Squark
Jul2-04, 01:03 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nHello dear group!\n\nFirstly, thx to Aaron Bergman for his help with nonrenormalization theorems.\n\nHere are some more questions about "Large N Field Theories, String Theory and Gravity"\nby Aharony, Gubser, Maldacena, Ooguri and Oz (heo-th/9905111), beyond those already\nposted on sci.physics.strings*.\n\n1) On page 132, D-instantons are discussed. It is explain they correspond to Yang-Mills\ninstantons in the dual CFT and that the spacetime location of the D-instanton\ncorresponds to the AdS_5 factor appearing in the moduli space of SU(N) instantons for\nany N > 1 and the S_5 factor which emerges for large N due to the fermionic zero\nmodes. The question is what happens when we consider n-point expectation values in\nthe dual CFT at a non-vacuum state. Assume this state approximates a certain\n(semi)classical spacetime in asymptotically AdS gravity. On the CFT side, the n-point\nfunction can be computed from a Euclidean path integral with a certain wavefunction\nfactor in it, and which includes integration over the same instanton moduli space. My\nguess is that the instanton contribution corresponds to th D-instanton contribution\nwhere the D-instanton is located at the endpoint of a spacelike geodesic beginning at\nand orthogonal to the AdS boundary, such that the value of the proper length parameter\nwhere the D-instanton is located and the point on the boundary where the geodesic\nbegins would yield the corresponding (i.e. dictated by the Yang-Mills instanton moduli)\npoint in AdS_5 x S_5 if spacetime was unperturbed AdS_5 x S_5. The point on the\nboundary is, of course, the location of the Yang-Mills instanton.\n\n2) On page 138 (section 4.3.3) it is said that if we deform N = 4 SU(N) Super-Yang-Mills\nby giving mass to all scalars and fermions, we get a theory that flows to pure Yang-Mills\nin the infrared. Now, pure Yang-Mills is not conformal, so it can\'t be an IR fixed point.\nPossibly it is meant that we get convergence of the two renormalization group flows\n(deformed SYM and pure YM) in the IR?\n\n3) On page 153, the BTZ black-hole in AdS_3 is discussed. It is said that a black hole\nwith minimal mass (R/8G, R being the curvature radius of AdS and G the\n3-dimensional Newton\'s constant) exists which preserves part of the supersymmetries,\nand it corresponds to the Ramond-Ramond vacuum in the dual CFT (whereas "clear"\nAdS corresponds to the Neveu-Schwarz-Neveu-Schwarz vacuum). Then, the entropy\nof this state in computed via the Bekenstein-Hawking formula (5.12) and via the dual\nCFT (5.13) and the two results match. Should I understand expression 5.13 represents\nthe degeneracy of the CFT\'s RR vacuum?\n\n4) On page 154, the canonical ensemble of AdS_3 quantum gravity is considered. On\nthe CFT side, we get a path integral living on a torus with NS-NS boundary conditions\nfor both circles (after making Euclidean time periodic). On the gravity side, we should\nconsider manifolds having this two-torus as its boundary. Now AdS_3 with time made\nperiodic is suggested. However, AdS_3 is Lorentzian while we are now look for\nEuclidean spacetimes, aren\'t we?! Possibly they really mean the Lobachevsky space?\n\n5) On page 159, the orbifold point of the dual CFT is examined. It is claimed this\nregime may be interpreted as a gas of winded strings. It is not clear to me how is this\npoissible since AdS_3 is simply connected (by definition it is the covering space of a\ncertain 2-nd order hypersurface).\n\n6) On page 173, a near extremal black string in a spacetime with 6 large dimesnions\nis considered. The compactified dimensions form a T_4 with volume v at infinity. The\nconfiguration carries D1-charge Q_1 and D5-charge Q_5. The spacetime is periodic\nalong the black string\'s direction with radius R_5. The following paragraph appears\non the botton of the page:\n"The near extremal black strings corresponds to the case R_5 is large and the total\nmass is just above the rest energy of the branes. By \'rest energy\' of the branes we\nmean the mass given by the BPS bound E = M - Q_5 R_5 sqrt(v) - Q_1 R_5 / sqrt(v)"\nIt would seem this expression should be zero in the extremal case i.e. near-extremal\nmeans E just above zero, not M just above E. Am I confused?\n\nThx in advance for any help!\n\n* I no longer post on sci.physics.strings because of the unseemly behavior of its\ncomoderator Lubos Motl (see the thread "quantizing gravity"), which comes in\ndirect conflict with the newsgroup\'s own charter. I believe that newsgroup is\ninappropriate for the discussion of its alleged subject matter as long as this\nman does not retire from his post.\n\nBest regards,\nSquark\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hello dear group!
