New Insights into 3D Conformal Gravity and Chiral Symmetries

Recent research by Nishant Gupta and Nemani V. Suryanarayana has introduced mixed boundary conditions for three-dimensional conformal gravity, which are consistent with the variational principle in its second-order formalism. This work highlights the chiral ( \Lambda )-( \mathfrak{bms}_4 ) algebra as the asymptotic symmetry algebra of these conditions. The chiral ( \Lambda )-( \mathfrak{bms}_4 ) algebra is recognized as one of the four chiral ( \mathcal{W} )-algebra extensions of ( \mathfrak{so}(2,3) ). It generalizes the chiral ( \mathfrak{bms}_4 ) algebra, which is known for its role in soft theorems of graviton MHV amplitudes in ( \mathbb{R}^{1,3} ) gravity, extending its application to scenarios with a non-zero negative cosmological constant.

The researchers calculated the corresponding charges using a modified covariant phase space formalism, demonstrating that these charges are finite and integrable. This realization of the non-linear ( \mathcal{W} )-algebra could have significant implications for understanding gravitational theories and their properties in various contexts, particularly in relation to cosmological models and quantum gravity.

The findings are detailed in the paper titled "Chiral ( \Lambda )-( \mathfrak{bms}_4 ) symmetry of 3d conformal gravity," which can be accessed through arXiv with the identifier arXiv:2405.20244.