https://doi.org/10.1140/epjc/s10052-019-7318-y
Regular Article - Theoretical Physics
vacua from matter-coupled 4D 
gauged supergravity
1
Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore, 117551, Singapore
2
String Theory and Supergravity Group, Department of Physics, Faculty of Science, Chulalongkorn University, 254 Phayathai Road, Pathumwan, Bangkok, 10330, Thailand
* e-mail: parinya.ka@hotmail.com
Received:
13
July
2019
Accepted:
17
September
2019
Published online:
26
September
2019
We study vacua within matter-coupled gauged supergravity in the embedding tensor formalism. We derive a set of conditions for the existence of solutions by using a simple ansatz for solving the extremization and positivity of the scalar potential. We find two classes of gauge groups that lead to vacua. One of them consists of gauge groups of the form 
with H being a compact group and 
a non-compact group with 
subgroup and dyonically gauged. These gauge groups are the same as those giving rise to maximally supersymmetric 
vacua. The and vacua arise from different coupling ratios between 
and 
factors. Another class of gauge groups is given by 
with SO(2, 1), 
and 
dyonically gauged. We explicitly check that all known vacua in gauged supergravity satisfy the aforementioned conditions, hence the two classes of gauge groups can accommodate all the previous results on vacua in a simple framework. Accordingly, the results provide a new approach for finding vacua. In addition, relations between the embedding tensors for gauge groups admitting and 
vacua are studied, and a new gauge group, 
, with a vacuum is found by applying these relations to 
gauge group in five dimensions.
© The Author(s), 2019
