论文标题
连续对称的状态密度的通用公式
A universal formula for the density of states with continuous symmetry
论文作者
论文摘要
我们考虑具有紧凑的谎言组全球对称$ g $的$ d $维统一的共形场理论，并表明，在高温$ t $和紧凑的考奇表面上，随机选择的状态在不可约合的统一表示$ r $ g $中的可能性与$ r $ g $成比例成比例$（\ operatatorName {dim} r）^2 \，\ exp [-c_2（r）/（b \，t^{d-1}）] $。我们使用Spurion分析来得出此公式，并将常数$ B $与域壁张力联系起来。我们还将其验证为免费的现场理论和全息形式的形状理论，并在这些情况下计算$ b $。这概括了Arxiv：2109.03838的结果，即当$ g $是有限的组时，概率与$（\ operatatorName {dim} r）^2 $成正比。作为该分析的副产品，我们阐明了在反DE保姆空间中具有非亚伯头发的黑洞的热力学特性。
We consider a $d$-dimensional unitary conformal field theory with a compact Lie group global symmetry $G$ and show that, at high temperature $T$ and on a compact Cauchy surface, the probability of a randomly chosen state being in an irreducible unitary representation $R$ of $G$ is proportional to $(\operatorname{dim}R)^2\,\exp[-c_2(R)/(b\, T^{d-1})]$. We use the spurion analysis to derive this formula and relate the constant $b$ to a domain wall tension. We also verify it for free field theories and holographic conformal field theories and compute $b$ in these cases. This generalizes the result in arXiv:2109.03838 that the probability is proportional to $(\operatorname{dim}R)^2$ when $G$ is a finite group. As a by-product of this analysis, we clarify thermodynamical properties of black holes with non-abelian hair in anti-de Sitter space.
