Anomalous dimensions from quantum Wilson lines

Abstract

We study the self-energy of a gravitating point particle in AdS${}_3$, and compare to operator dimensions in CFT${}_2$. In particular, we compute the one and two loop diagram contributions to the expectation value of an open Wilson line in the SL(2,R)$\times$ SL(2,R) Chern-Simons formulation of AdS${}_3$ gravity. This gives the two-point function of CFT primary operators to second order in a large $c$ expansion, and hence yields the scaling dimension $h(j,c)$ as a function of the SL(2,R) spin $j$. Comparison to CFT is made in the context of constructing Virasoro representations starting from representations of SL(2,R) current algebra. Our Wilson line computations follow the framework advanced recently by Fitzpatrick et. al., which is based on earlier work by H. Verlinde. We encounter some renormalization scheme ambiguities at the two-loop level which we are not able to fully resolve, hampering a definitive comparison with CFT expressions at this order.

17 pages

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Cited by in corpus (13)

• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• A Numerical Approach to Virasoro Blocks and the Information Paradox
• Conformal blocks from Wilson lines with loop corrections
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections
• Renormalization of gravitational Wilson lines
• Scalar Blocks as Gravitational Wilson Networks
• A note on the Virasoro blocks at order $1/c$
• Superconformal blocks from Wilson lines with loop corrections
• More on Wilson toroidal networks and torus blocks
• A view of the bulk from the worldline
• A note on the $\mathcal{N}=2$ super-${\mathcal{W}}_3$ holographic dictionary
• Gravitational Wilson lines in AdS${}_3$