Abstract
We analyze the residual gauge freedom in gravity, in four dimensions, in the light-cone gauge, in a formulation where unphysical fields are integrated out. By checking the invariance of the light-cone Hamiltonian, we obtain a set of residual gauge transformations, which satisfy the BMS algebra realized on the two physical fields in the theory. Hence, the BMS algebra appears as a consequence of residual gauge invariance in the bulk and not just at the asymptotic boundary. We highlight the key features of the light-cone BMS algebra and discuss its connection with the quadratic form structure of the Hamiltonian.
Highlights
In the light-cone formulation of gravity in four dimensions, one can gauge away the unphysical degrees of freedom and describe the dynamics of the theory in terms of the two physical states of the graviton
By checking the invariance of the light-cone Hamiltonian, we obtain a set of residual gauge transformations, which satisfy the BMS algebra realized on the two physical fields in the theory
We highlight the key features of the light-cone BMS algebra and discuss its connection with the quadratic form structure of the Hamiltonian
Summary
We impose the following three gauge choices [12, 13] on the dynamical variable gμν g−− = g−i = 0 , i = 1, 2. These choices are motivated by the fact that in Minkowski space, we have η−− = η−i = 0. Which may be solved by making the fourth and final gauge choice ψ φ=. Note that this gauge choice relates g+− and gij. Other constraint relations eliminate g++ and g+i resulting in the following action. This is the closed form expression for the light-cone gravity action [12, 13] — purely in terms of the physical degrees of freedom in the theory
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