论文标题
角色，旋转轨道和Duistermaat-Heckman积分
Characters, Coadjoint Orbits and Duistermaat-Heckman Integrals
论文作者
论文摘要
字符$χ_{kλ}（\ exp（h/k））$ coadighane-heckman（dh）集成符的差异$χ_{kλ}（\ exp（h/k））$不可减少的代表$ g $。这种现象将循环组的中央扩展的共同轨道概括为$ \ wideHat {lg} $以及圆圈$ \ wideHat {\ rm diff}（s^1）$的差异性。我们表明，仿射kac-moody代数和Virasoro代数的可集成模块的渐近学分量分解为标准形式的不同贡献和可以解释为正式的DH轨道整合的收敛贡献。 对于某些Virasoro模块，我们的结果与Stanford和Witten最近计算的正式DH积分相匹配。在这种情况下，$ k $尺度的起源与产生经典的保形块相同。此外，我们考虑了Virasoro coadhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhexhiist的空间，并建议在无限尺寸的情况下取代象征性体积。我们还考虑了Virasoro代数的其他模块（尤其是与最小模型相对应的模块），并且我们获得的DH型表达式与任何与任何Virasoro coadhexhexhexhexhexhexhexhexhexhexhechaint Orbits不符。 我们研究卷函数$ V（x）$，对应于Virasoro代数的coadhexhinexhoint Orbits的正式DH积分。我们表明，它们与Saad，Shenker和Stanford最近研究的Hankel Transform与光谱密度$ρ（e）$相关。
The asymptotics of characters $χ_{kλ}(\exp(h/k))$ of irreducible representations of a compact Lie group $G$ for large values of the scaling factor $k$ are given by Duistermaat-Heckman (DH) integrals over coadjoint orbits of $G$. This phenomenon generalises to coadjoint orbits of central extensions of loop groups $\widehat{LG}$ and of diffeomorphisms of the circle $\widehat{\rm Diff}(S^1)$. We show that the asymptotics of characters of integrable modules of affine Kac-Moody algebras and of the Virasoro algebra factorize into a divergent contribution of the standard form and a convergent contribution which can be interpreted as a formal DH orbital integral. For some Virasoro modules, our results match the formal DH integrals recently computed by Stanford and Witten. In this case, the $k$-scaling has the same origin as the one which gives rise to classical conformal blocks. Furthermore, we consider reduced spaces of Virasoro coadjoint orbits and we suggest a new invariant which replaces symplectic volume in the infinite dimensional situation. We also consider other modules of the Virasoro algebra (in particular, the modules corresponding to minimal models) and we obtain DH-type expressions which do not correspond to any Virasoro coadjoint orbits. We study volume functions $V(x)$ corresponding to formal DH integrals over coadjoint orbits of the Virasoro algebra. We show that they are related by the Hankel transform to spectral densities $ρ(E)$ recently studied by Saad, Shenker and Stanford.
