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## Gauge/Gravity Duality 3

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**Gauge/Gravity Duality 3**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 Prof Nick Evans**QCD-like Quark Summary**D3-D7 system introduces quarks Deforming AdS typically generates a hard wall Inducing confinement & chiral symmetry breaking**Magnetic Field Induced Chiral Symmetry Breaking Clifford**Johnson ab The F term is a gauge field living on the surface of the D7 brane… A is dual to the operators q g q …. and a baryon number background gauge field… So we can include a background magnetic field m m**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.. z 4 4 The electric field shreds the mesons into a quark gluon plasma… Karch, O’Bannon**Chemical Potential**At finite density the Fermi-sea of quarks fills up to an energy called the chemical potential We can think of m as a background vev for the temporal component of the photon…**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… (Although the condensate formation is controlled by the strong dynamics not the global symmetries….) 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**& can not be small relative to the string length….**The t period is 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 t 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 g q m u 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… 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…. u u There is still the ability to shift A (u)… vacuum manifold & pions?**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. ShockarXiv: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 ZamaklarJHEP 0802:071,2008. e-Print: arXiv:0709.3948 [hep-th]**Lets get phenomenological**YET 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**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 2 f f We can describe mass and condensate (but no dynamics – fit them)**Gauge fields to be dual to vector and axial-vector**currents… Parameter count r c m g o 5**In AdS/CFT Correspondence g5 is related to the ‘tHooft**coupling… but can fix phenomenologically… Fixing g5 2 One loop: AdS/QCD vector EoM**Now we can solve the EoM for**pions rhos axial-vector mesons (mass induced by background X vev) IMPOSE NEUMANN BOUNDARY CONDITIONS AT r o Now sub back into Lagrangian as eg And read off couplings such as**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**2 4 We have not included vevs for operators such as Tr F, Tr F …. We can use a D3-D7 system with a running dilaton and backreacted Tr F vev… it predicts c in terms of m too… 2 Constable Myers geometry..**“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….**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)? 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?!!)**Hadronization**NE, French,Threlfall 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…**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 production**The rho is described by a gauge field in 5d. There are a set of orthogonal functions 776 776 1742 1742 2533 3305 3305 4059 4059 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….**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. hadron rho We describe pseudo-Goldstones (Pi, K, eta) by pion basis at different quark mass Spin factor of (2J+1) on production rates**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 Plasma**Similar 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**Relativistic Hydrodynamics**Example: charge diffusion Conservation law Constitutive relation [Fick’s law (1855)] Diffusion equation Dispersion relation Expansion parameters:**First-order transport (kinetic) coefficients**Shear viscosity Bulk viscosity Charge diffusion constant Supercharge diffusion constant Thermal conductivity Electrical conductivity**Conclusions**Qualitative vs quantitative 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 BSM – unparticles, technicolour & susy breaking