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Holography as homotopy

Jul 16, 2023

50 pages

Published in:

JHEP 09 (2024) 161

Published: Sep 24, 2024

e-Print:

2307.08094 [hep-th]

DOI:

10.1007/JHEP09(2024)161

Report number:

HU-EP-23/22

View in:

ADS Abstract Service

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Abstract: (Springer)

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.

Note:

50 pages, 1 figure. v2: references added, typo corrected

AdS-CFT Correspondence
BRST Quantization
field theory: conformal
homotopy
algebra
cyclic
holography
AdS/CFT correspondence
Lie
duality

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