### Abstract

We use gauge-gravity duality to study the temperature dependence of the zero sound mode and the fundamental matter diffusion mode in the strongly coupled N=4 SU(N _{c}) supersymmetric Yang-Mills theory with N _{f} N=2 hypermultiplets in the N _{c}≫ 1, N _{c} ≫ N _{f} limit, which is holographically realized via the D3/D7 brane system. In the high density limit μ≫T, three regimes can be identified in the behavior of these modes, analogous to the collisionless quantum, collisionless thermal, and hydrodynamic regimes of a Landau Fermi liquid. The transitions between the three regimes are characterized by the parameters T/μ and (T/μ) ^{2}, respectively, and in each of these regimes the modes have a distinctively different temperature and momentum dependence. The collisionless-hydrodynamic transition occurs when the zero sound poles of the density-density correlator in the complex frequency plane collide on the imaginary axis to produce a hydrodynamic diffusion pole. We observe that the properties characteristic of a Landau Fermi-liquid zero sound mode are present in the D3/D7 system despite the atypical T ^{6}/μ ^{3} temperature scaling of the specific heat and an apparent lack of a directly identifiable Fermi surface.

Original language | English |
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Article number | 026004 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 85 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Jan 2012 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*85*(2), [026004]. https://doi.org/10.1103/PhysRevD.85.026004