nLab fluid/gravity correspondence

Idea

As a variant or special sector of the AdS/CFT correspondence, the fluid/gravity correspondence re-identifies aspects of (quantum) gravity (string theory) on asymptotically approximately anti de Sitter spacetimes with those of certain fluid dynamics on the asymptotic boundary.

Applications

To the quark-gluon plasma

For example some properties of the quark gluon plasma in quantum chromodynamics are captured well by fluid dynamics, and after realizing QCD on D4-D8-brane bound states (the AdS/QCD correspondence) AdS/CFT provides a handle on this fluid dynamics in terms of the (quantum) gravity (string theory) on an ambient bulk $\sim$ anti de Sitter spacetime.

To the relativistic Navier-Stokes equation

The fluid/gravity correspondence involves the relativistic Navier-Stokes equation on the fluid side. (BKLS 12 see Thillaisundaram 17)

But it seems to remain open whether the correspondence sheds much light on the non-relativistic Navier-Stokes equation (the one whose stability is a Millennium Problem).

Related concepts

• AdS/CFT correspondence

• AdS/QCD correspondence

• quark-gluon plasma

References

The concept originates with

• Sayantani Bhattacharyya, Veronika Hubeny, Shiraz Minwalla, Mukund Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 0802:045, 2008 (arXiv:0712.2456)

Relation to the Navier-Stokes equation:

• Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, Andrew Strominger, From Navier-Stokes To Einstein, J. High Energ. Phys. (2012) 2012: 146 (arXiv:1101.2451)

Review:

• Nicola Ambrosetti, James Charbonneau, Silke Weinfurtner, The fluid/gravity correspondence: Lectures notes from the 2008 Summer School on Particles, Fields, and Strings (arXiv:0810.2631)

• Mukund Rangamani, Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 : 224003, 2009 (arXiv:0905.4352)

• Veronika Hubeny, The Fluid/Gravity Correspondence: a new perspective on the Membrane Paradigm, Class. Quant. Grav. 28:114007, 2011 (arXiv:1011.4948)

• Veronika Hubeny, Shiraz Minwalla, Mukund Rangamani, The fluid/gravity correspondence (arXiv:1107.5780)

• Ashok Thillaisundaram, Aspects of fluid dynamics and the fluid/gravity correspondence, 2017 (CambridgeRepositor:1810/267097, pdf)

• Sumit Dey, Shounak De, Bibhas Ranjan Majhi, Gravity dual of Navier-Stokes equation of an uniformly rotating fluid through parallel transport (arXiv:2002.06801)