Holographic MesonsRCM & Thomson (hep-th/0605017)Kruczenski, Mateos, RCM & Winters (hep-th/0304032)

Outline: AdS/CFT with D7-branes fundamental matter3. Observations/Future Directions2. Gauge/Gravity with probe branes universal meson spectrumRCM + Thomson (hep-th/0605017)Arean + Ramallo (hep-th/0602174)Kruczenski, Mateos, RCM + Winters (hep-th/0304032)holographic mesonsKarch + Katz (hep-th/0205236)

Maldacena; Witten; Gubser, Klebanov & Polyakov; ..AdS/CFT from D3-branes:d=4 N =4 U(Nc) super-Yang-Millsequivalent tod=10 Type IIb superstrings in AdS5 X S5with Nc units of RR fluxsupergravity limit ~ large-N with strong `t Hooft couplingall adjoint fields!

(Karch and Katz)decoupling limit of Nc D3-branes with Nf D7-branesd=4 U(Nc) o.s., d=8 U(Nf) o.s.& bifundamental 3-7 o.s.black brane withLow-energy limit with D7D7D3Lr=LMinimum mass for 3-7 strings:Gauge coupling on D7s: brane theory N =4 U(Nc) SYM with fundamental matter throat geometry: AdS5 X S5 with Nf D7s xDecouples asymptotic (closed) stringsReduces brane theory to field theoryFundamental fields:

Field theory: SUSY: N =4 N =2 SO(6) SO(4) = SU(2)L X SU(2)R vector:4 Weyl fermions:3 complex scalars:N =4 U(Nc) super-Yang-Millscoupled to: Nf massive N =2 hypermultiplets2 complex scalars :2 Weyl fermions:adjoint in U(Nc)fund. in U(Nc) & global U(Nf)

horizonAdS boundaryGeometry:poleequatorS5S3SO(4) = rotational symmetry of S3D7

horizonAdS boundaryGeometry:poleequatorS5S3D7Mesons, bound states of fundamental fields, dual to open string states supported by D7-brane

Probe approximation: Nf /Nc 0The above construction does not take into account thegravitational back-reaction of the D7-branes! considering large-Nc limit with Nf fixed(see, however: Burrington et al; Kirsch & Vaman; Casero, Nunez & Paredes)Gauge/gravity dictionary:supergravity modes:Dq-brane modes:flavor indices

Mesons:lowest lying open string states are excitations of themassless 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 eqs of motion by separation of variablesVeffrdiscrete spectrumKruczenski, Mateos, RCM and Winters(hep-th/0304032)

Meson spectrum:massive supermultiplets with bosons and fermions= radial AdS quantum #= angular quantum # on S3 = R-chargeKruczenski, Mateos, RCM and Winters(hep-th/0304032)

Itzhaki, Maldacena, Sonnenschein & YankielowczGauge/Gravity Duality from Dp-branes:d=p+1 N =4 U(Nc) super-Yang-Millsequivalent tod=10 Type II superstrings in Dp-branethroat with Nc units of RR fluxdimensionless effective coupling:YM couplingdimensionful !(p

Itzhaki, Maldacena, Sonnenschein & YankielowczGauge/Gravity Duality from Dp-branes:d=p+1 N =4 U(Nc) super-Yang-Millsequivalent tod=10 Type II superstrings in Dp-branethroat with Nc units of RR fluxdimensionless effective coupling:(p

Itzhaki, Maldacena, Sonnenschein & YankielowczGauge/Gravity Duality from Dp-branes:d=p+1 N =4 U(Nc) super-Yang-Millsequivalent tod=10 Type II superstrings in Dp-branethroat with Nc units of RR fluxdimensionless effective coupling:(p

Fundamental matter (with small number of flavours)introduce probe branese.g., D3/D7 system generalizes to Dp/D(p+4)(p+1)-dim. gauge theorywith fundamental matterr, S3 ( embedded in S8p )Other systems: Dp/D(p+2)(p+1)-dim. gauge theory withfundamental matter on codim. 1 defectr, S2 ( embedded in S8p )

Other systems: Dp/D(p+2)(p+1)-dim. gauge theory withfundamental matter on codim. 1 defectr, S2 ( embedded in S8p )Dp/Dp(p+1)-dim. gauge theory withfundamental matter on codim. 2 defectr, S1 ( embedded in S8p )(have focused on SUSY configurations for stability)

Decoupling limit of Nc Dp-branes with Nf Dq-branesLow-energy limit with Fundamental fields:U(Nc) super-Yang-Millscoupled to Nf massive hypermultipletsfund. in U(Nc) & global U(Nf)Field theory:U(Nc) adjoint( SUSY: N =4 N =2 )Gravity theory:Dp-throat containing Dq probe brane

Geometry:poleequatorS8-pSnDqFree quarks appear with mass:

Geometry:poleequatorS8-pSnDqMesons, bound states of fundamental fields, dual to open string states supported by Dq-brane

(RCM & Thomson; Arean & Ramallo)Mesons:Calculation of masses for lowest lying mesons as for D3/D7Detailed results numerical as radial ODE has no analytic solution (except in D3 background) Spectra have universal features: discrete, deeply bound, mass gap( with)mass scale dictated by Holography!Veffreffective radial potentialdiscrete spectrum

Holography:(p+1)-dim. gauge theory(p+2)-dim. gravityradiusenergy gravity physics is local in radiusgauge physics must be local in energy!Probe branesupergravitywave-packetmeson physicsfocused at r =L(Horowitz & Polchinski)

Holography:Probe brane(Peet & Polchinski)String energy:Supergravity energy:Precisely matches meson energy scale with U=mq !Locality in energy preserved between open and closed strings!meson physicsfocused at r =Lsupergravitywave-packet

Mesons:Spectra have universal features: discrete, deeply bound, mass gap( with)mass scale dictated by Holography!

