度量仿射形式中具有射影不变性的Galileon和广义Galileon
Galileon and generalized Galileon with projective invariance in a metric-affine formalism
摘要：
我们研究标量张量理论尊重的度量仿射形式主义的投影不变性。度规-仿射形式主义是引力理论的一种表述，使得度规和联系首先是独立变量。在这种形式主义中，爱因斯坦-希尔伯特作用量在联系的移动下具有额外的不变性，称为投影不变性。考虑到标量张量理论的这种不变性，我们发现弯曲时空中的伽利略项至少在四次阶上是唯一指定的，这与协变伽利略项或协变伽利略项都不一致。在度量仿射形式中我们还发现了一个作用量，它等价于二次退化高阶标量张量（DHOST）理论的${}^2$ N-I/Ia类. DHOST的结构在度规-仿射形式中变得清晰，因为等效作用量在广义Galileon项中是线性的，并且与Ricci标量和Einstein张量的非最小耦合具有独立系数。DHOST的微调结构是通过整合出的连接。在这些理论中，费米子场和标量场之间的非最小耦合可以被预测。我们讨论可能的扩展，可能涉及的理论超越DHOST。
英文摘要：
We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon. We also find an action in the metric-affine formalism which is equivalent to class ${}^2$N-I/Ia of the quadratic degenerated higher order scalar-tensor (DHOST) theory. The structure of DHOST would become clear in the metric-affine formalism since the equivalent action is just linear in the generalized Galileon terms and non-minimal couplings to the Ricci scalar and the Einstein tensor with independent coefficients. The fine-tuned structure of DHOST is obtained by integrating out the connection. In these theories, non-minimal couplings between fermionic fields and the scalar field may be predicted. We discuss possible extensions which could involve theories beyond DHOST.
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