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Register a new userSupersymmetric domain walls in maximal 6D gauged supergravity I
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We find a large class of supersymmetric domain wall solutions from six-dimensional $N=(2,2)$ gauged supergravity with various gauge groups. In general, the embedding tensor lives in $mathbf{144}_c$ representation of the global symmetry $SO(5,5)$. We explicitly construct the embedding tensors in $mathbf{15}^{-1}$ and $overline{mathbf{40}}^{-1}$ representations of $GL(5)sim mathbb{R}^+times SL(5)subset SO(5,5)$ leading to $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)ltimesmathbb{R}^4_{boldsymbol{s}}$ gauge groups, respectively. These gaugings can be obtained from $S^1$ reductions of seven-dimensional gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)$ gauge groups. As in seven dimensions, we find half-supersymmetric domain walls for purely magnetic or purely electric gaugings with the embedding tensors in $mathbf{15}^{-1}$ or $overline{mathbf{40}}^{-1}$ representations, respectively. In addition, for dyonic gauge groups with the embedding tensors in both $mathbf{15}^{-1}$ and $overline{mathbf{40}}^{-1}$ representations, the domain walls turn out to be $frac{1}{4}$-supersymmetric as in the seven-dimensional analogue. By the DW/QFT duality, these solutions are dual to maximal and half-maximal super Yang-Mills theories in five dimensions. All of the solutions can be uplifted to seven dimensions and further embedded in type IIB or M-theories by the well-known consistent truncation of the seven-dimensional $N=4$ gauged supergravity.
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We continue the study of supersymmetric domain wall solutions in six-dimensional maximal gauged supergravity. We first give a classification of viable gauge groups with the embedding tensor in $mathbf{5}^{+7}$, $bar{mathbf{5}}^{+3}$, $mathbf{10}^{-1}$, $mathbf{24}^{-5}$, and $overline{mathbf{45}}^{+3}$ representations of the off-shell symmetry $GL(5)subset SO(5,5)$. We determine an explicit form of the embedding tensor for gauge groups arising from each representation together with some examples of possible combinations among them. All of the resulting gauge groups are of a non-semisimple type with abelian factors and translational groups of different dimensions. We find $frac{1}{2}$- and $frac{1}{4}$-supersymmetric domain walls with $SO(2)$ symmetry in $SO(2)ltimes mathbb{R}^8$ and $SO(2)ltimes mathbb{R}^6$ gauge groups from the embedding tensor in $mathbf{24}^{-5}$ representation and in $CSO(2,0,2)ltimes mathbb{R}^4$, $CSO(2,0,2)ltimes mathbb{R}^2$, and $CSO(2,0,1)ltimes mathbb{R}^4$ gauge groups with the embedding tensor in $overline{mathbf{45}}^{+3}$ representations. These gauge groups are parametrized by a traceless matrix and electrically and magnetically embedded in $SO(5,5)$ global symmetry, respectively.
We compare the dynamics of maximal three-dimensional gauged supergravity in appropriate truncations with the equations of motion that follow from a one-dimensional E10/K(E10) coset model at the first few levels. The constant embedding tensor, which describes gauge deformations and also constitutes an M-theoretic degree of freedom beyond eleven-dimensional supergravity, arises naturally as an integration constant of the geodesic model. In a detailed analysis, we find complete agreement at the lowest levels. At higher levels there appear mismatches, as in previous studies. We discuss the origin of these mismatches.
We obtain Yang-Mills $SU(2)times G$ gauged supergravity in three dimensions from $SU(2)$ group manifold reduction of (1,0) six dimensional supergravity coupled to an anti-symmetric tensor multiplet and gauge vector multiplets in the adjoint of $G$. The reduced theory is consistently truncated to $N=4$ 3D supergravity coupled to $4(1+textrm{dim}, G)$ bosonic and $4(1+textrm{dim}, G)$ fermionic propagating degrees of freedom. This is in contrast to the reduction in which there are also massive vector fields. The scalar manifold is $mathbf{R}times frac{SO(3,, textrm{dim}, G)}{SO(3)times SO(textrm{dim}, G)}$, and there is a $SU(2)times G$ gauge group. We then construct $N=4$ Chern-Simons $(SO(3)ltimes mathbf{R}^3)times (Gltimes mathbf{R}^{textrm{dim}G})$ three dimensional gauged supergravity with scalar manifold $frac{SO(4,,1+textrm{dim}G)}{SO(4)times SO(1+textrm{dim}G)}$ and explicitly show that this theory is on-shell equivalent to the Yang-Mills $SO(3)times G$ gauged supergravity theory obtained from the $SU(2)$ reduction, after integrating out the scalars and gauge fields corresponding to the translational symmetries $mathbf{R}^3times mathbf{R}^{textrm{dim}, G}$.
Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in $mathcal{N}=2$ super-Yang-Mills (SYM) theory coupled to $N_f$ fundamental hypermultiplets. Our results are valid in $Dle 6$ dimensions, where the upper bound corresponds to six-dimensional chiral $mathcal{N}=(1,0)$ SYM theory. By exploiting a close connection with $mathcal{N}=4$ SYM theory - and, equivalently, six-dimensional $mathcal{N}=(1,1)$ SYM theory - we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding $D$-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning $N_f$ enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in $D=4$. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with $mathcal{N}=(1,1)$ and $mathcal{N}=(2,0)$ supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in $D=5-2epsilon$ and show that it non-trivially cancels out as expected.
We investigate a family of SU(3)$times$U(1)$times$U(1)-invariant holographic flows and Janus solutions obtained from gauged $mathcal{N}=8$ supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new phases in which M2 branes polarize partially or even completely into M5 branes. We derive the eleven-dimensional supersymmetries and show that the eleven-dimensional equations of motion and BPS equations are indeed satisfied as a consequence of their four-dimensional counterparts. Apart from elucidating a whole new class of eleven-dimensional Janus and flow solutions, our work provides extensive and highly non-trivial tests of the recently-derived uplift formulae.
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