Gauge/Gravity Duality 3

Prof Nick Evans

AdS/CFT Correspondence

Quarks with QCD-like physics

TODAY

Electric/Magnetic fields

Chemical potential

Sakai-Sugimoto model

AdS-QCD

Improvement & Perfection

Hadronization, jet quenching

Transport Properties

QCD-like Quark SummaryD3-D7 system introduces quarks

Deforming AdS typically generates a hard wall

Inducing confinement & chiral symmetry breaking

Magnetic Field Induced Chiral Symmetry Breaking Clifford Johnson

The F term is a gauge field living on the surface of the D7 brane…

A is dual to the operators q q …. and a baryon number background gauge field…

So we can include a background magnetic field

ab

Electric Field

There is now an horizon-like surface at

r = E R

It behaves like a black hole horizon with the embeddings falling into the surface..

The electric field shreds the mesons into a quark gluon plasma…

4z4

Karch, O’Bannon

At finite density the Fermi-sea of quarks fills up to an energy called the chemical potential

We can think of as a background vev for the temporal component of the photon…

Chemical Potential

Myers et al have argued for the new solutions with a spike to the origin as the physical solutions…

The spike represents strings stretching between the D3 and the D7 ie quarks induced in the vacuum by the chemical potential.

Sakai Sugimoto Model

A standard complaint about the D3-D7 system is that it does not have non-abelian chiral symmetries… and there’s no well understood hard wall…

Sakai & Sugimoto proposed a model that does have non-abelian chiral symmetries… but at the expense of being intrinsically 5 dimensional…Type IIA

D4s wrapped on a circle

(Although the condensate formation is controlled by the strong dynamics not the global symmetries….)

The period is & can not be small relative to the string length….

The 5d SYMs theory becomes a non-supersymmetric YMs theory in 4d... but the compactification scale controls the strong coupling scale… the UV is strongly coupled too…

The geometry is singular at u when the direction degenerates… there’s a cone like structure

KK

Flavour is provided by a D8 brane

The solutions wrap round the end of the cone and head back to infinity… SS interpreted this as the non-perturbative version of a weakly coupled D8 – D8 system… dynamical mass generation…

At large u SU(N) but broken in the IR to sub-group SU(N)

Chiral symmetry breaking for chiral quarks…

2

Vacuum Manifold & Pions

The SU(N) gauge field living on the D8 world volume is naturally dual to q q

But there is also the A component… the Lagrangian is independent of the u dependence of this field if its only u dependent… the vacuum manifold… hence massless pions…

u

Its generally agreed that the condensate is described by a string between the branes that transforms under both L & R symmetries… Aharony’s OWLS or Kiritsis’ tachyon

Its phase is the pion but can be moved by a gauge transform into A (u)…u

Quark Mass In SS

The literature is confused and contradictory on this front….

Perturbatively non-anti-podal D8 D8 configurations look unstable

SS dismissed them as unphyiscal…

There are though probe embeddings in the geometry for non-anti-podal cases… they have a bigger effective mass….

There is still the ability to shift A (u)… vacuum manifold & pions?

u

u

NJL Interpretation (Chicago)

By moving the D8 away from anti-podal an NJL operator has been switched on that drives chiral symmetry breaking in addition to the QCD dynamics enlarging the mass gap…

A consequence is that chiral symmetry breaking and confinement can be separated at finite temperature…. (Aharony)

Or is it a hard mass? (NE)

We have changed the boundary conditions on the OWLS…. But symmetry? Expect:

5d… strongly coupled UV… confusion about including mass…

Personally I prefer the cleaner D3-D7 system even without the non-abelian chiral symmetries…

Magnetic fields in SS

Meson Spectra and Magnetic Fields in the Sakai-Sugimoto Model.

Clifford V. Johnson, Arnab Kundu . arXiv:0904.4320 [hep-th]

Electric fields in SS

Universal Holographic Chiral Dynamics in an External Magnetic Field. Veselin G. Filev, Clifford V. Johnson, Jonathan P. Shock arXiv:0903.5345 [hep-th]

Chemical potential in SS

Rho meson condensation at finite isospin chemical potential in a holographic model for QCD. Ofer Aharony , Kasper Peeters , Jacob Sonnenschein, Marija Zamaklar JHEP 0802:071,2008. e-Print: arXiv:0709.3948 [hep-th]

Lets get phenomenological

Of course these theories are NOT QCD

* large N

* extra undecoupled

super-partners

* mesons masses << quark

masses

So of course they will only describe QCD quantitatively upto corrections of order 100% (right?!!)

Rho vs pi mass in a backreacted dilaton flow… slope 0.57

Lattice large N data.. Slope 0.52.. little N dependence

YET

AdS/QCD

Holography does encode the maximal space-time symmetries in an entirely new way…

Plus the phenomena of confinement, chiral symmetry breaking & bound states…

The dual models share conformal behaviour in the UV with QCD (one strongly coupled.. One slow running at weak coupling

So lets try to construct a very generic toy model of QCD using these features….

