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## Shear sum rules at finite chemical potential

### Citations

445 |
Ordinary Differential Equations
- Arnold
- 1975
(Show Context)
Citation Context ...r − r+)−i ω Fh , r → r+, (3.29) r3Fφ′(r) → 0, r →∞. One might suspect that there might be singularities in φ which also gives zeros of the Green’s function. However as discussed in [13], a theorem of =-=[15]-=- guarantees that the solution is smooth with respect to a parameter ω if the differential equation and the boundary conditions are smooth with respect to it. This ensures that there cannot be singular... |

152 |
Non-extreme black holes of five-dimensional
- Behrndt, Cvetič, et al.
- 1999
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Citation Context ... corresponding to the Cartan’s of SO(6), it is possible to turn on 3 independent chemical potentials. The gravity dual of this system is given by the R-charged black hole of Behrndt, Cvetic and Sabra =-=[17]-=-. Using the differential equation of the massless minimally coupled scalar in this background, we obtain the retarded Green’s function of the Txy component of the stress tensor. Examining this differe... |

139 | Petkou, “Implications of Conformal Invariance in Field Theories for General Dimensions,” Annals Phys
- Osborn, C
- 1994
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Citation Context ... the sum rule from the OPE of the stress tensor [8]. This OPE is given by Tµν(x)Tρσ(0) ∼ CT Iµν,ρσ x8 + Âµνρσαβ(x)Tαβ(0) + · · · . (3.72) Â contains various Lorentz structures which can be found in =-=[16]-=-. The important property of them which is seen form conformal invariance is that they all scales like 1/x4. Now we take the Fourier transform of the above OPE and set q = 0 and ω → ∞. By a simple scal... |

85 |
Starinets, “Minkowski space correlators
- Son, O
- 2002
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Citation Context ...ss scalar in the background (3.2). The k = 0 mode satisfies the following equation ∂2rφ+ ( F ′ F + 3 r ) ∂rφ+ ω2 F 2 φ = 0, (3.6) where F = r2 L2 f. (3.7) The procedure to obtain the Green’s function =-=[14]-=- is to first impose in going boundary conditions at the horizon r+ and obtain φ at the boundary r → ∞. Once this is done, the Green’s function at temperature T is given by GR(ω, T ) = ĜR(ω, T ) +Gcon... |

69 |
Hydrodynamics with triangle anomalies,
- Son, Surowka
- 2009
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Citation Context ... at finite chemical potential. It will be interesting to see if the effects of triangle anomalies can be seen from the sum rule just as hydrodynamics was modified on the account of triangle anomalies =-=[26]-=-. Finally we mention that chemical potential is an important parameter in the QCD phase diagram and it will be interesting to see if sum rules can be derived in this context. Acknowledgments We wish t... |

51 |
Multitrace operators, boundary conditions
- Witten
(Show Context)
Citation Context ...ndary. Then the expectation value of the operator dual to φi is obtained by substituting the redefinitions (4.64) and in the background value of Xi and reading out the value of N 2 8π2L3 βi [20]. See =-=[21, 22]-=- for earlier work. They are given by 〈O1〉 = N 2 8π2L3 β1 = N2 8π2 r2+ L4 k1 + k2 − 2k3√ 6 , (4.70) 〈O2〉 = N 2 8π2L3 β2 = N2 8π2 r2+ L4 k1 − k2√ 2 . Note that these expectation values have mass dimensi... |

45 |
Boundary Conditions and New Dualities: Vector Fields
- Marolf, Ross
(Show Context)
Citation Context ...at the boundary. Then the expectation value of the operator dual to φi is obtained by substituting the redefinitions (4.64) and in the background value of Xi and reading out the value of N 2 8π2L3 βi =-=[20]-=-. See [21, 22] for earlier work. They are given by 〈O1〉 = N 2 8π2L3 β1 = N2 8π2 r2+ L4 k1 + k2 − 2k3√ 6 , (4.70) 〈O2〉 = N 2 8π2L3 β2 = N2 8π2 r2+ L4 k1 − k2√ 2 . Note that these expectation values hav... |

44 |
TASI lectures on branes, black holes and anti-de Sitter space
- Duff
- 2001
(Show Context)
Citation Context ...corresponding to the Cartan’s of SO(8) therefore it is possible to turn on 4 independent chemical potentials. The gravity dual of this system is given by the non-extremal R-charged black hole in AdS4 =-=[23]-=-. Using the same methods developed for the D3-brane case it is possible to show that the retarded Green’s function of the Txy component of the stress tensor satisfies property 1. To ensure that it sat... |

26 |
Double trace’ deformations, boundary conditions and space-time singularities
- Berkooz, Sever, et al.
(Show Context)
Citation Context ...ndary. Then the expectation value of the operator dual to φi is obtained by substituting the redefinitions (4.64) and in the background value of Xi and reading out the value of N 2 8π2L3 βi [20]. See =-=[21, 22]-=- for earlier work. They are given by 〈O1〉 = N 2 8π2L3 β1 = N2 8π2 r2+ L4 k1 + k2 − 2k3√ 6 , (4.70) 〈O2〉 = N 2 8π2L3 β2 = N2 8π2 r2+ L4 k1 − k2√ 2 . Note that these expectation values have mass dimensi... |

