# Gaugings of N=4 three dimensional gauged supergravity with exceptional
coset manifolds

Research paper by **Parinya Karndumri**

Indexed on: **27 Jul '12**Published on: **27 Jul '12**Published in: **High Energy Physics - Theory**

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#### Abstract

Some admissible gauge groups of N=4 Chern-Simons gauged supergravity in three
dimensions with exceptional scalar manifolds $G_{2(2)}/SO(4)$,
$F_{4(4)}/USp(6)\times SU(2)$, $E_{6(2)}/SU(6)\times SU(2)$,
$E_{7(-5)}/SO(12)\times SU(2)$ and $E_{8(-24)}/E_7\times SU(2)$ are identified.
In particular, a complete list of all possible gauge groups is given for the
theory with $G_{2(2)}/SO(4)$ coset space. We also study scalar potentials for
all of these gauge groups and find some critical points. In the case of
$F_{4(4)}/USp(6)\times SU(2)$ target space, we give some semisimple gauge
groups which are maximal subgroups of $F_{4(4)}$. Most importantly, we
construct the $SO(4)\ltimes \mathbf{T}^6$ gauged supergravity which is
equivalent to N=4 SO(4) Yang-Mills gauged supergravity. The latter is proposed
to be obtained from an $S^3$ reduction of $(1,0)$ six dimensional supergravity
coupled to two vector and two tensor multiplets. The scalar potential of this
theory on the scalar fields which are invariant under SO(4) is explicitly
computed. Depending on the value of the coupling constants, the theory admits
both dS and AdS vacua when all of the 28 scalars vanish. The maximal N=4
supersymmetric $AdS_3$ should correspond to the $AdS_3\times S^3$ solution of
the $(1,0)$ six dimensional theory. Finally, some gauge groups of the theories
with $E_{6(2)}/SU(6)\times SU(2)$, $E_{7(-5)}/SO(12)\times SU(2)$ and
$E_{8(-24)}/E_7\times SU(2)$ scalar manifolds are identified.