For a ghost-free modification of the Polyakov action on a fixed 2D black hole background, the Hawking flux at infinity is unchanged; only diagonal stress-energy components and entropy get non-local corrections.
On thermal field fluctuations in ghost-free theories
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We study the response of a scalar thermal field to a $\delta$-probe in the context of non-local ghost-free theories. In these theories a non-local form factor is inserted into the kinetic part of the action which does not introduce new poles. For the case of a static $\delta$-potential we obtain an explicit expression for the thermal Hadamard function and use it for the calculation of the thermal fluctuations. We then demonstrate how the presence of non-locality modifies the amplitude of these fluctuations. Finally, we also discuss the fluctuation-dissipation theorem in the context of ghost-free quantum field theories at finite temperature.
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Ghost-free modification of the Polyakov action and Hawking radiation
For a ghost-free modification of the Polyakov action on a fixed 2D black hole background, the Hawking flux at infinity is unchanged; only diagonal stress-energy components and entropy get non-local corrections.