22 |
Spectral sum rules for the quark-gluon plasma,” Phys
- Romatschke, Son
(Show Context)
Citation Context ...his framework to obtain sum rules. Obtaining sum rules within this frame work provides information of the analytic structure of the Green’s functions in the strongly coupled limit. Romatschke and Son =-=[8]-=- derived two sum rules for the stress – 1 – tensor two point function for strongly coupled N = 4 Yang-Mills theory. This was then generalized for Chamblin-Reall backgrounds which are dual to non-confo... |

21 |
Superfluid black branes
- Donos, Gauntlett
(Show Context)
Citation Context ...d quantization. One the other hand when ∆ is chosen to be 1 the quantization of the scalar obey the alternate quantization. For the neutral scalars in the M2-brane background it has been seen earlier =-=[24, 25]-=- that one must chose the alternate quantization. Let us denote the three operators dual to these bulk scalar fields as Oi which have dimension 1 each. We now read out the expectation values of these o... |

18 |
Bulk viscosity of QCD matter near the critical temperature
- Kharzeev, Tuchin
(Show Context)
Citation Context .... Introduction Sum rules play an important role in constraining spectral densities of strongly coupled fluids. There are important sum rules which constrain spectral densities of stress tensor in QCD =-=[1, 2, 3, 4, 5]-=- and the Ferrell-Glover-Tinkham sum rule satisfied by current-current correlation function in the BCS superconductor [6, 7]. The gauge gravity duality provides a framework for evaluating the two point... |

18 |
Universal properties of bulk viscosity near the QCD phase transition,” Phys
- Karsch, Kharzeev, et al.
(Show Context)
Citation Context .... Introduction Sum rules play an important role in constraining spectral densities of strongly coupled fluids. There are important sum rules which constrain spectral densities of stress tensor in QCD =-=[1, 2, 3, 4, 5]-=- and the Ferrell-Glover-Tinkham sum rule satisfied by current-current correlation function in the BCS superconductor [6, 7]. The gauge gravity duality provides a framework for evaluating the two point... |

14 | Sum Rules from an Extra Dimension
- Gulotta, Herzog, et al.
(Show Context)
Citation Context ...for Chamblin-Reall backgrounds which are dual to non-conformal theories in [9, 10]. The sum rule for the R-charge correlator in strongly coupled N = 4 Yang-Mills was obtained in [1]. As emphasized in =-=[11]-=-, sum rules are the consequences of analyticity of the Green’s function in the complex frequency plane. From the field theory point of view this results from the unitarity and causality of the field t... |

10 | A shear spectral sum rule in a non-conformal gravity dual,” arXiv:1006.4667 [hep-th - Springer, Gale, et al. |

9 |
Bulk spectral functions in single and multi-scalar gravity duals,” arXiv:1010.2760 [hep-th
- Springer, Gale, et al.
(Show Context)
Citation Context ...rules for the stress – 1 – tensor two point function for strongly coupled N = 4 Yang-Mills theory. This was then generalized for Chamblin-Reall backgrounds which are dual to non-conformal theories in =-=[9, 10]-=-. The sum rule for the R-charge correlator in strongly coupled N = 4 Yang-Mills was obtained in [1]. As emphasized in [11], sum rules are the consequences of analyticity of the Green’s function in the... |

6 |
R-charge thermodynamical spectral sum rule
- Baier
(Show Context)
Citation Context .... Introduction Sum rules play an important role in constraining spectral densities of strongly coupled fluids. There are important sum rules which constrain spectral densities of stress tensor in QCD =-=[1, 2, 3, 4, 5]-=- and the Ferrell-Glover-Tinkham sum rule satisfied by current-current correlation function in the BCS superconductor [6, 7]. The gauge gravity duality provides a framework for evaluating the two point... |

6 |
Lattice Gauge Theory Sum Rule for the Shear
- Meyer
(Show Context)
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5 |
Conductivity of superconducting films: A sum rule
- Ferrell, Glover
- 1958
(Show Context)
Citation Context ...um rules which constrain spectral densities of stress tensor in QCD [1, 2, 3, 4, 5] and the Ferrell-Glover-Tinkham sum rule satisfied by current-current correlation function in the BCS superconductor =-=[6, 7]-=-. The gauge gravity duality provides a framework for evaluating the two point functions of various conserved currents of strongly coupled theories which admit a gravity dual. Thus one can use this fra... |

4 |
The Bulk Channel
- Meyer
(Show Context)
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3 |
Determination of the superconducting skin depth from the energy gap and sum
- Tinkham, Ferrell
- 1959
(Show Context)
Citation Context ...um rules which constrain spectral densities of stress tensor in QCD [1, 2, 3, 4, 5] and the Ferrell-Glover-Tinkham sum rule satisfied by current-current correlation function in the BCS superconductor =-=[6, 7]-=-. The gauge gravity duality provides a framework for evaluating the two point functions of various conserved currents of strongly coupled theories which admit a gravity dual. Thus one can use this fra... |