Firstly, thx to Aaron Bergman for his help with nonrenormalization theorems.
Here are some more questions about "Large N Field Theories, String Theory and Gravity"
by Aharony, Gubser, Maldacena, Ooguri and Oz (heo-th/9905111), beyond those already
posted on sci.physics.strings*.
1) On page 132, D-instantons are discussed. It is explain they correspond to Yang-Mills
instantons in the dual CFT and that the spacetime location of the D-instanton
corresponds to the AdS_5 factor appearing in the moduli space of SU(N) instantons for
any N > 1 and the S_5 factor which emerges for large N due to the fermionic zero
modes. The question is what happens when we consider n-point expectation values in
the dual CFT at a non-vacuum state. Assume this state approximates a certain
(semi)classical spacetime in asymptotically AdS gravity. On the CFT side, the n-point
function can be computed from a Euclidean path integral with a certain wavefunction
factor in it, and which includes integration over the same instanton moduli space. My
guess is that the instanton contribution corresponds to th D-instanton contribution
where the D-instanton is located at the endpoint of a spacelike geodesic beginning at
and orthogonal to the AdS boundary, such that the value of the proper length parameter
where the D-instanton is located and the point on the boundary where the geodesic
begins would yield the corresponding (i.e. dictated by the Yang-Mills instanton moduli)
point in AdS_5 x S_5 if spacetime was unperturbed AdS_5 x S_5. The point on the
boundary is, of course, the location of the Yang-Mills instanton.
2) On page 138 (section 4.3.3) it is said that if we deform N = 4 SU(N) Super-Yang-Mills
by giving mass to all scalars and fermions, we get a theory that flows to pure Yang-Mills
in the infrared. Now, pure Yang-Mills is not conformal, so it can't be an IR fixed point.
Possibly it is meant that we get convergence of the two renormalization group flows
(deformed SYM and pure YM) in the IR?
3) On page 153, the BTZ black-hole in AdS_3 is discussed. It is said that a black hole
with minimal mass (R/8G, R being the curvature radius of AdS and G the
3-dimensional Newton's constant) exists which preserves part of the supersymmetries,
and it corresponds to the Ramond-Ramond vacuum in the dual CFT (whereas "clear"
AdS corresponds to the Neveu-Schwarz-Neveu-Schwarz vacuum). Then, the entropy
of this state in computed via the Bekenstein-Hawking formula (5.12) and via the dual
CFT (5.13) and the two results match. Should I understand expression 5.13 represents
the degeneracy of the CFT's RR vacuum?
4) On page 154, the canonical ensemble of AdS_3 quantum gravity is considered. On
the CFT side, we get a path integral living on a torus with NS-NS boundary conditions
for both circles (after making Euclidean time periodic). On the gravity side, we should
consider manifolds having this two-torus as its boundary. Now AdS_3 with time made
periodic is suggested. However, AdS_3 is Lorentzian while we are now look for
Euclidean spacetimes, aren't we?! Possibly they really mean the Lobachevsky space?
5) On page 159, the orbifold point of the dual CFT is examined. It is claimed this
regime may be interpreted as a gas of winded strings. It is not clear to me how is this
poissible since AdS_3 is simply connected (by definition it is the covering space of a
certain 2-nd order hypersurface).
6) On page 173, a near extremal black string in a spacetime with 6 large dimesnions
is considered. The compactified dimensions form a T_4 with volume v at infinity. The
configuration carries D1-charge Q_1 and D5-charge Q_5. The spacetime is periodic
along the black string's direction with radius R_5. The following paragraph appears
on the botton of the page:
"The near extremal black strings corresponds to the case R_5 is large and the total
mass is just above the rest energy of the branes. By 'rest energy' of the branes we
mean the mass given by the BPS bound E = M - Q_5 R_5 \sqrt(v) - Q_1 R_5 / \sqrt(v)"
It would seem this expression should be zero in the extremal case i.e. near-extremal
means E just above zero, not M just above E. Am I confused?
Thx in advance for any help!
* I no longer post on sci.physics.strings because of the unseemly behavior of its
comoderator Lubos Motl (see the thread "quantizing gravity"), which comes in
direct conflict with the newsgroup's own charter. I believe that newsgroup is
inappropriate for the discussion of its alleged subject matter as long as this
man does not retire from his post.
