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Register a new userA comment on finite temperature correlations in integrable QFT
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H. Saleur
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I discuss and extend the recent proposal of Leclair and Mussardo for finite temperature correlation functions in integrable QFTs. I give further justification for its validity in the case of one point functions of conserved quantities. I also argue that the proposal is not correct for two (and higher) point functions, and give some counterexamples to justify that claim.
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We study the entanglement entropy and the mutual information in coupled harmonic systems at finite temperature. Interestingly, we find that the mutual information does not vanish at infinite temperature, but it rather reaches a specific finite value, which can be attributed to classical correlations solely. We further obtain high and low temperature expansions for both quantities. Then, we extend the analysis performed in the seminal paper by Srednicki (Phys. Rev. Lett. 71, 666 (1993)) for free real scalar field theories in Minkowski space-time in 3+1 dimensions at a thermal state. We find that the mutual information obeys an area law, similar to that obeyed by the entanglement entropy at vanishing temperature. The coefficient of this area law does not vanish at infinite temperature. Then, we calculate this coefficient perturbatively in an $1/mu$ expansion, where $mu$ is the mass of the scalar field. Finally, we study the high and low temperature behaviour of the area law term.
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Weyl anomaly leads to novel anomalous currents in a spacetime with boundaries. Recently it is found that the anomalous current can be significantly enhanced by the high temperature for free theories, which could make the experimental measurement easier. In this paper, we investigate holographic anomalous currents at a finite temperature. It is found that the holographic current is still enhanced by the high temperature in dimensions higher than three. However, the temperature dependence is quite different from that of free theories. This may be due to the fact that the holographic CFT is strongly coupled and there is non-zero resistance in the holographic model. Remarkably, the temperature dependence of holographic anomalous currents is universal in the high temperature limit, which is independent of the choices of background magnetic fields.
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