论文标题
Alpha Prime的零杂种黑洞机械师的第一定律
The first law of heterotic stringy black hole mechanics at zeroth order in alpha prime
论文作者
论文摘要
我们使用瓦尔德（Wald）的形式，协变量的谎言衍生物和动量图，在杂质超弦有效作用的背景下重新衍生了黑洞力学的第一定律。该理论的Kalb-ramond田地强度具有Abelian Chern-Simons术语，该术语诱导了Kalb-Ramond Field的Nicolai-Townsend转换。我们展示了如何根据明显的量规数量来处理所有这些规则的对称性。在Chern-Simons术语的情况下，存在保守指控的几个定义，但是形式主义只会挑选其中一个在第一定律中发挥作用。 这项工作是在Alpha Prime中衍生第一定律的第一步，在Kalb-Ramond Field强度中包括更复杂的，更复杂的非亚伯利亚语Lorentz（“引力”）和Yang-Mills Chern-Simons项。第一定律的推导是朝着明显规模不变的熵公式推导的必要步骤，该公式仍然缺乏文献。反过来，需要此熵公式来比较明确的宏观和微观黑洞熵。
We re-derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in alpha prime, using Wald's formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In presence of Chern-Simons terms, several definitions of the conserved charges exist, but the formalism picks up only one of them to play a role in the first law. This work is a first step towards the derivation of the first law at first order in alpha prime where, more complicated, non-Abelian, Lorentz ("gravitational") and Yang-Mills Chern-Simons terms are included in the Kalb-Ramond field strength. The derivation of a first law is a necessary step towards the derivation of a manifestly gauge-invariant entropy formula which is still lacking in the literature. In its turn, this entropy formula is needed to compare unambiguously macroscopic and microscopic black hole entropies.
