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Solvable Lie Algebras in Supergravity and Superstrings=   
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Pietro Fré
Bonn February 2002
An algebraic  characterization of superstring dualities
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In   D < 10        = ;  the structure of Superstring      Theory = is governed...
<= span style=3D'font-size:150%;color:white;mso-color-index:4'>•The geometry of the scalar manifold M
<= span style=3D'font-size:150%;color:white;mso-color-index:4'>•M =3D G/H is mostly= a non compact coset manifold
<= span style=3D'font-size:150%;color:white;mso-color-index:4'>•Non compact cosets = admit an algebraic description in terms of solvable Lie = algebras&= #13;
•
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charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
Before the gauging
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nBy compactification from <= span lang=3DIT style=3D'font-size:88%;color:red'>higher dimensions. In this case the scalar manifold is iden= tified as the moduli space of the internal compact manifold
<= span style=3D'font-size:88%'>nBy dir= ect construction of each supergravity  in the chosen dimension. In this case one uses the a priori constraints provided by supers= ymmetry. In par= ticular holonomy and the need to reconcile p+1 forms with scalars
Two ways to determine G/H or anyhow the = scalar manifold = ;
= DUALITIES
Special Geometries <= /span>
The second method is more general, the = first knows more about superstrings, but the two must be consistent <= /span>
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The scalar manifold of supergravities is  necessarily a non compact G/H, except:
In the exceptional cases the scalar coset= is not necessarily but
can be chosen to be a non compact coset. Namely Special
Geometries include classes of non compact coset manifolds&#= 13;
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quoted-printable Content-Type: text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
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Scalar cosets in d= =3D4
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P4KY93Dq27HnfD+CmPdxH7KWylg3EexxVqTSaztief0Oja2q8jNleQo61IAGoE6zH//Z ------=_NextPart_01C3E99F.F2977570 Content-Location: file:///C:/6517A0D4/bonlect_files/slide0033.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
Scalar manif= olds by dimensions in maximal supergrav= ities
Rather then by number of supersymmetries we can go by dimensions=
at fixed number of supercharges. This is what we have done above=
for the maximal nu= mber of susy charges, i.e. 32.
These scalar geometries can be derived by sequential
toroidal compactifications.
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How to determine the scalar cosets G/H from supersymmetry
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text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
.....and symplectic or pseudorthogonal representations
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How to retrieve the = D=3D4 table
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Essentials of Duality Rotations= 3;
The scalar potential V(f) is introduced by the gauging. Prior to th= at we have invariance under duality rotations of electric and <= span lang=3DIT style=3D'color:red;mso-color-index:6'>magnetic field stren= gths
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text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
Duality Rotation Gro= ups
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
The symplec= tic or pseudorthogonal embedding in D=3D2r
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.......continued
This embedding is the key point in the construction
of  N-extended supergravity lagrangians in even
dimensions. It determines the form of the= kinetic matrix o= f the self-dual p+1 forms and later controls= the gauging procedures.
D= =3D4,8
D=3D6,10
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The symplec= tic case
D=3D4,8
This is the basic object en= tering susy rules and later fermion shif= ts and the scalar potential
= = <= ![endif]> = <= ![endif]> =
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
The Gaillar= d and Zumino master formula
We have:&= #13;
&= #13;
A gen= eral expression for the vector kinetic matrix in terms of the = symplectically embedded coset representatives. = This matrix is also named the period matrix because when we have= Calabi Yau compactifications= the scalar manifold is no longer a coset manifold and the kinetic matrix of vectors = can instead be determined form algebraic geometry as the period= matrix of the Calabi Yau 3-fold
&= #13;
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Summarizing:
nThe = scalar sector of supergravities is “mostly” a non compact<= /span> coset U/H
<= span style=3D'font-size:88%'>nThe = isometry group U acts as a duality grou= p on vector fields or p-forms
<= span style=3D'font-size:88%;color:red;mso-color-index:6'>nU includes target space T-duality and strong/weak coupling S-duality.
<= span style=3D'font-size:88%'>nFor = non compact U/H we have a general mathematical theory that describes them in terms <= /span>of solvable Lie algebras.....
n
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Solvable Lie algebra description...
