Built on

S. Ferrara, A. F. Grillo and R. Gatto, “Manifestly conformal covariant operator-product expansion,” Lett. Nuovo Cim. 2S2
1971
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, “The shadow operator formalism for conformal algebra. vacuum expectation values and operator products,” Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
I. Bena, “On the construction of local fields in the bulk of AdS(5) and other spaces,” Phys. Rev. D 62
2000
Earlier work this paper cites.
K. Skenderis and S. N. Solodukhin, “Quantum effective action from the AdS/CFT correspondence,” Phys. Lett. B 472
2000
Earlier work this paper cites.
A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev. D 74
2006
Earlier work this paper cites.
A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, “Local bulk operators in AdS/CFT: A Holographic description of the black hole interior,” Phys. Rev. D 75
2007
Earlier work this paper cites.

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2016

Bulk fields from the boundary OPE

Guica, Monica

Understand

Previous work has established an equality between the geodesic integral of a free bulk field in AdS and the contribution of the conformal descendants of its dual CFT primary operator to the OPE of two other operators inserted at the endpoints of the geodesic.

Working in the context of the AdS$_3$/CFT$_2$ correspondence, we extend this relation to include the $1/N$ corrections to the bulk field obtained by dressing it with i) a $U(1)$ current and ii) the CFT stress tensor.
In the former case, we argue that the contribution of the Ka\v{c}-Moody descendants to the respective boundary OPE equals the geodesic integral of a particular $U(1)$-dressed bulk field, which is framed to the boundary via a split Wilson line.
In the latter case, we compute the gravitational $1/N$ corrections to the bulk field in various gauges, and then write a CFT expression for a putative bulk field whose geodesic integral captures the contribution of Virasoro descendants to the OPE of interest.

Built on

S. Ferrara, A. F. Grillo and R. Gatto, “Manifestly conformal covariant operator-product expansion,” Lett. Nuovo Cim. 2S2
1971
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, “The shadow operator formalism for conformal algebra. vacuum expectation values and operator products,” Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
I. Bena, “On the construction of local fields in the bulk of AdS(5) and other spaces,” Phys. Rev. D 62
2000
Earlier work this paper cites.
K. Skenderis and S. N. Solodukhin, “Quantum effective action from the AdS/CFT correspondence,” Phys. Lett. B 472
2000
Earlier work this paper cites.
A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev. D 74
2006
Earlier work this paper cites.
A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, “Local bulk operators in AdS/CFT: A Holographic description of the black hole interior,” Phys. Rev. D 75
2007
Earlier work this paper cites.