It has been known for a while that the effective geometrical description of compactified strings on $d$-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an $O(d,d)$ pairing $η$ and an $O(2d)$ generalized metric $\mathcal{H}$. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing $ω$. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure $(η,ω,\mathcal{H})$ and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics.
Universidad de Buenos Aires（布宜诺斯艾利斯大学）；CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA)（阿根廷国家科学研究委员会-布宜诺斯艾利斯大学，布宜诺斯艾利斯物理研究所 (IFIBA)）；Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA)（天文与空间物理研究所 (IAFE, 阿根廷国家科学研究委员会-布宜诺斯艾利斯大学)）
Constraints on generalized Eddington-inspired Born-Infeld branes
Palatini的$f(|\hatΩ|)$引力是Eddington启发的Born-Infeld引力的推广，其中$Ω_{~N}^{K}\equivδ_{~N}^{K}+bg^{KL}R_{LN}(Γ)$是由时空度量$g$和独立连接$Γ$构造的辅助张量。本文利用$f(|\hatΩ|)=|\hatΩ|^{\frac{1}{2}+n}$在厚膜情形下研究了$f(|\hatΩ|)$理论，并给出了对膜模型的一些约束条件。我们终于找到了由单个标量场产生的厚膜的解析解。负能量密度的行为表明，在额外维度的原点，厚膜是局部化的。在我们的膜世界中，翘曲因子在额外维度的边界处是发散的，而膜系统是渐近反$-$ de Sitter的。结果表明，膜的张量扰动是稳定的，无质量引力子局域在厚膜上。因此，有效的爱因斯坦-希尔伯特作用量可以在低能近似下重建。根据最近对引力平方反比定律的检验，我们给出了$f(|\hatΩ|)$膜上的一些约束。
