Holography as homotopy.

Autor: Chiaffrino, Christoph, Ersoy, Talha, Hohm, Olaf
Zdroj: Journal of High Energy Physics; Sep2024, Vol. 2024 Issue 9, p1-50, 50p
Abstrakt: We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or L∞ algebra. We extend this dictionary to theories defined on manifolds with a boundary, including the conformal boundary of AdS, taking into account the cyclic structure needed to define an action with the correct boundary terms. Projecting fields to their boundary values then defines a homotopy retract, which in turn implies that the cyclic L∞ algebra of the bulk theory is equivalent, up to homotopy, to a cyclic L∞ algebra on the boundary. The resulting action is the ‘on-shell action’ conventionally computed via Witten diagrams that, according to AdS/CFT, yields the generating functional for the correlation functions of the dual CFT. These results are established with the help of new techniques regarding the homotopy transfer of cyclic L∞ algebras. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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