论文标题
带有重力的真实领域的纯连接公式
A pure connection formulation with real fields for Gravity
论文作者
论文摘要
我们研究了一个$（1,3）$纯连接公式在四个维度上，用于实现的领域，灵感来自Capovilla，Dell和Jacobson Complex Complex综合自我双重方法。还考虑了CMPR BF动作，考虑到Lie代数$ \ Mathfrak {so（1,3）} $的更通用的cartan杀伤形式，并通过完善Lagrange倍增器的结构，我们集成了度量变量以获得纯连接动作。一旦我们获得了这一动作，我们就会对拉格朗日乘数施加某些限制，以使运动方程式导致我们进入了一个无扭转型的共同扁平的爱因斯坦歧管，以两个数字进行了参数。最后，我们表明，通过适当的参数选择，可以获得自偶空间（反）de sitter。
We study an $SO(1,3)$ pure connection formulation in four dimensions for real-valued fields, inspired by the Capovilla, Dell and Jacobson complex self-dual approach. By considering the CMPR BF action, also, taking into account a more general class of the Cartan-Killing form for the Lie algebra $\mathfrak{so(1,3)}$ and by refining the structure of the Lagrange multipliers, we integrate out the metric variables in order to obtain the pure connection action. Once we have obtained this action, we impose certain restrictions on the Lagrange multipliers, in such a way that the equations of motion led us to a family of torsionless conformally flat Einstein manifolds, parametrized by two numbers. Finally, we show that, by a suitable choice of parameters, that self-dual spaces (Anti-) De Sitter can be obtained.
