A class of globally scale-invariant scalar-tensor theories have been proposed to be invariant under a larger class of transformations that take the form of local Weyl transformations supplemented by a restriction that the conformal factor satisfies a covariant Klein-Gordon equation. The action of these theories indeed seems to be invariant under such transformations up to boundary terms, this property being referred to as ``restricted Weyl symmetry''. However, we find that corresponding equations of motion are not invariant under these transformations. This is a paradox, that is explained by realizing that the restriction condition on the conformal factor forces the restricted Weyl transformation to be a nonlocal transformation. For nonlocal transformations would-be boundary terms cannot in general be discarded from the action. Moreover, variations of trajectories cannot be assumed to vanish at boundaries of the action when deriving equations of motion. We illustrate both of these less known properties by considering a series of simple examples. Finally, we apply these observations to the case of globally scale-invariant scalar-tensor theories to demonstrate that restricted Weyl transformations are, in fact, not symmetries of the full system.
Gravitating magnetic monopole via the spontaneous symmetry breaking of pure $R^2$ gravity
纯$R^2$引力等价于具有宇宙学常数和无质量标量场的爱因斯坦引力，并具有比标度对称性更大的所谓限制外尔对称性。考虑了由纯$R^2$引力、SU（2）Yang-Mills场和非最小耦合的无质量Higgs场（标量的三重态）组成的限制Weyl不变作用量。当限制的外尔对称自发破缺时，它等价于具有宇宙学常数的爱因斯坦-杨-米尔斯-希格斯（EYMH）作用量和大质量的希格斯粒子与引力的非最小耦合，即通过一个项$\tildeξ R |Φ|^2$。当限制外尔对称性没有自发破缺时，闵可夫斯基时空的线性化不会在原始$R^2$引力中产生引力子，因此它不会引力。然而，我们表明，在我们的理论的破规范部门，希格斯场获得非零真空期望值，闵可夫斯基时空是一个可行的引力背景解决方案。然后，我们得到了非零耦合常数$\tildeξ=1/6$在三种不同背景下的数值引力磁解：Minkowski，反德西特（AdS）和德西特（dS），所有这些都是在我们的限制Weyl不变量理论实现。
The Saito determinant for extended affine Weyl discriminant strata
University of Sheffield（谢菲尔德大学）；CNRS, DR 13, Montpellier（法国国家科学研究中心，DR 13，蒙彼利埃）；Università di Milano-Bicocca（米兰比可卡大学）；INFN sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）
Covariant Phase Space and Carroll-Weyl $χ$ Symmetry of Carroll Non-BPS D$_p$-branes
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，UCAS）；Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，UCAS）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
