Superconductivity in the copper oxide ceramics stands as a grand challenge problem as its solution is fundamentally rooted in the physics of strong coupling. In such problems, traditional calculational schemes based on the properties of single particles fail. Rather, the physics of strong coupling resides in collective behaviour, signified typically by the emergence of new degrees of freedom at low energy. Typifying the pivotal role played by strong correlations is the fact that the parent state of the high-temperature copper oxide superconductors is an insulator but the band is partially full. Other features of the normal state that indicate a serious departure from the standard theory of metals are the presence of a gap in the single-particle spectrum without long-range superconducting order, the much-debated pseudogap state, and the strange metal in which the resistivity increases as a linear function of temperature rather than the quadratic dependence indicative of most metals.

Twenty-four years after the discovery of superconductivity in the copper oxide ceramics (hereafter cuprates), the central problem remains the anomalous properties of the normal state, despite extensive research on this problem. This Theme Issue is devoted to the recent theoretical, as well as experimental, advances that have contributed to solving this problem. This Theme Issue emphasizes the new directions the research in this field is taking. Two possible outcomes of strong correlations are (i) new degrees of freedom at low energy not found in the ultra-violet-complete theory or (ii) new statistics. The paper by Zaanen & Overbosch [1] emphasizes the latter, while two other papers, one by Phillips [2] and one by Faulkner *et al*. [3], emphasize the former. In the paper by Phillips [2], an explicit construction of the low-energy degrees of freedom is offered by an exact integration of the unwanted high-energy scales. This work stands in contrast to standard projective schemes in that it retains dynamical spectral weight transfer, the key ingredient that distinguishes a Mott from a band insulator. The work by Faulkner *et al*. [3] brings to bear the gauge/gravity duality on this problem. They find that a suitably chosen gravity theory can give rise to a metallic state with T-linear resistivity if the scaling dimension of a probe operator is appropriately chosen. The remaining theoretical paper by Galanakis *et al*. [4] reports the results of extensive numerical work on the Hubbard model. They find evidence for a quantum critical point at which the dynamical spectral weight transfer vanishes, as proposed in the work by Phillips. The two experimental papers emphasize fundamentally different aspects of the normal state. The paper by Hussey *et al.* [5] quantifies the extent to which T-linear resistivity pervades the phase diagram of the cuprates, while the paper by Sebastian *et al*. [6] addresses the recent observations of quantum oscillations in the normal state of the cuprates. This Theme Issue is timely and vital in that it reorientates the ways of looking at this problem and offers new answers to the persistent questions of the normal state of the cuprates.

## Footnotes

One contribution of 7 to a Theme Issue ‘Normal state of the copper oxide high-temperature superconductors’.

- This journal is © 2011 The Royal Society