AI 中文总结
本文研究渐近AdS₃时空量子引力的波函数与T$\bar{T}$形变环面配分函数的关系，通过可逆积分变换实现体波函数与形变配分函数的相互重构，还探讨了其在德西特全息等方向的推广。
AI 中文摘要
我们研究渐近AdS$_3$时空中量子引力的波函数及其与$T\bar{T}$形变环面配分函数的关系。我们证明，形变后的配分函数由体波函数的可逆积分变换给出，其核编码了$T\bar{T}$耦合与体中径向或时间坐标之间的关系。该变换的可逆性使得可以从$T\bar{T}$形变配分函数族中重构体波函数。在CFT极限下，核有效地定域在渐近边界，恢复了标准全息关系，即环面上的配分函数由体波函数的边界值决定。对于有限形变，核将有效全息屏从渐近边界移开并扩展为有限体区域。固定耦合下的$T\bar{T}$形变配分函数对应于以形变尺度设定的径向或时间位置为中心、有限宽度的体波包。在欧几里得符号下，该构造自然产生于Rindler AdS$_3$的波函数；经双重威克转动后，它可被解释为无渐近边界的闭合AdS$_3$环面宇宙的洛伦兹描述。最后，我们讨论将当前构造推广到德西特环面宇宙的情况及其对德西特全息的意义，并提及向更一般空间拓扑和高维时空的可能推广。
英文摘要
We study wavefunctions of quantum gravity in asymptotically AdS$_3$ spacetimes and their relation to $T\bar{T}$-deformed torus partition functions. We show that the deformed partition function is given by an invertible integral transform of bulk wavefunctions, with a kernel encoding the relation between the $T\bar{T}$ coupling and the radial or temporal coordinate in the bulk. The invertibility of the transform allows the bulk wavefunction to be reconstructed from the family of $T\bar{T}$-deformed partition functions. In the CFT limit, the kernel effectively localizes at the asymptotic boundary, recovering the standard holographic relation in which the partition function on the torus is determined by the boundary value of the bulk wavefunction. For finite deformation, the kernel shifts the effective holographic screen away from the asymptotic boundary and broadens it into a finite bulk region. A $T\bar{T}$-deformed partition function at fixed coupling corresponds to a finite-width bulk wavepacket centered around a radial or temporal location set by the deformation scale. In Euclidean signature, the construction arises naturally from wavefunctions of Rindler AdS$_3$, while after a double Wick rotation it admits a Lorentzian interpretation in terms of closed AdS$_3$ torus universes without asymptotic boundaries. Finally, we discuss the extension of the present construction to de Sitter torus universes and its implications for de Sitter holography, and comment on possible generalizations to more general spatial topologies and higher-dimensional spacetimes.
Comments28 pages, 4 figures. v2: a reference added
