Supersymmetric boundary algebras in AdS3 gravity: constraints, Dirac brackets and non-locality
Abstract
We study supersymmetric boundary dynamics in AdS3 gravity by treating boundary conditions as constrained reductions of a generic Chern-Simons boundary phase space. We focus on how the constraint structure controls the locality and physical field content of the reduced asymptotic symmetry algebra. For supersymmetric Kac--Moody boundary conditions, the surviving bosonic currents remain local, whereas the fermion--fermion Dirac bracket contains the inverse of a field-dependent first-order differential operator and is therefore intrinsically non-local. Imposing an additional fermionic constraint reveals a further structure: after the bosonic second-class reduction, it becomes first class and generates a fermionic gauge redundancy. Generically the remaining fermionic field can be gauged away, while special backgrounds with periodic zero modes support non-trivial physical fermionic sectors. We further employ the Batalin--Fradkin--Tyutin formalism to eliminate the non-locality of the reduced symmetry algebra by converting the second-class constraints into an equivalent local first-class system on an enlarged phase space.
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BibTeX
@misc{banerjee2026supersymmetric,
title = {{Supersymmetric boundary algebras in AdS$_3$ gravity: constraints, Dirac brackets and non-locality}},
author = {Nabamita Banerjee and Vedant Bhutra and Suvankar Dutta and Soumava Kundu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20112},
eprint = {2609.20112},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20112},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Supersymmetric boundary algebras in AdS_3 gravity: constraints, Dirac brackets and non-locality
AU - Nabamita Banerjee
AU - Vedant Bhutra
AU - Suvankar Dutta
AU - Soumava Kundu
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.20112
UR - https://arxiv.org/abs/2609.20112
AB - We study supersymmetric boundary dynamics in AdS_3 gravity by treating boundary conditions as constrained reductions of a generic Chern-Simons boundary phase space. We focus on how the constraint structure controls the locality and physical field content of the reduced asymptotic symmetry algebra. For supersymmetric Kac--Moody boundary conditions, the surviving bosonic currents remain local, whereas the fermion--fermion Dirac bracket contains the inverse of a field-dependent first-order differential operator and is therefore intrinsically non-local. Imposing an additional fermionic constraint reveals a further structure: after the bosonic second-class reduction, it becomes first class and generates a fermionic gauge redundancy. Generically the remaining fermionic field can be gauged away, while special backgrounds with periodic zero modes support non-trivial physical fermionic sectors. We further employ the Batalin--Fradkin--Tyutin formalism to eliminate the non-locality of the reduced symmetry algebra by converting the second-class constraints into an equivalent local first-class system on an enlarged phase space.
ER -