论文标题
一致的截断至3维超级
Consistent truncations to 3-dimensional supergravity
论文作者
论文摘要
我们展示了如何构建10-/11维超重度的一致截断到3维的超重力，从而保留了各种量的超对称性。我们表明，与较高的维度一样，可以根据特殊字段理论中的广义$ g $结构来定义一致的截断，其中3维情况的$ g \ subset e_ {8（8）} $。与较高的维度不同，$ e_ {8（8）} $的广义谎言衍生物特殊字段理论需要一组“协变量约束”字段才能得到明确定义，我们展示了如何从$ g $结构本身构建这些字段。我们证明了一致的截断的几个一般特征，使我们可以排除许多三维测量超级重力的更高维度。特别是，我们表明，量规组的紧凑部分最多可以是$ \ mathrm {so}（9）$，并且在7或8维的球体上没有一致的截断，以使得球体的完整等轴测组被衡量。此外，我们对哪些物质耦合$ {\ cal n} \ geq 4 $衡量的超级重新构成可以从一致的截断中产生。最后，我们给出了三个维度一致截断的几个示例。其中包括$ s^7 $上的IIA和IIB超级截断，导致两个不同的$ {\ cal n} = 16 $衡量的超级格栅，以及$ h^{p，7-p} $上的更通用的IIA/IIB截断。我们还展示了如何在$ s^5 $ fibred在Riemann表面上构建一致的截断。这些结果导致3维$ {\ cal n} = 4 $测量的超级重力，具有标量歧管$ {\ cal m} = \ frac {\ mathrm {so}（so}（6,4）} {\ mathrm {so} \ frac {\ mathrm {su}（2,1）} {\ Mathrm {s}（\ Mathrm {\ mathrm {u}（2）（2）\ times \ times \ Mathrm {u}（1））} $ at $表面包含$ {\ cal n} =（2,2）$ ads $ _3 $ vacua。
We show how to construct consistent truncations of 10-/11-dimensional supergravity to 3-dimensional gauged supergravity, preserving various amounts of supersymmetry. We show, that as in higher dimensions, consistent truncations can be defined in terms of generalised $G$-structures in Exceptional Field Theory, with $G \subset E_{8(8)}$ for the 3-dimensional case. Differently from higher dimensions, the generalised Lie derivative of $E_{8(8)}$ Exceptional Field Theory requires a set of "covariantly constrained" fields to be well-defined, and we show how these can be constructed from the $G$-structure itself. We prove several general features of consistent truncations, allowing us to rule out a higher-dimensional origin of many 3-dimensional gauged supergravities. In particular, we show that the compact part of the gauge group can be at most $\mathrm{SO}(9)$ and that there are no consistent truncations on a 7-or 8-dimensional product of spheres such that the full isometry group of the spheres is gauged. Moreover, we classify which matter-coupled ${\cal N} \geq 4$ gauged supergravities can arise from consistent truncations. Finally, we give several examples of consistent truncations to three dimensions. These include the truncations of IIA and IIB supergravity on $S^7$ leading to two different ${\cal N}=16$ gauged supergravites, as well as more general IIA/IIB truncations on $H^{p,7-p}$. We also show how to construct consistent truncations on compactifications of IIB supergravity on $S^5$ fibred over a Riemann surface. These result in 3-dimensional ${\cal N}=4$ gauged supergravities with scalar manifold ${\cal M} = \frac{\mathrm{SO}(6,4)}{\mathrm{SO}(6) \times \mathrm{SO}(4)} \times \frac{\mathrm{SU}(2,1)}{\mathrm{S}(\mathrm{U}(2)\times\mathrm{U}(1))}$ with a $\mathrm{ISO}(3)\times\mathrm{U}(1)^4$ gauging and for hyperboloidal Riemann surfaces contain ${\cal N}=(2,2)$ AdS$_3$ vacua.
