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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.
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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.
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.
In this paper we investigate in detail the correspondence between E10 and Romans massive deformation of type IIA supergravity. We analyse the dynamics of a non-linear sigma model for a spinning particle on the coset space E10/K(E10) and show that it reproduces the dynamics of the bosonic as well as the fermionic sector of the massive IIA theory, within the standard truncation. The mass deformation parameter corresponds to a generator of E10 outside the realm of the generators entering the usual D=11 analysis, and is naturally included without any deformation of the coset model for E10/K(E10). Our analysis thus provides a dynamical unification of the massless and massiv
States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in five dimensions. These supersymmetric solutions provide examples of consistent truncation from type IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. We offer an interpretation of these surprising features in terms of ensembles of brane distributions.
We argue that recent results in string perturbation theory indicate that the four-graviton amplitude of four-dimensional N=8 supergravity might be ultraviolet finite up to eight loops. We similarly argue that the h-loop M-graviton amplitude might be finite for h<7+M/2.
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