Kavli Affiliate: Hirosi Ooguri
| First 5 Authors: Monica Jinwoo Kang, Jaeha Lee, Hirosi Ooguri, ,
| Summary:
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.
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