Abstract
We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2)_k current algebras, the levels of which are given by k=l/(4G_N), where l is the AdS radius and G_N the three-dimensional Newton constant.
Highlights
Case the asymptotic symmetry algebra (ASA) consists of two copies of the Virasoro algebra with central charge c = 3l/(2GN ), i.e., the two-dimensional (2D) conformal algebra
The asymptotic symmetry algebra consists of two sl(2)k current algebras, the levels of which are given by k = l/(4GN ), where l is the AdS radius and GN the threedimensional Newton constant
A few years ago Troessaert constructed more general bc’s for 3D Einstein gravity that involve four state-dependent functions [17]. His ASA consists of two Virasoro and two u(1)k current algebras, which contains the other ASA’s as special cases
Summary
Our goal is achieved more in the CS formulation, which is why we start with this formulation.
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