SUSY embedding: no brane bendingbare mass = constituent mass Goldstone modes: symmetry breaking may require massless modesHolographic meson scale: SUSY versus nonSUSY:bare mass constituent massnonSUSY embedding: brane bends(eg, Sakai & Sugimoto model)Holographic meson scale set by constituent mass!

Conclusions/future directions: holographic meson spectra have universal features: discrete, deeply bound, mass gap mass scale dictated by holography meson interactions: scale as in large N

Meson interactions:Continue expansion of D7-brane action beyond 2nd order substitute and integrate out r and S34th order:agrees with standard large N of course, for fixed :glueballsmesons Applies for generalholographic theory

Conclusions/future directions: holographic meson spectra have universal features: discrete, deeply bound, mass gap mass scale dictated by holography meson interactions: scale as in large N form factors: proportional to MgapHong, Yoon & Strassler (hep-th/0312071)

Hong, Yoon & Strassler (hep-th/0312071) Form factors in D3/D7: exam mesons with various external probes:where charge radius given by Mgapin particular, does NOT scale with quantum numbers (surprise since ) similar results should apply in general holographic theory (since Mgap sets scale of radial profile in all cases)

Observations/future directions: holographic meson spectra have universal features: discrete, deeply bound, mass gap mass scale dictated by holography meson interactions: scale as in large N form factors: proportional to MgapHong, Yoon & Strassler (hep-th/0312071) degeneracies broken for nonconformal backgrounds

Degeneracies in meson spectra: for D3 background/conformal gauge theory with D7/D5/D3 probe branes, spectra only depend on = radial AdS quantum #= angular quantum # on S3 = R-chargee.g., NOT true for nonconformal backgrounds: grows

shrinks geff grows with geff decreases with in accord with M ~ mq / geff

Observations/future directions: holographic meson spectra have universal features: discrete, deeply bound, mass gap mass scale dictated by holography meson interactions: scale as in large N form factors: proportional to MgapHong, Yoon & Strassler (hep-th/0312071) degeneracies broken for nonconformal backgrounds beyond probe approximation; Nf /Nc finite(see: Burrington et al; Kirsch & Vaman; Casero, Nunez & Paredes)

Beyond probe approximation; Nf /Nc finite intriguing hint from Erdmenger & Kirsch (hep-th/0408113):study D2/D6 with Nf /Nc finite in far infrared M2/M6geometric singularityscaling of meson masses match probe results:M ~ mq / geff ~ mq / Nc perhaps no surprise given demands of holography

Observations/future directions: holographic meson spectra have universal features: discrete, deeply bound, mass gap mass scale dictated by holography meson interactions: scale as in large N form factors: proportional to MgapHong, Yoon & Strassler (hep-th/0312071) degeneracies broken for nonconformal backgrounds beyond probe approximation; Nf /Nc finite(see: Burrington et al; Kirsch & Vaman; Casero, Nunez & Paredes) mesons with large spin

Mesons with large J (in D3/D7 system):Classical rotating open strings attached to D7-braneNambu-Goto action:Ansatz:eom:bc:(string ends to D7)T

solve E(J) numerically:Spinning meson spectrum:Reggebehaviournonrelativistic Coulombbound statesapplies in general with:

Observations/future directions: holographic meson spectra have universal features: discrete, deeply bound, mass gap mass scale dictated by holography meson interactions: scale as in large N form factors: proportional to MgapHong, Yoon & Strassler (hep-th/0312071) degeneracies broken for nonconformal backgrounds beyond probe approximation; Nf /Nc finite(see: Burrington et al; Kirsch & Vaman; Casero, Nunez & Paredes) mesons with large spin

Holography: shadows on the wallDanielsson, Keski-Vakkuri & KruczenskiAdS/CFT dictionary allows us to see glue cloudsassociated with quark/meson states eg, SUGRA dilaton is dual to ; so evaluate asymptotic dilaton sourced by particular (macroscopic) string configuration for static quark (infinite straight string):in agreement with the Wilson loop calculation for thepotential between such external quarksMaldacena; Rey & Yee

horizonAdS boundaryDynamical Quarks: easy to repeat calculations for finite mass quarksD7Static/infinite-massquarks

Holography: for finite mass quark (straight string ending on D7):wherefor large |x|for small |x|?

Holographic Mesons:AProfile A:exotichybrid states

Holographic Mesons:AProfile B:B

Holographic Mesons:AProfile C:BC

Conclusions:Flavor physics is fun!