论文标题
引力二元性，palatini变化和边界术语：摘要
Gravitational duality, Palatini variation and boundary terms: A synopsis
论文作者
论文摘要
我们考虑$ f（r）$ gravity和Born-infeld-inenstein（bie）重力，在该配方中，将指标和连接独立处理并整合了指标，以仅根据连接而找到相应的模型，而原型的治疗方法是Eddington-Schrödinger（ES）duality duality duality duality duality of Cosmological einstein einstein和Eddingtonton之间。对于尺寸$ d \ ne2 $，我们发现这需要$ f（r）$具有使模型Weyl不变性的特定形式，并且其减少的Eddington还等同于具有某些参数的Bie。对于$ d = 2 $尺寸，在不适用二重性的情况下，我们发现这两个模型都是Weyl不变的，并且等同于Bosonic String的一阶公式。我们还讨论了在具有非零边界的歧管上很好地定义的变分原理所需的边界项的形式。这需要修改重力的Gibbons-Hawking-York（GHY）边界项。这种修改还意味着公式和连接配方之间的二重性是一致的，并包括边界项。
We consider $f(R)$ gravity and Born-Infeld-Einstein (BIE) gravity in formulations where the metric and connection are treated independently and integrate out the metric to find the corresponding models solely in terms of the connection, the archetypical treatment being that of Eddington-Schrödinger (ES) duality between cosmological Einstein and Eddington theories. For dimensions $D\ne2$, we find that this requires $f(R)$ to have a specific form which makes the model Weyl invariant, and that its Eddington reduction is then equivalent to that of BIE with certain parameters. For $D=2$ dimensions, where ES duality is not applicable, we find that both models are Weyl invariant and equivalent to a first order formulation of the bosonic string. We also discuss the form of the boundary terms needed for the variational principle to be well defined on manifolds with non-null boundaries. This requires a modification of the Gibbons-Hawking-York (GHY) boundary term for gravity. This modification also means that the dualities between metric and connection formulations are consistent and include the boundary terms.
