View Full Version : BPS membranes with three boundaries
Urs Schreiber
Nov2-04, 09:36 AM
<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>Lubos asked (http://golem.ph.utexas.edu/string/archives/000461.html#c001690)\nabout literature on BPS membranes in the "pair of pants" shape.\n\nProbably litarature on supersymmetric 3-string junctions in string networks\nwill have something about this, since these junctions come from membranes\nwith 3 boundaries.\n\nA quick search turned up\n\nYukata Matsuo & Kazumi Okuyama: BPS condition of String Junction from M\nTheory,\nhep-th/9712070\n\n(around equation (3))\n\nand\n\nCurtis Callan & Larus Thorlacius: Worldsheet Dynamics of String Junctions,\nhep-th/9803097.\n\nIf anyone knows more and better references, please let us know!\n\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>Lubos asked (http://golem.ph.utexas.edu/string/archives/000461.html#c001690)
about literature on BPS membranes in the "pair of pants" shape.
Probably litarature on supersymmetric 3-string junctions in string networks
will have something about this, since these junctions come from membranes
with 3 boundaries.
A quick search turned up
Yukata Matsuo & Kazumi Okuyama: BPS condition of String Junction from M
Theory,
http://www.arxiv.org/abs/hep-th/9712070
(around equation (3))
and
Curtis Callan & Larus Thorlacius: Worldsheet Dynamics of String Junctions,
http://www.arxiv.org/abs/hep-th/9803097.
If anyone knows more and better references, please let us know!
Lubos Motl
Nov2-04, 03:16 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>On Tue, 2 Nov 2004, Urs Schreiber wrote:\n\n> Yukata Matsuo & Kazumi Okuyama: BPS condition of String Junction from M\n> Theory,\n> hep-th/9712070\n\nThanks for your research, Urs! That\'s an interesting paper, but it does\nnot seem relevant for the fivebrane worldvolume theory, as far as I see.\nString junctions of (p,q) strings exist in type IIB; if you want to\ndescribe them in M-theory, it must be M-theory on a T^2 torus, at least.\n\nI thought that the pants diagrams relevant for fivebranes should already\nexist in the infinite space, and the circles arising as the boundaries of\nthe pants membrane within the fivebranes should be closed, but\ntopologically trivial. Incidentally, it seems likely that some extra\nphysics inside the fivebrane would have to protect the circle from\nshrinking.\n\n> Curtis Callan & Larus Thorlacius: Worldsheet Dynamics of String Junctions,\n> hep-th/9803097.\n\nRight, this is also junctions. It\'s hard to see how these things can\ncreate BPS states for fivebranes. Maybe the whole idea that there are BPS\npants membranes stretched between the fivebranes in the flat space was\njust a miscommunication or my misunderstanding of something?\n______________________________________ ________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\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>On Tue, 2 Nov 2004, Urs Schreiber wrote:
> Yukata Matsuo & Kazumi Okuyama: BPS condition of String Junction from M
> Theory,
> http://www.arxiv.org/abs/hep-th/9712070
Thanks for your research, Urs! That's an interesting paper, but it does
not seem relevant for the fivebrane worldvolume theory, as far as I see.
String junctions of (p,q) strings exist in type IIB; if you want to
describe them in M-theory, it must be M-theory on a T^2 torus, at least.
I thought that the pants diagrams relevant for fivebranes should already
exist in the infinite space, and the circles arising as the boundaries of
the pants membrane within the fivebranes should be closed, but
topologically trivial. Incidentally, it seems likely that some extra
physics inside the fivebrane would have to protect the circle from
shrinking.
> Curtis Callan & Larus Thorlacius: Worldsheet Dynamics of String Junctions,
> http://www.arxiv.org/abs/hep-th/9803097.
Right, this is also junctions. It's hard to see how these things can
create BPS states for fivebranes. Maybe the whole idea that there are BPS
pants membranes stretched between the fivebranes in the flat space was
just a miscommunication or my misunderstanding of something?
