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Renormalization of gravitational Wilson lines
- Source :
- Journal of High Energy Physics, Vol 2019, Iss 6, Pp 1-44 (2019), Journal of High Energy Physics
- Publication Year :
- 2019
- Publisher :
- SpringerOpen, 2019.
-
Abstract
- We continue the study of the Wilson line representation of conformal blocks in two-dimensional conformal field theory; these have an alternative interpretation as gravitational Wilson lines in the context of the AdS$_3$/CFT$_2$ correspondence. The gravitational Wilson line involves a path-ordered exponential of the stress tensor, and its expectation value can be computed perturbatively in an expansion in inverse powers of the central charge $c$. The short-distance singularities which occur in the associated stress tensor correlators require systematic regularization and renormalization prescriptions, whose consistency with conformal Ward identities presents a subtle problem. The regularization used here combines dimensional regularization and analytic continuation. Representation theoretic arguments, based on SL(2,R) current algebra, predict an exact result for the Wilson line anomalous dimension and, by building on previous work, we verify that the perturbative calculations using our regularization and renormalization prescriptions reproduce the exact result to order $1/c^3$ included. We also discuss a related, but somewhat simpler, Wilson line in Wess-Zumino-Witten models that yields current algebra conformal blocks, and we emphasize the distinction between Wilson lines constructed out of non-holomorphic and purely holomorphic currents.<br />Comment: 47 pages
- Subjects :
- Physics
High Energy Physics - Theory
Nuclear and High Energy Physics
Conformal Field Theory
010308 nuclear & particles physics
Conformal field theory
Analytic continuation
High Energy Physics::Lattice
Current algebra
FOS: Physical sciences
AdS-CFT Correspondence
01 natural sciences
Renormalization
AdS/CFT correspondence
Dimensional regularization
High Energy Physics - Theory (hep-th)
Regularization (physics)
0103 physical sciences
lcsh:QC770-798
lcsh:Nuclear and particle physics. Atomic energy. Radioactivity
010306 general physics
Central charge
Mathematical physics
Subjects
Details
- Language :
- English
- ISSN :
- 10298479
- Volume :
- 2019
- Issue :
- 6
- Database :
- OpenAIRE
- Journal :
- Journal of High Energy Physics
- Accession number :
- edsair.doi.dedup.....50f0aa8a7b1c4928dfee197e32bb5cb4