Gianluca Grignani- Testing AdS/CFT at string loops

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    VmpvnlaVmpvnla OfPOfP)@EV ov)@EV ov pvznlapvznla kiixpkiixp

    Anolk}`o AznalolnAnolk}`o AznalolnXmz}ano ]lnumzpnv~ % NLELXmz}ano ]lnumzpnv~ % NLEL

    A,Aznaloln+ B,Izpmkkn+ J, Zobofoliun`d+ A,Q,Pmbmliee olf F, ^i}la+

    Fnumzaml`m `ol`mkkovnil olf kiix `izzm`vnilp nl pvznla enmkf vdmiz~ il o

    xkolm oum jo`cazi}lf+ GDMX 8=?:78?1+:88= m"Xznlv Oz`dnum7dmx"vd)8=84?:5A,Aznaloln+ B,Izpmkkn+ J, Zobofoliun`d+ A,Q,Pmbmliee olf F, ^i}la+

    OfP)@EV umzp}p pvznla kiixp+ GDMX 857868+:885+

    m"Xznlv Oz`dnum7dmx"vd)858=848

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    OfP)@EV

    Botnbokk~ p}xmzp~bbmvzn` ^ola"Bnkkp vdmiz~ il 6F ekov pxo`m nvd ao}am

    azi}x P]$L. olf `i}xknla `ilpvolv a^B

    np mto`vk~ mq}nuokmlv vi

    v~xm NNJ p}xmzpvznla vdmiz~ il jo`cazi}lf OfP=TP= nvd L }lnvp ie ="eizb

    ek}t vdzi}ad P= , Vdm zofn}p ie `}zuov}zm np

    v Diiev `i}xknlaolf

    Pvznla pvovmao}am nluoznolv

    `ibxipnvm ixmzovizMlmza~ `ileizbok fnbmlpnil ie

    `ibxipnvm ixmzoviz

    Vdnp np o moc `i}xknla pvzila `i}xknla f}oknv~

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    Vdm Xmlzipm knbnv ie OfP=TP= amibmvz~ anump o xx"oum pxo`m

    vzolpumzpm PI$6.tPI$6. p~bbmvz~

    Ezmm pvznlap ozm mto`vk~ pikuojkm nl vdm knadv"`ilm ao}am

    knadv"`ilm

    Dobnkvilnol

    kmumk bov`dnla `ilfnvnil

    Vdm olokiai}p knbnv ie P}xmz ^ola"Bnkkp `ol jm vocml $JBL. fmvonkmf

    bov`dnla ie JBL ixmzovizp nl vdm kozam L+ xkoloz knbnv olf ezmm pvznla pvovmp

    ezmm pvznlapxkoloz knbnv

    pvznla nlvmzo`vnilplil"xkoloz `izzm`vnilp

    $ilainla. bov`dnla nlvmzo`vnilp nl knadv"`ilm pvznla enmkf vdmiz~ il o xx"

    oum jo`cazi}lf olf ^ola"Bnkkp vdmiz~ `ibx}vovnilp

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    Lil xkoloz `izzm`vnilp nl ^olaLil xkoloz `izzm`vnilp nl ^ola""Bnkkp Vdmiz~Bnkkp Vdmiz~

    Pvznla kiix `izzm`vnilp vi vdm mlmza~ ie vdm :"ip`nkkoviz $:"nbx}znv~. pvovmp

    P~bbmvzn` vzo`mkmpp7

    Vzo`m7

    Nl L26 P^B vdmzm ozm 5 p`okoz enmkfp

    Pmkm`v o `ibjnlovnil ie vdmb

    dn`d np `dozamf }lfmz o ]$?. p}jazi}x ie vdm Z P~bbmvz~

    F}ok JBL ixmzoviz7

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    Dop liv jmml `ibx}vmf }pnla pvznla vdmiz~/

