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Strange metals at finite ’t Hooft coupling

  • Regular Article - Theoretical Physics
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Abstract

In this paper, we consider the AdS–Schwarzschild black hole in light-cone coordinates which exhibits non-relativistic z=2 Schrodinger symmetry. Then, we use the AdS/CFT correspondence to investigate the effect of finite-coupling corrections to two important properties of the strange metals which are the Ohmic resistivity and the inverse Hall angle. It is shown that the Ohmic resistivity and inverse Hall angle are linearly and quadratically temperature dependent in the case of \(\mathcal{R}^{4}\) corrections, respectively, while in the case of Gauss–Bonnet gravity, we find that the inverse Hall angle is quadratically temperature dependent and the Ohmic conductivity can never be linearly temperature dependent.

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Notes

  1. One should notice that in the Schrödinger spacetime this part of the metric is very important because of the non-trivial Kalb–Ramond field [26].

  2. In AdS5×S 5 AdS black brane background, e −ϕ is a constant and it can be absorbed in \(\mathcal{N}\).

  3. One may refer to [14] for more explanation of this point.

  4. We have assumed G xx =G yy =G zz .

  5. To compare the results, two plasmas can be taken to have the same temperatures. Then we express the results in terms of the temperature of hot plasma without any corrections, \(T_{\mathcal{R}^{4}}(1-k)=T\).

  6. It should be noticed that we are interested in the case of small temperature regime.

  7. We consider plasmas at fixed temperature, then express the results in terms of the temperature of hot plasma without any corrections, \(\frac{T_{\mathrm{GB}}}{\sqrt{N}}=T\).

  8. Certainly, this class must be study more in details and other properties should be investigated.

  9. One also finds the other choice in [24] as \(\tilde{A}=(\tilde{E}_{b}y+h_{+}(u))\,dx^{+}+h_{-}(u)\,dx^{-}+h_{y}(u)\,dy+(\tilde {B}_{b}y)\,dz\).

  10. Interestingly, the metric function G yy does not change in the presence of \(\mathcal{R}^{2}\) corrections i.e. G yy (u)=u 2.

  11. A 0, A 4, and A 8 depend on the electric field, Gauss–Bonnet coupling and parameter b.

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Acknowledgements

It is a pleasure to thank M. Ali-Akbari, M. Alishahiha and M. Sheikh-Jabbari for very useful discussions and especially thank Bom Soo Kim for reading the manuscript and useful comments. Also we are very grateful to and thank M. Sohani for carefully reading the draft. We would like to thank the referee of EPJC for giving constructive comments which helped improving the paper. This research was supported by Shahrood University of Technology.

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  1. Physics Department, Shahrood University of Technology, P.O. Box 3619995161, Shahrood, Iran

    Kazem Bitaghsir Fadafan

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Fadafan, K.B. Strange metals at finite ’t Hooft coupling. Eur. Phys. J. C 73, 2281 (2013). https://doi.org/10.1140/epjc/s10052-013-2281-5

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