论文标题
相互作用量子场的字符串
Strings from interacting quantum fields
论文作者
论文摘要
我们将gopakumar在大N自由量子场理论[1]中的gopakumar的微观衍生物推广到扰动扩张中的相互作用理论。为简单起见，我们考虑了一个$φ^H $相互作用的矩阵标量字段。使用Schwinger的适当时间配方并按照LOOP $ \ ELL $的数量组织feynman图上的总和，我们表明，无数情况下的两点函数可以表示为$ ADS_ {D+1} $的大量散装标量的超出边界传播量的总和。大规模理论的两点函数具有与边界到结合的传播器相同的结构，但在几何形状上与与AD不同。总和中的系数包含有关相互作用QFT的假定字符串几何形状的信息。我们还考虑了现场理论中的三点函数，并表明它可以作为无限的总和，这一次是在三个散装到边界传播器的产物上。详细讨论了分歧和重新规定的问题。 我们还注意到场理论和弦振幅之间的相似之处令人着迷。特别是，我们观察到，在大N限制中，在全息方向上嵌入字符串函数对应于Feynman图的schwinger参数的连续限制，而$ \ ell $ diverges的限制为限制。这提供了直接从现场理论幅度出现的全息尺寸的解释。
We generalize Gopakumar's microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories in perturbative expansion. For simplicity we consider a matrix scalar field with $Φ^h$ interaction in d dimensions. Using Schwinger's proper time formulation and organizing the sum over Feynman diagrams by the number of loops $\ell$, we show that the two-point function in the massless case can be expressed as a sum over boundary-to-boundary propagators of massive bulk scalars in $AdS_{d+1}$ with masses determined by $\ell$. The two-point function of the massive theory has the same structure given by a sum over boundary-to-boundary propagators but on a geometry different than AdS. The coefficients in the sum contain information on the putative string geometry dual to the interacting QFT. We also consider the three-point function in the field theory and show that it can again be given as an infinite sum, this time over the products of three bulk-to-boundary propagators. The issue of divergences and renormalization is discussed in detail. We also notice an intriguing similarity between field theory and string amplitudes. In particular we observe that, in the large-N limit, embedding function of string in the holographic direction corresponds to a continuum limit of Schwinger parameters of Feynman diagrams in the limit where $\ell$ diverges. This provides an interpretation of the holographic dimension emerging directly from field theory amplitudes.