    Vdm ilk~ ouonkojkm eizb}kovnil ie pvznla vdmiz~ nl dn`d

    nlvmzo`vnilp `ol jm `ibx}vmf np

    xx"oum knadv"`ilm pvznla enmkf vdmiz~

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    Knadv"`ilm Pvznla Enmkf Vdmiz~

    pvznla enmkf ixmzoviz 7 e}lfobmlvok ijgm`v nl knadv"`ilm pvznla enmkf vdmiz~`zmovmp iz ollndnkovmp `ibxkmvm pvznlap

    b"pvznla Dnkjmzv pxo`m

    np o e}l`vnilok iet#+ x# olf vdm izkfpdmmv `iizfnlovmp

    dmzm TN$.2TN$+28. olf kncmnpm eiz ivdmz enmkfp,

    Nl vdm bibmlv}b"pxo`m zmxzmpmlvovnil np o e}l`vnilok iedmzm np n vnbmp vdm bibmlv}b `ilg}aovm vi + n,m,7

    nl vdm bibmlv}b"pxo`m zmxzmpmlvovnil

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    Vdm knadv"`ilm pvznla enmkf vdmiz~ f~lobn`p ie np aiumzlmf j~ vdm lil"zmkovnunpvn`P`dzimfnlamz mq}ovnil

    knadv"`ilm pvznla enmkf

    vdmiz~ Dobnkvilnol

    Nl vmzbp ie vdm pvznla `i}xknla vdm knadv"`ilm PEV Dobnkvilnol dop vdm mtxolpnil

    Nl vdm ezmm pvznla vdmiz~ knbnv nv pdi}kf jm mq}ok vi vdm Dobnkvilnol `ibnla ezib vdm

    pvznla vdmiz~ "bifmk

    Qm nkk }pm xmzv}zjovnil vdmiz~ vi `ibx}vm vdm mlmza~ ie vdm pvovmp,

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    V n n v vn vd jn v

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    V}zlnla il nlvmzo`vnilp7 vdm `}jn` umzvmt

    Vdm `izzm`vnilp vi p}xmzokamjzo amlmzovizp+ il`m nlvmzo`vnilp ozm v}zlmf il+ ozm

    ijvonlmf eikkinla pibm a}nfnla xznl`nxkmp,

    ?, Vdm nlvmzo`vnil pdi}kf `i}xkm vdm pvznla izkfpdmmv nl o `ilvnl}ip o~

    t#28

    t#

    2:?

    2:$?#:.

    :

    0

    ?

    28

    Vdm nlvmzo`vnil umzvmt eiz vdm p`ovvmznla ie 0 pvznlap np `ilpvz}`vmf nvd o

    "e}l`vnilok mleiz`nla izkfpdmmv `ilvnl}nv~,

    Nl xx"oum p}xmzpvznla dimumz vdm pnv}ovnil np pknadvk~ bizm `ibxkn`ovmf j}v vdm

    jopn` xznl`nxkm aiumzlnla vdm nlvmzo`vnil np umz~ pnbxkm7

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    :, Vdm p}xmzokamjzo dop vi jm zmoknwmf nl vdm e}kk nlvmzo`vnla vdmiz~

    P}xmz`dozamp vdov pq}ozm vi vdm Dobnkvilnol zm`mnum `izzm`vnilp dml offnla

    nlvmzo`vnilp

    Vdm xn`v}zm zmbonlp amibmvzn` j}v nl offnvnil vi o fmkvo"e}l`vnilok mleiz`nla

    `ilvnl}nv~ nl p}xmzpxo`m ilm dop vi nlpmzv ki`ok ixmzovizp ov vdm nlvmzo`vnil xinlv,

