The uplift of SO(8) gauged N=8 supergravity to 11-dimensional supergravity is well studied in the literature. It is given by consistent relations between the respective vector and scalar fields of both theories. For example, recent work provided non-linear uplift Ansätze for the scalar degrees of freedom on the internal manifold: the inverse metric and the three-form flux with mixed index structure. However, one always found the metric of the compactified manifold by inverting the inverse metric --- a task that was only possible in particular cases, e.g. for the G$_2$, SO(3)$\times$SO(3) or SU(3)$\times$U(1)$\times$U(1) invariant solutions of 11-dimensional supergravity.
In this paper, I present a direct non-linear uplift Ansatz for the internal metric in terms of the four-dimensional scalars and the Killing forms on the compactified background manifold. Based on this formula, I also find new uplift Ansätze for the warp factor and the full three-form flux. Finally, I provide a direct non-linear uplift Ansatz for the internal four-form field-strength in terms of the metric, the flux as well as the four-dimensional scalars and background Killing forms. This new formula does not require to calculate the derivative of the flux.
My results may be generalized to other compactifications, e.g. the reduction from type IIB supergravity to five dimensions.
We introduce fusion $U_q(G^{(1)}_2)$ vertex models related to fundamental representations. The eigenvalues of their row to row transfer matrices are derived through analytic Bethe ans{ä}tze. By combining these results with our previous studies on functional relations among transfer matrices(the $T$-system), we conjecture explicit eigenvalues for a wide class of fusion models. These results can be neatly expressed in terms of a Yangian analogue of the Young tableaux.
We derive new ansaetze for the 4-form field strength of D=11 supergravity corresponding to uplifts of four-dimensional maximal gauged supergravity. In particular, the ansaetze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity---in this way they provide an explicit uplift of all four-dimensional consistent truncations of D=11 supergravity. The new ansaetze provide a substantially simpler method for uplifting d=4 flows compared to the previously available method using the 3-form and 6-form potential …
We provide the M-theory uplift of de Sitter vacua of SO(5,3) and SO(4,4) gaugings of maximal supergravity in 4 dimensions. We find new non-compact backgrounds that are squashed hyperboloids with non-trivial flux for the 3-form potential. The uplift requires a new non-linear ansatz for the 11-dimensional metric and for the 3-form potential that reduces to the known one leading to the 7-sphere solution in the case of the SO(8) gauging.
Through the construction of a complete non-linear Kaluza-Klein reduction ansatz from type IIB supergravity to Romans' F(4) gauged supergravity, we identify a recently discovered supersymmetric AdS_6 solution as the IIB uplift of the supersymmetric vacuum of Romans' theory. We present new IIB uplifts of a number of known solutions of Romans' theory and comment on supersymmetry in higher-dimensions where it is expected.
We consider self-duality equation of U(1) gauge fields on Euclidean AdS_4 space, and find a simple finite action solution. With a suitable ansatz, we are able to embed this solution into the 10d supergravity background of AdS_4\times CP^3. Further, we show that the solution can be uplifted to an exact solution in 11d supergravity background of AdS_4\times SE_7.
A procedure is described to construct generalised Scherk-Schwarz uplifts of gauged supergravities. The internal manifold, fluxes, and consistent truncation Ansatz are all derived from the embedding tensor of the lower-dimensional theory. We first describe the procedure to construct generalised Leibniz parallelisable spaces where the vector components of the frame are embedded in the adjoint representation of the gauge group, as specified by the embedding tensor. This allows us to recover the generalised Scherk-Schwarz reductions known in the literature and to prove a no-go result for the uplif…
We consider the most general class of supersymmetric solutions of D=11 supergravity consisting of a warped product of AdS_5 with a six-dimensional internal manifold N_6, which are dual to N=2 super conformal field theories in d=4. For any such N_6 we construct the full non-linear Kaluza-Klein ansatz for the reduction of D=11 supergravity on N_6 down to D=5 SU(2)xU(1) gauged supergravity, at the level of the bosonic fields. This allows one to uplift any solution of the D=5 supergravity to obtain a solution of D=11 supergravity for any given N_6. Using an explicit N_6, corresponding to M5-branes…
We study holographic dual descriptions of very special conformal field theories with the T(2) symmetry. After constructing solutions in effective five dimensional Einstein gravity coupled with massive two-form fields, we uplift them to the ten dimensional type IIB supergravity, via a consistent truncation ansatz, to derive new analytical solutions in string theory. From the Kaluza-Klein ansatz in terms of the internal Sasaki-Einstein space, we obtain their field theory interpretation with concrete realizations in a large class of holographic $\mathcal{N}=1$ supersymmetric conformal field theor…
