Abstract
We obtain the subleading soft theorem for a generic theory of quantum gravity, for arbitrary number of soft photons and gravitons and for arbitrary number of finite energy particles with arbitrary mass and spin when all the soft particles are soft in the same rate. This result is valid at tree level for spacetime dimensions equal to four and five and to all loop orders in spacetime dimensions greater than five. We verify that in classical limit, low energy photon and graviton radiation decouple from each other.
Highlights
In [83, 84] the double soft graviton theorem was analysed from asymptotic symmetry point of view and symmetry interpretation was found for consecutive limit i.e. when one of the soft graviton is softer than the other one
In four dimensions soft theorem was explored beyond tree level in [88] using extension of the infrared treatment developed in [89, 90] and it was shown that new non-analytic terms appear in soft momentum expansion in the form of logarithmic functions of soft energy
Our goal in this paper is to derive subleading soft theorem for a generic theory of quantum gravity, for arbitrary number of soft photons and gravitons and for arbitrary number of finite energy particles with arbitrary mass and spin when all the soft particles are soft in the same rate
Summary
We will consider a generic theory of quantum gravity which is UV complete and background independent and is given in the form of 1PI effective action. For covariantization with respect to photon background we need the action (2.11) to be invariant under global U(1) transformation Φα → [exp(iQθ)]αβΦβ , where θ is the parameter of U(1) global transformation and Q is the U(1) transformation generator on real field.1 This requires the following property of the kinetic operator, QγαKγβ + Kαγ Qγβ = 0. The fourth term comes from the spin connection part in covariant derivative There is another source of three point vertex associated with soft photon coming from the non-minimally coupled field strength with two finite energy fields having most general form: S(3). We want to evaluate the vertex given in figure 4 associated with three soft fields This kind of vertex cannot be obtained by covariantizing the 1PI effective action but one needs to explicitly add most general gauge and general coordinate invariant terms involving only soft fields in the action. The soft photon propagator with momentum k in Feynman gauge with the endpoints μ and ν takes the form: Dμν (k)
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