论文标题
Rademacher扩展和2D CFT的光谱
Rademacher Expansions and the Spectrum of 2d CFT
论文作者
论文摘要
Rademacher对分析数理论的经典结果为非阳性重量模块化形式的傅立叶系数提供了一个精确的公式。我们采用类似的技术来研究二维单一形成型田间理论的光谱，没有延长的手性代数和$ c> 1 $。通过利用分区函数的完整模块化约束，我们就该理论的光谱提出了光谱密度的表达式。该表达式是根据rademacher扩展给出的，该扩展为旋转$ j \ neq 0 $收敛。对于有限数量的轻型操作员，表达与Maloney，Witten和Keller开发的Poincare Construction的变体一致。通过此框架，我们研究了分区功能双重对纯重力的负密度的存在，并提出了一种治愈这种消极性的方案。
A classical result from analytic number theory by Rademacher gives an exact formula for the Fourier coefficients of modular forms of non-positive weight. We apply similar techniques to study the spectrum of two-dimensional unitary conformal field theories, with no extended chiral algebra and $c>1$. By exploiting the full modular constraints of the partition function we propose an expression for the spectral density in terms of the light spectrum of the theory. The expression is given in terms of a Rademacher expansion, which converges for spin $j \neq 0$. For a finite number of light operators the expression agrees with a variant of the Poincare construction developed by Maloney, Witten and Keller. With this framework we study the presence of negative density of states in the partition function dual to pure gravity, and propose a scenario to cure this negativity.
