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Register a new userGeneralized ADT charges and asymptotic symmetry algebra
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Authors
Shailesh Kulkarni
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Using the expressions for generalized ADT current and potential in a self consistent manner, we derive the asymptotic symmetry algebra on AdS$_3$ and the near horizon extremal BTZ spacetimes. The structure of symmetry algebra among the conserved charges for asymptotic killing vectors matches exactly with the known results thus establishing the algebraic equivalence between the well known existing formalisms for obtaining the conserved charges and the generalized ADT charges.
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We present a method for finding, in principle, all asymptotic gravitational charges. The basic idea is that one must consider all possible contributions to the action that do not affect the equations of motion for the theory of interest; such terms include topological terms. As a result we observe that the first order formalism is best suited to an analysis of asymptotic charges. In particular, this method can be used to provide a Hamiltonian derivation of recently found dual charges.
This is a review of selected topics from recent work on symmetry charges in asymptotically flat spacetime done by the author in collaboration with U. Kol and R. Javadinezhad. First we reinterpret the reality constraint on the boundary graviton as the gauge fixing of a new local symmetry, called dual supertranslations. This symmetry extends the BMS group and bears many similarities to the dual (magnetic) gauge symmetry of electrodynamics. We use this new gauge symmetry to propose a new description of the TAUB-NUT space that does not contain closed time-like curves. Next we summarize progress towards the definition of Lorentz and super-Lorentz charges that commute with supertranslations and with the soft graviton mode.
To study quantum gravity in asymptotically flat spacetimes, one would like to understand the algebra of observables at null infinity. Here we show that the Bondi mass cannot be observed in finite retarded time, and so is not contained in the algebra on any finite portion of ${mathscr{I}}^+$. This follows immediately from recently discovered asymptotic entropy bounds. We verify this explicitly, and we find that attempts to measure a conserved charge at arbitrarily large radius in fixed retarded time are thwarted by quantum fluctuations. We comment on the implications of our results to flat space holography and the BMS charges at ${mathscr{I}}^+$.
We associate vertex operators to space-time diffeomorphisms in flat space string theory, and compute their algebra, which is a diffeomorphism algebra with higher derivative corrections. As an application, we realize the asymptotic symmetry group BMS3 of three-dimensional flat space in terms of vertex operators on the string worldsheet. This provides an embedding of the BMS3 algebra in a consistent theory of quantum gravity. Higher derivative corrections vanish asymptotically. An appendix is dedicated to alpha prime corrected algebras in conformal field theory and string theory.
BMS group (and its various generalizations) at null infinity have been studied extensively in the literature as the symmetry group of asymptotically flat spacetimes. The intricate relationship between soft theorems and the BMS symmetries have also motivated the definition of such asymptotic symmetries to time-like infinity. Although the vector fields that generate the (generalized) BMS algebra at time-like infinity was defined in the literature, the algebra has not been investigated. In this paper, we fill this gap. We show that the super-translations and vector fields that generate sphere diffeomorphisms close under the modified Lie bracket proposed by Barnich et al.
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