# Presentation: 192952

## 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 setup
- II) Spectral functions of holographic mesons,
-    decay widths
- III) 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 mapped
- into a weakly coupled gravity theory.
- Idea is to try and do calculations using the gravity theory to gain
- some 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 plasma
- of gluons & adjoint matter
- deconfined, screening,
- finite corr. lengths, . . .

- strongly-coupled plasma
- of gluons & fundamental matter
- deconfined, screening,
- finite corr. lengths, . . .

**T>T****C**

**T>>T****C**

**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 mesons

- IV) 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 with
- changing momentum and other parameters?
- _BROADER QUESTION_ (for the future):
- Do these features have anything in common with
- Lattice 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**_

## Behaviour of effective holographic potential with changing momentum

- Bound state

- Horizon

- Holographic
- direction

- _Behaviour of effective holographic potential with changing momentum_

**Notes:**
Pause after bound state click

## 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_

## 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

- n

- q

- = 0
-    0.06
-    0.15
-    0.25

- Quasiparticles

## nq = 0.25

- nq = 0.25

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

- 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 = 0.9954

- 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]

- 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

## Slide 23

## Slide 24

## Mesons:

- lowest lying open string states are excitations of the
- massless modes on D7-brane: vector, scalars (& spinors)

- their dynamics is governed by usual worldvolume action:

**free spectrum:**
-  expand action to second order in fluctuations
-  solve linearized eq’s of motion by separation of variables

- Veff

- r

- discrete
-     spectrum

- Kruczenski, Mateos, RCM and Winters
- (hep-th/0304032)

**Mesons stable**

## Reminder about large N counting:

_**Reminder about large N counting:**_

- counts # of d.o.f.

- entropy density:

- counts # of d.o.f.

- in our limit, thermodynamics dominated by adjoint fields;
- we are calculating small corrections due to fundamental matter

*these dominate over quantum effects, eg, Hawking radiation,*

## Brane entropy:

_**Brane entropy:**_

- 1st order phase transition

- Transition temperature:

## Need an extra dial: “Quark” density

- Kobayashi, Mateos, Matsuura, RCM & Thomson [hep-th/0611099]

- Mateos, Matsuura, RCM & Thomson [arXiv:0709.1225]; . . . . .

- Need an extra dial: “Quark” density

- electric field lines can’t end in empty
-   space; nq produces neck

- D7-brane gauge field:

- asymptotically (ρ→∞):

- BH embedding with tunable horizon