Abstract
We discuss radiation in theories with scalar fields. Our key observation is that even in flat spacetime, the radiative fields depend qualitatively on the coupling of the scalar field to the Ricci scalar: for non-minimally coupled scalars, the radiative energy density is not positive definite, the radiated power is not Lorentz invariant and it depends on the derivative of the acceleration. We explore implications of this observation for radiation in conformal field theories. First, we find a relation between two coefficients that characterize radiation, that holds in all the conformal field theories we consider. Furthermore, we find evidence that for a 1/2-BPS probe coupled to mathcal{N} = 4 super Yang-Mills, and following an arbitrary trajectory, the spacetime dependence of the one-point function of the energy momentum tensor is independent of the Yang-Mills coupling.
Highlights
JHEP03(2020)087 where |x| is the distance between the static Wilson line, placed at the origin, and the point where the measure takes place
Our key observation is that even in flat spacetime, the radiative fields depend qualitatively on the coupling of the scalar field to the Ricci scalar: for non-minimally coupled scalars, the radiative energy density is not positive definite, the radiated power is not Lorentz invariant and it depends on the derivative of the acceleration
Radiation in conformal field theories requires considering conformally coupled scalars (ξ = 1/6) instead of minimally coupled ones, ξ = 0, as done in the field theory computations of [17, 18]. Once we take this observation into account, we find that already at the level of free theory, radiation for a free conformal scalar displays the features that were found holographically for N = 4 super Yang-Mills: the radiated power is not Lorentz invariant, it depends on aand the radiated energy density is not everywhere positive
Summary
Consider a probe coupled to a field theory, following an arbitrary, prescribed, timelike trajectory zμ(τ ). One evaluates the energy-momentum tensor with the retarded solution. One defines the radiative part of the energy-momentum tensor Trμν as the piece that decays as 1/r2 so it yields a nonzero flux arbitrarily far away from the source. Integrating over the solid angle we obtain dP μ/dτ It is a 4-vector [28] that gives the rate of energy and momentum emitted by the probe. From it one can define two quantities. Following Rohrlich [1], we define a second quantity, the invariant radiation rate R as. (2.4) is the most general form that R can take, if it depends only on Lorentz invariants evaluated at a single retarded time
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