谱函数的自举：关于Liouville的唯一性和BTZ的普适性
Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ
摘要：
我们引入谱函数，捕获分布的OPE系数和态密度在二维共形场论，并表明，非平凡的上限和下限的谱函数可以从半定规划。我们发现大量的数值证据表明，OPEs只涉及标量Virasoro原色在c>1 CFT必然由刘维理论的结构常数。结合模自举法的分析结果，我们推测Liouville理论是唯一的幺正c>1的CFT，它的原色具有有界自旋.我们还利用谱函数方法研究了CFT谱上的模约束，并讨论了我们的结果对大c和大gap的CFT的一些意义，特别是BTZ谱密度在多大程度上具有普适性.
英文摘要：
We introduce spectral functions that capture the distribution of OPE coefficients and density of states in two-dimensional conformal field theories, and show that nontrivial upper and lower bounds on the spectral function can be obtained from semidefinite programming. We find substantial numerical evidence indicating that OPEs involving only scalar Virasoro primaries in a c>1 CFT are necessarily governed by the structure constants of Liouville theory. Combining this with analytic results in modular bootstrap, we conjecture that Liouville theory is the unique unitary c>1 CFT whose primaries have bounded spins. We also use the spectral function method to study modular constraints on CFT spectra, and discuss some implications of our results on CFTs of large c and large gap, in particular, to what extent the BTZ spectral density is universal.
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