We construct a consistent reduction ansatz of eleven-dimensional supergravity to $N=2$ $SO(4)$ seven-dimensional gauged supergravity with topological mass term for the three-form field. The ansatz is obtained from a truncation of the $S^4$ reduction giving rise to the maximal $N=4$ $SO(5)$ gauged supergravity. Therefore, the consistency is guaranteed by the consistency of the $S^4$ reduction. Unlike the gauged supergravity without topological mass having a half-supersymmetric domain wall vacuum, the resulting 7D gauged supergravity theory admits a maximally supersymmetric $AdS_7$ critical poin…
We present non-linear uplift ansaetze for all the bosonic degrees of freedom and dual fields in the 7-sphere reduction of D=11 supergravity to maximal SO(8) gauged supergravity and test them for the SO$(7)^{\pm}$ invariant solutions. In particular, we complete the known ansaetze for the internal components of the metric and 4-form flux by constructing a non-linear ansatz for the internal components of the dual 7-form flux. Furthermore, we provide ansaetze for the complete set of 56 vector fields, which are given by more general structures than those available from standard Kaluza-Klein theory.…
We give a large class of supersymmetric domain walls in maximal seven-dimensional gauged supergravity with various types of gauge groups. Gaugings are described by components of the embedding tensor transforming in representations $\mathbf{15}$ and $\overline{\mathbf{40}}$ of the global symmetry $SL(5)$. The embedding tensor in $\mathbf{15}$ representation leads to $CSO(p,q,5-p-q)$ gauge groups while gaugings in $\overline{\mathbf{40}}$ representation describes $CSO(p,q,4-p-q)$ gauge groups. These gaugings admit half-supersymmetric domain walls as vacuum solutions. On the other hand, gaugings …
We study supersymmetric solutions within seven-dimensional $N=2$ gauged supergravity coupled to three vector multiplets in seven dimensions. The gauged supergravity contains six vector fields that gauge the $SO(4)\sim SO(3)\times SO(3)$ symmetry and admits two $N=2$ supersymmetric $AdS_7$ vacua with $SO(4)$ and $SO(3)_{\textrm{diag}}\subset SO(3)\times SO(3)$ symmetries. We consider solutions interpolating between two asymptotically locally $AdS_7$ geometries in the presence of a three-form field. For a particular value of the two $SO(3)$ gauge coupling constants, the $SO(3)_{\textrm{diag}}$ s…
We consider the Attractor Equations of particular $\mathcal{N}=2$, d=4 supergravity models whose vector multiplets' scalar manifold is endowed with homogeneous symmetric cubic special Kähler geometry, namely of the so-called $st^{2}$ and $stu$ models. In this framework, we derive explicit expressions for the critical moduli corresponding to non-BPS attractors with vanishing $\mathcal{N}=2$ central charge. Such formulæhold for a generic black hole charge configuration, and they are obtained without formulating any \textit{ad hoc} simplifying assumption. We find that such attractors are related …
We study RG flow solutions in (1,0) six dimensional supergravity coupled to an anti-symmetric tensor and Yang-Mills multiplets corresponding to a semisimple group $G$. We turn on $G$ instanton gauge fields, with instanton number $N$, in the conformally flat part of the 6D metric. The solution interpolates between two (4,0) supersymmetric $AdS_3\times S^3$ backgrounds with two different values of $AdS_3$ and $S^3$ radii and describes an RG flow in the dual 2D SCFT. For the single instanton case and $G=SU(2)$, there exist a consistent reduction ansatz to three dimensions, and the solution in thi…
We study a number of supersymmetric solutions in the form of $Mkw_3\times S^3$- and $AdS_3\times S^3$-sliced domain walls in the maximal gauged supergravity in seven dimensions. These solutions require non-vanishing three-form fluxes to support the $AdS_3$ and $S^3$ subspaces. We consider solutions with $SO(4)$, $SO(3)$, $SO(2)\times SO(2)$ and $SO(2)$ symmetries in $CSO(p,q,5-p-q)$, $CSO(p,q,4-p-q)$ and $SO(2,1)\ltimes \mathbf{R}^4$ gauge groups. All of these solutions can be analytically obtained. For $SO(5)$ and $CSO(4,0,1)$ gauge groups, the complete truncation ansatze in terms of eleven-d…
The auxiliary-deformed Breitenlohner-Maison model: duality frames and higher-dimensional origin
Asia Pacific Center for Theoretical Physics (APCTP), Postech（亚太理论物理中心（APCTP），浦项科技大学）；High Energy Physics Research Unit, Faculty of Science Chulalongkorn University（朱拉隆功大学理学院高能物理研究单元）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））
We consider the conditions for integrating out heavy chiral fields and moduli in N=1 supergravity, subject to two explicit requirements. First, the expectation values of the heavy fields should be unaffected by low energy phenomena. Second, the low energy effective action should be described by N=1 supergravity. This leads to a working definition of decoupling in N=1 supergravity that is different from the usual condition of gravitational strength couplings between sectors, and that is the relevant one for inflation with moduli stabilization, where some light fields (the inflaton) can have lon…
