论文标题
广告中的一环字符串振幅
One-loop string amplitudes in AdS$_5\times$S$^5$: Mellin space and sphere splitting
论文作者
论文摘要
我们研究单粒子运算符的单层振幅的字符串校正$ {\ cal o} _p $ in $ ads_5 \ times s^5 $。超级重力中的树级相关器享有意外的10D形式对称性。因此，人们观察到双跟踪操作员的异常尺寸的频谱中的部分变性，与此同时，对于不同外部电荷的许多不同相关器的平等性$ p_ {i = 1,2,3,4} $。一环的贡献有望提高这种奖励性能，并且可以从树级数据和与操作员产品扩展的一致性中预测其精确形式。在这里，我们为$ \ langle {\ cal o} _ {p_1} {\ cal O} _ {p_2} {\ cal o} _ {p_3} {p_3} {\ cal o} {p_4} _ {p_4} _ { $ p_ {i} $。我们的公式通过我们称为“球体拆分”的功能，明确说明了不同相关器之间的奖励变性。虽然树级的梅林振幅带有一个单个交叉对称内核，该内核定义了$ ads_5 \ times s^5 $振幅的极点结构，但我们的一环幅度自然地将$ S^5 $部分分为两个单独的贡献。通过大型$ p $限制，该振幅与相应的平面IIB振幅具有显着的一致性。
We study string corrections to one-loop amplitudes of single-particle operators ${\cal O}_p$ in $AdS_5 \times S^5$. The tree-level correlators in supergravity enjoy an accidental 10d conformal symmetry. Consequently, one observes a partial degeneracy in the spectrum of anomalous dimensions of double-trace operators and at the same time equality of many different correlators for different external charges $p_{i=1,2,3,4}$. The one-loop contribution is expected to lift such bonus properties, and its precise form can be predicted from tree-level data and consistency with the operator product expansion. Here we present a closed-form Mellin space formula for $\langle {\cal O}_{p_1}{\cal O}_{p_2}{\cal O}_{p_3} {\cal O}_{p_4}\rangle$ at order $(α')^3$, valid for arbitrary external charges $p_{i}$. Our formula makes explicit the lifting of the bonus degeneracy among different correlators through a feature we refer to as `sphere splitting'. While tree-level Mellin amplitudes come with a single crossing symmetric kernel, which defines the pole structure of the $AdS_5\times S^5$ amplitude, our one-loop amplitude naturally splits the $S^5$ part into two separate contributions. The amplitude also exhibits a remarkable consistency with the corresponding flat space IIB amplitude through the large $p$ limit.
