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Gravity/Fluid Correspondence and Its Application on Bulk Gravity with U(1) Gauge Field Ya-Peng Hu College of Science, Nanjing University of Aeronautics.

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Presentation on theme: "Gravity/Fluid Correspondence and Its Application on Bulk Gravity with U(1) Gauge Field Ya-Peng Hu College of Science, Nanjing University of Aeronautics."— Presentation transcript:

1 Gravity/Fluid Correspondence and Its Application on Bulk Gravity with U(1) Gauge Field
Ya-Peng Hu College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing (南京航空航天大学) Reference: Y.P Hu and J.H Zhang, Adv.High Energy Phys (2014) [arXiv: hep-th]

2 Mainly based on: S.Bhattacharyya, V.E.Hubeny, S.Minwalla and M.Rangamani, JHEP 0802, 045 (2008) M.Rangamani, Class. Quant.Grav.26, (2009) J.Erdmenger, M.Haack, M.Kaminski and A.Yarom, JHEP 0901, 055 (2009) [arXiv: [hep-th]]. J. Hur, K. K. Kim and S. J. Sin, JHEP 0903, 036 (2009) N.Banerjee, et al. JHEP 1101, 094 (2011) D.T.Son and P.Surowka, Phys. Rev. Lett. 103, (2009) [arXiv: [hep-th]]. Y.P.Hu, P.Sun and J.H.Zhang, Phys. Rev. D 83, (2011) Y. P. Hu and C. Y. Park, Phys. Lett. B 714, 324 (2012)

3 Outline A. Introduction 1) Gravity/Fluid correspondence
2) Fundamental algorithm and procedure in Gravity/Fluid correspondence B. Applications of Gravity/Fluid correspondence on the Bulk Gravity with 𝑈(1) Gauge Field 1) The simplest case 2) In the presence of an external field 3) Adding 𝑈(1) Chern-Simons term in the bulk C. Conclusion and discussion

4 A. Introduction 1) Gravity/Fluid correspondence
Long wavelength limit in AdS/CFT correspondence: any quantum field effectively described by hydrodynamics; CFT becomes conformal fluid Gravity/Fluid correspondence application: conformal viscous fluid stress tensor can be deduced from the dual gravity (hep-th/ ) Stress tensor of viscous fluid with conformal symmetry broken Stress tensor of conformal viscous fluid

5 2) Fundamental algorithm and procedure in Gravity/Fluid correspondence
Black brane solution  Boosted black brane solution  Perturbative black brane solution  Boundary stress tensor (or other quantities) in the bulk Stress tensor (or other quantities) of the dual fluid on the boundary For example Black brane solution Boosted black brane solution

6 Perturbative black brane solution
Boundary stress tensor (asymptotical AdS5) Stress tensor of the dual fluid on the boundary

7 B. Applications on the Bulk Gravity with 𝑈(1) Gauge Field: The simplest case
1) Einstein-Maxwell gravity 2) RN-AdS black brane solution: in Eddington-Finkelstin coordinate system

8 3) Boosted RN-AdS black brane solution
: boundary coordinates : boost velocities; constants : projector onto spatial directions : raise and lower the indices in boundary

9 4) Perturbative solution (to first order)
5) The stress tensor and Charged current of dual fluid Stress tensor of dual fluid:

10 Charged current of dual fluid:

11 B. Applications on the Bulk Gravity with 𝑈(1) Gauge Field: In the presence of an external field
1) Key point: a constant external field added into the boosted black brane solution 2) Peturbative solution: coefficients changed by the external field 3) Results: stress tensor same; charged current changed

12 B. Applications on the Bulk Gravity with 𝑈(1) Gauge Field: Adding 𝑈(1) Chern-Simons term in the bulk
2) Results: stress tensor same; charged current changed

13 3) External field chosen: two cases

14 C. Conclusion and discussion
1) Gravity/Fluid correspondence: long wavelength limit in AdS/CFT correspondence 2) Fundamental algorithm and procedure in Gravity/Fluid correspondence 3) Stress tensor of Conformal viscous fluid deduced 4) Applications of Gravity/Fluid correspondence on the Bulk Gravity with 𝑈(1) Gauge Field: stress tensor; Charged current of dual fluid 5) Three cases: The simplest case; In the presence of an external field; Adding 𝑈(1) Chern-Simons term in the bulk

15 6) Results: stress tensor same; charged current changed 7) Anomalous effects (related to Chern-Simons terms): anomalous magnetic effect and vortical effect; 8) Other Chern-Smions effects, i.e. gravitational Chern- Simons term in the bulk 9) Holographic fluid at finite cutoff surface

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