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Loops in AdS: From the Spectral Representation to Position Space · Around

2019

Loops in AdS: From the Spectral Representation to Position Space

Carmi, Dean

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We compute a family of scalar loop diagrams in $AdS$.

We use the spectral representation to derive various bulk vertex/propagator identities, and these identities enable to reduce certain loop bubble diagrams to lower loop diagrams, and often to tree-level exchange or contact diagrams.
An important example is the computation of the finite coupling 4-point function of the large-$N$ conformal $O(N)$ model on $AdS_3$.
Remarkably, the re-summation of bubble diagrams is equal to a tree-level contact diagram: the $\bar{D}_{1,1,\frac{3}{2},\frac{3}{2}} (z,\bar z)$ function.

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