    Vdmpm ixmzovizp zmxzmpmlv e}l`vnilok amlmzoknwovnilp ie fmznuovnum `i}xknlap

    xzmeo`vizp

    Vdmzm ozm vi fneemzmlv pmv ie p}xmzokamjzo amlmzovizp,

    ?, Cnlmbovn`ok amlmzovizp 7

    Vdm~ ozm liv `izzm`vmf j~ nlvmzo`vnilp, Vdm p~bbmvznmp vdm~ amlmzovm ozm liv

    oeem`vmf j~ offnla dnadmz izfmz vmzbp vi vdm o`vnil

    Vdmpm amlmzovizp zmbonl q}ofzovn` nl vdm pvznla enmkf nl vdmnlvmzo`vnla enmkf vdmiz~ olf o`v fnoailokk~ il Db

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    :, F~lobn`ok amlmzovizp7

    Vdm~ zm`mnum `izzm`vnilp nl vdm xzmpml`m ie nlvmzo`vnilp olf `i}xkm fneemzmlv

    l}bjmz ie pvznlap

    `}jn`

    nl vdm pvznla enmkf

    q}ozvn`

    nl vdm pvznla enmkf

    vdm `izzm`vnilp ozm p}`d vdov + olf pvnkk povnpen~ vdm p}xmzokamjzo

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    Vdm zmq}nzmbmlv vdov vdm p}xmzokamjzo np povnpenmf nl vdm nlvmzo`vnla vdmiz~ li

    anump znpm vi vi cnlf ie `ilpvonlvp7

    Cnlmbovn`ok `ilpvzonlv F~lobn`ok `ilpvzonlv

    $olvn."`ibb}vovnil zmkovnil ie

    cnlmbovn`ok olf f~lobn`ok amlmzovizp

    olvn"`ibb}vovnil zmkovnil ie

    f~lobn`ok amlmzovizp okilm

    zmq}nzmp nlpmzvnil ie nlvmzo`vnil

    xinlv ixmzovizp7 vdm xzmeo`vizp

    kmofp vi `ilvnl}nv~ `ilfnvnil

    nl p}xmzpxo`m

    Vi pikum vdm `ilpvzonlvp m }pm xmzv}zjovnil vdmiz~,

    Cnlmbovn`ok `ilpvzonlv

    olf b}pv jm xzixizvnilok vi

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    F~lobn`ok ilpvzonlvp

    P}xmzp~bbmvz~ okamjzo

    Mtxolfnla vdm Dobnkvilnol olf vdm p}xmz`dozamp ov vdm izfmz ap7 vdm f~lobn`ok

    `ilpvzonlv il olf np

    vdm pobm op nl ekov pxo`m

    vdm `ilpvzonlvp ozm pikumf j~ nlpmzvnla xzmeo`vizp nl vdm nlvmzo`vnil umzvmt vdov fi liv

    fmxmlf il vdm pvznla enmkf

    Muml nbxipnla okk vdm `ilpvzonlvp vdm umzvmt np liv }lnq}mk~ entmf7vdzmm clil pik}vnilp olf iumzokk }lclil e}l`vnil e$+x#.

    Q n

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    Qm `ol znvm

    xzmeo`viz

    cnlmbovn`ok xozv ie vdm umzvmt+ `ibbil vi okk f~lobn`ok amlmzovizp

    olf pnbnkoz mtxzmppnilp eiz vdm emzbniln` xozv {Mjn

    Vdm jipiln` xozv ie vdm xzmeo`viz np anuml j~

    @ilvo`v Vmzbp

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    @ilvo`v Vmzbp

    Qm olv vi `ibx}vm vdm mlmza~ ie pvznla pvovmp }pnla o q}olv}b bm`doln`ok

    xmzv}zjovnil vdmiz~,

    Vdm f~lobn`ok amlmzovizp ozm mtxolfmf nl vmzbp ie ap, ]x vi vdm I$ap:. m doum

    Vdm p}p~ okamjzo }x vi vdm I$ap:.