AdS/QCD – Son et al, Pomarol et al

AdS5, no S5 since no SO(6) in QCD

To include confinement & a mass gap we simply impose a hard wall at r = r - crude but simple…0

Include the “D7 embedding field” simply as an N x N scalar of m = -3

We can describe mass and condensate (but no dynamics – fit them)

ff2

Gauge fields to be dual to vector and axial-vector currents…

Parameter count

r

c

m

g

o

5

Fixing g5In AdS/CFT Correspondence g5 is related to the ‘tHooft coupling… but can fix phenomenologically…

One loop:2

AdS/QCD vector EoM

Now we can solve the EoM for

pions

rhos

axial-vector mesons

(mass induced by background X vev)

Now sub back into Lagrangian as eg

And read off couplings such as

IMPOSE NEUMANN BOUNDARY CONDITIONS AT ro

3 parameter fit

Pomarol computed Gasser Leutwyler coeffs too…

Glueballs & Baryons

Solve the Dirac equation in AdS… of course in AdS/CFT baryons are N heavy… for N=3 they may be more mesonic (di-quark + quark)

IR Hard wall vs IR Softwall

In all the models so far discussed masses of excited states grow like n (the level number)…. Some people argue they should grow like sqrt(n)…

Sqrt(n) behaviour can be included by an appropriate dilaton

Karch, Son,..

Improving the IR

We have not included vevs for operators such as Tr F, Tr F ….2 4

We can use a D3-D7 system with a running dilaton and backreacted Tr F vev… it predicts c in terms of m too…

Constable Myers geometry..

2

“Improved” Results

Fit about the same quality (one fewer parameter) … you could add in more parameters to play role of other vevs… but loose predictivity…

Perfecting the UV

Need to start doing effective field theory with a cut off in the UV…

Anomalous dimensions at the UV cut off

1/r n

We are now essentially reparametrizing QCD….

Of course these theories are NOT QCD

* large N

* extra undecoupled

super-partners

* mesons masses << quark

masses

So of course they will only describe QCD quantitatively upto corrections of order 100% (right?!!)

Re-examine Success

Is there really a weakly coupled gravity description of QCD?

Should there be a string theory of QCD (away from large N)?

Are we getting more out that we put in (cautious yes)?

Can we systematically improve and remain predictive (probably not)?

Hadronization

We can follow the evolution of a point like string as the ends separate… the string falls first in a 1/r potential then hits a hard wall forming a QCD string…

The quarks, in the absence of string breaking, bounce about the centre of mass due to the string tension…

NE, French,Threlfall

Hadronization – string breaking and rho emission

breaking by hand….

Hadronization – some naive estimates of production rates

We made a toy holographic model of the whole QCD spectrum and then dumped energy in equal amounts into all modes.. Then HERWIG decay chain….

NE, Tedder

Rho productionThe rho is described by a gauge field in 5d. There are a set of orthogonal functions

If we expand a Gaussian (centred on r=0, width 300MeV) initial condition in terms of these basis functions

We obtain the yields: rho 15 rho* 3 rho** 0….

776

1742

25333305

4059

776

1742

3305

4059

Pion Holography

We have basis functions

for pseudo-Goldstones…

To do the whole QCD spectra we are now going to cheat.. “create a phenomenological model”

We simply rescale r coordinate by m /m – the Gaussian does not

stretch and we see a suppressed yield.

We describe pseudo-Goldstones (Pi, K, eta) by pion basis at different quark mass

Spin factor of (2J+1) on production rates

rhohadron

Fit parameters Gaussian Width

Gaussian Height

The stress energy tensor contributions (rho vs pion) in our holographic

model depends on the ‘tHooft coupling ( AdS radius R) – we fit it.

Strange quarks are massive and hence their production in the

perturbative regime is suppressed. We model this with a

strangeness suppression factor

Sigma need not be integer due to mixing – eg eta(548) is 32%

strange

Hadronization – some naive estimates of production rates

We made a toy holographic model of the whole QCD spectrum and then dumped energy in equal amounts into all modes.. Then HERWIG decay chain….

NE, Tedder

Quarks in a Dense QCD PlasmaSimilar computations have been done in a black hole background to describe jet quenching in RHIC fireballs

Larry Yaffe’s calculations of the shock wave produced by a moving quark

RHIC seeing a mach cone in away side jet data (??!!)

Transport Properties of a Gauge Plasma & RHIC

Another exciting new arena has been computing transport properties of the high temperature plasma eg by putting electric fields in the black hole geometry… (can’t use lattice)

Attention has focused on the ratio of viscosity to entropy density that turns out to be universal for all theories with a gravity dual… and rather small (smaller than any known material)… but in agreement with (rough) RHIC estimates – the fireball thermalizes very quickly (elliptic flow = shape dependence!)

Son & Starinets

[Fick’s law (1855)]

Conservation law

Constitutive relation

Diffusion equation

Dispersion relation

Expansion parameters:

Relativistic Hydrodynamics

Example: charge diffusion

First-order transport (kinetic) coefficientsFirst-order transport (kinetic) coefficients

Shear viscosity

Bulk viscosity

Charge diffusion constant

Supercharge diffusion constant

Thermal conductivity

Electrical conductivity

Conclusions

We now know that some strongly coupled gauge theories have a weakly coupled gravitational description

Some of these theories display confinement, chiral symmetry breaking and a thermal transition to a deconfined phase…

They are NOT QCD but they provide new insights into QCDs behaviour and provide novel starting points for models of QCD

AdS/QCD; Hadronization; Transport properties of gauge plasmas

Qualitative vs quantitative

BSM – unparticles, technicolour & susy breaking