The fast life of holographic mesons

Aninda Sinha

Perimeter Institute, Canada.

with Robert Myers arXiv:0802.nnnn

Quark Matter 2008,

Jaipur, India

PLAN

I) Motivation and setupII) Spectral functions of holographic

mesons, decay widthsIII) Conclusion

I) Motivation and setup

Behaviour of strongly coupled QCD is of interest to RHIC and early universe cosmology.

Unfortunately, theoretical tools are rather limited.

Recently, string theory tools involving gauge/gravity duality have been used to gain some insight into the nature of this interesting regime.

limitation: large NC and large ’t Hooft coupling

AdS/CFT relates N=4 , d=4 supersymmetric Yang Mills theory and its deformations to a theory of gravity in Anti-de-Sitter space (a space with negative cosmological constant) arising as a solution to d=10 superstring theory. In particular, the effective gravity theory is on AdS5 x S5.

The strongly coupled regime of the gauge theory is mappedinto a weakly coupled gravity theory.

Idea is to try and do calculations using the gravity theory to gainsome insight into the strong coupling region of the gauge theory.

QCD N=4 SYM

confinement,discrete spectrum,

scattering, . . . .

conformal,continuous spectrum,

no S-matrix, SUSY, . . . .

very different !!

T=0

strongly-coupled plasmaof gluons & adjoint matterdeconfined, screening,finite corr. lengths, . . .

strongly-coupled plasmaof gluons & fundamental

matterdeconfined, screening,finite corr. lengths, . . .

T>TC

T>>TC

quite similar !! cf

runs to weak coupling remains strongly-coupled

very different !!

Baryon density n causes brane to reach horizon

q

Free quark

1) Start with black hole in AdS to get finite temperature, have deconfined adjoint matter

II) Add D-brane to get flavour

RECIPE FOR HOLOGRAPHIC QUARK GLUON SOUP

[Aharony, Fayazuddin, Maldacena; Karch, Katz; Kruczenski, Mateos, Myers, Winters]

III) String falls into black hole and melts mesonsIV) Mass of meson, decay controlled by baryon density and geometry of D-brane (quark bare mass and condensate depend on these)

SPECIFIC QUESTION:

What can we say about the masses and lifetimes of holographic mesons at strong coupling? What is the nature of the spectral functions withchanging momentum and other parameters?

BROADER QUESTION (for the future):

Do these features have anything in common withLattice data and/or real world?

Spectral functions from AdS/CFT

F,G,R are functions of r which is the holographic direction. Spectral function is defined as

For us is large.

Can recast in terms of an effective Schrodinger equation

Bound state

Horizon

Holographic direction

Behaviour of effective holographic potential with changing momentum

Behaviour of effective holographic potential with changing momentum

Behaviour of effective holographic potential with changing momentum

Behaviour of effective holographic potential with changing momentum

Behaviour of effective holographic potential with changing momentum

Behaviour of effective holographic potential with changing momentum

Behaviour of effective holographic potential with changing momentum

Behaviour of effective holographic potential with changing momentum

II) Spectral functions and widths

nq = 0 0.06 0.15 0.25

Quasiparticles

nq = 0.25

Speed limit from spectral peaks [Liu, Rajagopal, Wiedemann; Mateos, Myers, Thomson; Ejaz, Faulkner, Liu, Rajagopal, Wiedemann; Athanasiou, Liiu, Rajagopal; Myers, AS]

Real part of quasinormal frequency

nq = 0.25

vmax = 0.9954

vmax = 0.6512

vmax = 0.3427

Dispersion relations for first 3 peaks for different parameters

At same temperature, higher vmax means higher bare quark mass.Equivalently, keeping bare quark mass fixed, higher vmax means lower temperature.

Widths as function of momenta [Myers, AS]

V=0.34

V=0.65

V=0.99

Location where effective potential has no minima

Conclusion

Holographic methods suggest finite velocity effects in the dispersion relations. Arise quite generally due to red-shift in the dual gravity picture.

Finite baryon density induces quasiparticle widths to grow dramatically with momenta. Can be quite general but needs further investigation.

THANKS FOR LISTENING