Best regards,
Squark
Firstly, thx to Aaron Bergman for his help with nonrenormalization theorems.
Here are some more questions about "Large N Field Theories, String Theory and Gravity"
by Aharony, Gubser, Maldacena, Ooguri and Oz (heo-th/9905111), beyond those already
posted on sci.physics.strings*.
1) On page 132, D-instantons are discussed. It is explain they correspond to Yang-Mills
instantons in the dual CFT and that the spacetime location of the D-instanton
corresponds to the AdS_5 factor appearing in the moduli space of SU(N) instantons for
any N > 1 and the S_5 factor which emerges for large N due to the fermionic zero
modes. The question is what happens when we consider n-point expectation values in
the dual CFT at a non-vacuum state. Assume this state approximates a certain
(semi)classical spacetime in asymptotically AdS gravity. On the CFT side, the n-point
function can be computed from a Euclidean path integral with a certain wavefunction
factor in it, and which includes integration over the same instanton moduli space. My
guess is that the instanton contribution corresponds to th D-instanton contribution
where the D-instanton is located at the endpoint of a spacelike geodesic beginning at
and orthogonal to the AdS boundary, such that the value of the proper length parameter
where the D-instanton is located and the point on the boundary where the geodesic
begins would yield the corresponding (i.e. dictated by the Yang-Mills instanton moduli)
point in AdS_5 x S_5 if spacetime was unperturbed AdS_5 x S_5. The point on the
boundary is, of course, the location of the Yang-Mills instanton.
2) On page 138 (section 4.3.3) it is said that if we deform N = 4 SU(N) Super-Yang-Mills
by giving mass to all scalars and fermions, we get a theory that flows to pure Yang-Mills
in the infrared. Now, pure Yang-Mills is not conformal, so it can't be an IR fixed point.
Possibly it is meant that we get convergence of the two renormalization group flows
(deformed SYM and pure YM) in the IR?
3) On page 153, the BTZ black-hole in AdS_3 is discussed. It is said that a black hole
with minimal mass (R/8G, R being the curvature radius of AdS and G the
3-dimensional Newton's constant) exists which preserves part of the supersymmetries,
and it corresponds to the Ramond-Ramond vacuum in the dual CFT (whereas "clear"
AdS corresponds to the Neveu-Schwarz-Neveu-Schwarz vacuum). Then, the entropy
of this state in computed via the Bekenstein-Hawking formula (5.12) and via the dual
CFT (5.13) and the two results match. Should I understand expression 5.13 represents
the degeneracy of the CFT's RR vacuum?
4) On page 154, the canonical ensemble of AdS_3 quantum gravity is considered. On
the CFT side, we get a path integral living on a torus with NS-NS boundary conditions
for both circles (after making Euclidean time periodic). On the gravity side, we should
consider manifolds having this two-torus as its boundary. Now AdS_3 with time made
periodic is suggested. However, AdS_3 is Lorentzian while we are now look for
Euclidean spacetimes, aren't we?! Possibly they really mean the Lobachevsky space?
5) On page 159, the orbifold point of the dual CFT is examined. It is claimed this
regime may be interpreted as a gas of winded strings. It is not clear to me how is this
poissible since AdS_3 is simply connected (by definition it is the covering space of a
certain 2-nd order hypersurface).
6) On page 173, a near extremal black string in a spacetime with 6 large dimesnions
is considered. The compactified dimensions form a T_4 with volume v at infinity. The
configuration carries D1-charge Q_1 and D5-charge Q_5. The spacetime is periodic
along the black string's direction with radius R_5. The following paragraph appears
on the botton of the page:
"The near extremal black strings corresponds to the case R_5 is large and the total
mass is just above the rest energy of the branes. By 'rest energy' of the branes we
mean the mass given by the BPS bound E = M - Q_5 R_5 \sqrt(v) - Q_1 R_5 / \sqrt(v)"
It would seem this expression should be zero in the extremal case i.e. near-extremal
means E just above zero, not M just above E. Am I confused?
Thx in advance for any help!
* I no longer post on sci.physics.strings because of the unseemly behavior of its
comoderator Lubos Motl (see the thread "quantizing gravity"), which comes in
direct conflict with the newsgroup's own charter. I believe that newsgroup is
inappropriate for the discussion of its alleged subject matter as long as this
man does not retire from his post.
Best regards,
Squark