
p
,
1
)
∼
S
O
(
4
-
p
,
p
)
⋉
R
4
⊂
S
O
(
4
,
4
)
gauge groups with $$p=0,1,2.$$
p
=
0
,
1
,
2
.
More interesting gauge groups can be obtained by turning on more than one representation of the embedding tensor subject to the quadratic constraints. In particular, we consider gaugings in both $${\textbf{56}}^{-1}$$
56
-
1
and $${\textbf{8}}^{+3}$$
8
+
3
representations giving rise to larger $$SO(5-p,p)$$
S
O
(
5
-
p
,
p
)
and $$SO(4-p,p+1)$$
S
O
(
4
-
p
,
p
+
1
)
gauge groups for $$p=0,1,2.$$
p
=
0
,
1
,
2
.
In this case, we also give a number of half-supersymmetric domain wall solutions preserving different residual symmetries. The solutions for gaugings obtained only from $${\textbf{56}}^{-1}$$
56
-
1
representation are also included in these results when the $${\textbf{8}}^{+3}$$
8
+
3
part is accordingly turned off.
Publisher
Springer Science and Business Media LLC