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Differential Geometry= =3D Algebra =
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Maximal Susy implies= Er+1 series
Scalar fields are associated with positive roots or Cartan generators =
= = = <= ![endif]>
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file:///C:/6517A0D4/bonlect_files/slide0044.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
How to build the sol= vable algebra =
Given the Real form of= the algebra U, for each positive root
 there is an appropriate step operator belonging to such= a real form
=
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
...in the sequential toroidal compactification
The sequential toroidal compactificat= ion has an alge= braic counterpart in the embedding of subalgebras
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Sequential Embeddings of Subalgebras and Superstrings=
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file:///C:/6517A0D4/bonlect_files/slide0049.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
The type IIA chain = of subalgebras&= #13;
W is a nilpotent algebra = with including no Cartan
ST algebra
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Type IIA versus Type IIB decomposition of the Dynkin diagram
Dilaton
Ramond scalars
The dilaton
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The Type IIB chain of subalgebras&= #13;
U duality in D=3D10 =
= <= ![endif]>
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and other Supergravity Tools in Brane Physics
A decompos= ition that mixes NS and RR states (=3D U dua= lity)
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charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics
The electric subalge= bra
In the symplectic representation this is the onl= y off diagonal root that mixes electric and magnetic <= /span>field strengths
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Understand= ing  type IIA / type IIB
T-duality  algebraically
Two way= s of = choosin= g the sim= ple roots
Chirality with respect to T algebra=
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The two realizations= of E7(7)
The two realizations correspond to attaching the 7th root in two different positions<= /b>
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Dilaton and radii are in the CSA
The extra dimensions are compactified on circles o= f various radii
<= ![if !vml]>
&= #13;
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Outer Automorphisms of the
S T subalgebra 
&= #13;
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An explicit example = of T duality
= =
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The Maximal Abelian = Ideal
From
Number of vector fields in SUGRA in D+1 dimensions
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Conclusions: =
n= (thanks to my collaborator, Mario Trigiante)
nThe Solvable Lie algebra representation has= many applications, in particular:
<= span style=3D'font-size:113%;color:white;mso-color-index:4'>nClassification of p= -brane and black hole solutions
<= span style=3D'font-size:113%;color:white;mso-color-index:4'>nClassification and construction of supergravity gaugings
<= span style=3D'font-size:113%;color:white;mso-color-index:4'>nStudy of supersymme= try breaking patterns and super Higgs phenomena
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068.htm",1,-1,1),new hrefList("slide0070.htm",1,-1,1),new hrefList("slide00= 40.htm",1,-1,1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide004= 2.htm",1,-1,1),new hrefList("slide0043.htm",1,-1,1),new hrefList("slide0044= .htm",1,-1,1),new hrefList("slide0045.htm",1,-1,1),new hrefList("slide0046.= htm",1,-1,1),new hrefList("slide0048.htm",1,-1,1),new hrefList("slide0049.h= tm",1,-1,1),new hrefList("slide0037.htm",1,-1,1),new hrefList("slide0050.ht= m",1,-1,1),new hrefList("slide0038.htm",1,-1,1),new hrefList("slide0039.htm= ",1,-1,1),new hrefList("slide0051.htm",1,-1,1),new hrefList("slide0047.htm"= ,1,-1,1),new hrefList("slide0052.htm",1,-1,1),new hrefList("slide0053.htm",= 1,-1,1),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide0073.htm",1= ,-1,1),new hrefList("slide0072.htm",1,-1,1)); function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) { var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix(); function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') { href=3Dnew String(document.location.href) Start=3Dhref.indexOf('!')+1 End=3Dhref.lastIndexOf('/')+1 if (End < Start) return href.substring(0, Start) else return href.substring(0, End) } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ToggleOtlPane() { frmset=3Ddocument.all("PPTHorizAdjust") frm=3Ddocument.all("PPTOtl") if( gOtlOpen ) frmset.cols=3D"*,100%" else frmset.cols=3D"25%,*" gOtlOpen=3D!gOtlOpen frm.noResize=3D!frm.noResize UpdOtNavPane() } function ToggleNtsPane() { frmset=3Ddocument.all("PPTVertAdjust") frm=3Ddocument.all("PPTNts") if( gNtsOpen ) frmset.rows=3D"100%,*" else frmset.rows=3D"*,20%" gNtsOpen=3D!gNtsOpen UpdNtsPane() } function ClearMedia() { if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() { if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else return gCurSld } function GetNumSlds() { if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; PPTSld.location.replace(MHTMLPrefix+obj.mSldHref) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 PPTSld.location.replace(MHTMLPrefix+href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); function ImgBtn( oId,bId,w,action ) { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } function TxtBtn( oId,oeId,action,chkState ) { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new TxtBtn( "nb_nts","nb_ntsElem",parent.ToggleNtsPan= e,GetNtsState ) gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","nb_prevBorder",30,parent.GoToP= revSld ) gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","nb_nextBorder",30,parent.GoToN= extSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D new ImgBtn( "nb_voice","nb_voiceBorder",18,parent.= ToggleVNarration ) gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlTxt","nb_otlTxtBorder",23,parent= .ToggleOtlText ) gBtnArr["nb_nts"].m_flagId=3D "notes_flag" gBtnArr["nb_nts"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr= row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { history.back(); PPTSld.event.ca= ncelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; s.fontFamily=3DsFont s.fontSize=3D"9pt" s.paddingLeft=3D2 } function CreateSeparator( node ) { var sObj=3DCreateItem( node ) SetCMBorder(sObj,"menu","menu") var s=3DsObj.style s.borderTopColor=3D"threedshadow" s.borderBottomColor=3D"threedhighlight" s.height=3D1 s.fontSize=3D"0px" } function CreateItem( node ) { var elem=3DPPTSld.document.createElement("DIV") node.insertBefore( elem ) return elem } function SetCMBorder( o,ltClr,rbClr ) { var s=3Do.style s.backgroundColor=3D"menu" s.borderStyle=3D"solid" s.borderWidth=3D1 s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr } ------=_NextPart_01C3E99F.F2977570 Content-Location: file:///C:/6517A0D4/bonlect_files/fullscreen.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; 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charset="us-ascii" Gaugings and other Supergravity Tools in Brane Physics ------=_NextPart_01C3E99F.F2977570 Content-Location: file:///C:/6517A0D4/bonlect_files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
Slide Show
Outline
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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