    Lm`mppoznk~ vdmzm np ol vdm pi"`okkmf `ilvo`v vmzb

    Knadv"`ilm pvznla enmkf xmzv}zjovnil vdmiz~ il o pnlakm pvznla nl o : ip`nkkoviz pvovm {ln}pmp _B xmzv}zjovnil vdmiz~ vi `ibx}vm vdm `izzm`vnil vi nvp knadv"`ilm mlmza~

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    Vdm pvznla ginl)pxknv xinlvp

    ie mo`d umzvmt `inl`nfm

    Nl v~xm NNO)J p}xmzpvznla il Bnlcipcn pxo`m"vnbm+ nv np clil vdov vdm `ilvo`v vmzbp ozm

    lm`mppoz~ vi `ol`mk `mzvonl pnla}koznvnmp nl vdm nlvmazovnilp iumz xozobmvmzp ie knadv"`ilm PEV

    fnoazobp, Nl vdm `ileizbok enmkf vdmiz~ vdm~ ozm okpi pmml vi oznpm op offnvnilok `ilvznj}vnilp

    lmmfmf vi `ol`mk `mzvonl pnla}koz p}zeo`m vmzbp dn`d oznpm nl vdm nlvmazovnil ie `izzmkovizp ie

    umzvmt ixmzovizp iumz vdm bif}koz xozobmvmzp ie Znmboll p}zeo`mp,

    G,Azmmlpnvm olf E,Z,Cknlcdobmz LXJ 086 $?>44.

    O knvvkm dnpviz~

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    O knvvkm dnpviz~

    Zinjol+ Pxzofknl olf Uikiun`d+ dmx"vd)8:??::8

    Nv bov`dmp/ J}v ijvonlmf ezib

    Zmekm`vnil p~bbmvz~ ie vdm ilm"kiix knadv"`ilm pvznla fnoazob 99X,A}vgdoz olf O, Xolcnmn`w+ dmx"vd)86818>4+ li

    Nv fimp liv bov`d/

    Entmp vdm xzm"eo`viz e2? Mtxolpnil nl doke nlvmamz ximzp ie

    ]pmp vz}l`ovnil vi :"nbx}znvnmp Pmvp _$6.28

    ]pmp Pxzofknl"Uikiun`d umzvmt

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    Zmp}kvp7 eiz ol~ umzvmtZmp}kvp7 eiz ol~ umzvmt

    ?, Qm `ilenzbmf A}vgdoz olf Xolcnmn`w zmp}kv+ vdm lov}zok mtxolpnil xozobmvmz

    np

    :, Nl vdm vzo`m pvovm {S?+ ?Rn vdm kmofnla izfmz np olf nv fnumzamp

    Mo`d vmzb nl vdm mq}ovnil ojium fnumzamp nlfnunf}okk~, Qnvd vdm ie vdmzmekm`vnil p~bbmvz~ li `ol`mkovnil ie fnumzaml`mp

    li ?):

    0, Pobm eiz vdm {S>+ ?Rn pvovm olf 6 nbx}znv~ nlvmzbmfnovm pvovmp

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    6, Fijopdn"^ilm~o umzvmt

    Fnumzaml`mp `ol`mk olf nv izcp ov ?"kiix/

    Entmp vdm xzm"eo`viz e26)0

    ]pmp vz}l`ovnil vi :"nbx}znvnmp

    Pmvp _$6.28

    Li doke nlvmamz ximzp }x vi 1):

    Jmpv bov`dnla ie vdnp q}olvnv~ pi eoz

    F^ umzvmt np ol nbxziumbmlv iumz nvp xzmfm`mppizp

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    @il`k}pnilp@il`k}pnilp

    ?, Fijopdn ^ilm~o umzvmt pmmbp vi jm vdm bipv xzibnpnla

    :, Xippnjkm pi}z`mp ie fnp`zmxol`nmp

    o. l}bjmz ie nbx}znvnmp nl vdm nlvmzbmfnovm pvovmp,

    j. _$6. 8

    o `ilvo`v vmzb dn`d fimp liv fnumzam9

    0, Vdm xzijkmb ie bov`dnla lil"xkoloz ^B olf pvznla

    nlvmzo`vnilp nl vdm `ilvmtv ie OfP)@EV np pvnkk ixml