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Urs Schreiber
Nov3-04, 07:03 AM
<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>On Tue, 2 Nov 2004, Lubos Motl wrote:\n\n> Right, this is also junctions. It\'s hard to see how these things can\n> create BPS states for fivebranes.\n\n\nI see. I had the vague idea they might be generalizable.\n\n\n> Maybe the whole idea that there are BPS\n> pants membranes stretched between the fivebranes in the flat space was\n> just a miscommunication or my misunderstanding of something?\n\n\nHm. It could make one suspicious that the first hit when googling for "M2\nBPS pants" is... your blog entry where you ask for references about them.\n;-)\n\nSo what\'s the conclusion? Should these 3-boundary membranes that you and\nAndy Neitzke talked about exist but have just not been studied, or don\'t\nthey exist after all?\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>On Tue, 2 Nov 2004, Lubos Motl wrote:
> Right, this is also junctions. It's hard to see how these things can
> create BPS states for fivebranes.
I see. I had the vague idea they might be generalizable.
> Maybe the whole idea that there are BPS
> pants membranes stretched between the fivebranes in the flat space was
> just a miscommunication or my misunderstanding of something?
Hm. It could make one suspicious that the first hit when googling for "M2
BPS pants" is... your blog entry where you ask for references about them.
;-)
So what's the conclusion? Should these 3-boundary membranes that you and
Andy Neitzke talked about exist but have just not been studied, or don't
they exist after all?
Urs Schreiber
Nov22-04, 02:05 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>Here is a followup to a recent discussion:\n\nA while ago Lubos wrote:\n\n\n> On Tue, 2 Nov 2004, Urs Schreiber wrote:\n>\n> > Yukata Matsuo & Kazumi Okuyama: BPS condition of String Junction from M\n> > Theory,\n> > hep-th/9712070\n>\n> Thanks for your research, Urs! That\'s an interesting paper, but it does\n> not seem relevant for the fivebrane worldvolume theory, as far as I see.\n> String junctions of (p,q) strings exist in type IIB; if you want to\n> describe them in M-theory, it must be M-theory on a T^2 torus, at least.\n\n\nOk, but if it (n^3 scaling via pant-like membranes) works in this\ncase, wouldn\'t it already be interesting?\n\n\n> > Curtis Callan & Larus Thorlacius: Worldsheet Dynamics of String Junctions,\n> > hep-th/9803097.\n>\n> Right, this is also junctions. It\'s hard to see how these things can\n> create BPS states for fivebranes.\n\n\nThere is the notion of a (p,q) web of 5-branes, which looks like it is\njust what is needed here. It is described in\n\nAharony, Hanany & Kol:\nWebs of (p,q) 5-branes, Five Dimensional Field Theories and Grid\nDiagrams,\nhep-th/9710116\n\nand expanded on for instance in\n\nKol & Rahmfeld:\nBPS Spectrum of 5 Dimensional Field Theories, (p,q) Webs and Curve\nCounting,\nhep-th/9801067\n\nA string network of (p,q) branes may end on a "web" of (p,q) 5-branes,\nwhere (1,0) 5-branes are D5s, whjile (0,1) 5-branes are NS5s.\n\nIf the 5-branes wrap circles in IIB, this entire (p,q) string network\nending on a (p,q) 5-brane web configuration lifts to a network of M2s\nending on (1-cycles in) M5s (wrapping (p,q) cycles on a T^2), which is\nessentially what we are looking for.\n\n\n> I thought that the pants diagrams relevant for fivebranes should already\n> exist in the infinite space, and the circles arising as the boundaries of\n> the pants membrane within the fivebranes should be closed, but\n> topologically trivial. Incidentally, it seems likely that some extra\n> physics inside the fivebrane would have to protect the circle from\n> shrinking.\n\n\nThe 5-brane must wrap cycles as must the boundary of the membranes\nending on them in the above context. But if this is how it is, would\nit make these configurations less relevant or interesting for the\nspeculation that the ~n^3 degrees of freedom are given by membrane\n"pants"?\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>Here is a followup to a recent discussion:
A while ago Lubos wrote:
> On Tue, 2 Nov 2004, Urs Schreiber wrote:
>
> > Yukata Matsuo & Kazumi Okuyama: BPS condition of String Junction from M
> > Theory,
> > http://www.arxiv.org/abs/hep-th/9712070
>
> Thanks for your research, Urs! That's an interesting paper, but it does
> not seem relevant for the fivebrane worldvolume theory, as far as I see.
> String junctions of (p,q) strings exist in type IIB; if you want to
> describe them in M-theory, it must be M-theory on a T^2 torus, at least.
Ok, but if it (n^3 scaling via pant-like membranes) works in this
case, wouldn't it already be interesting?
> > Curtis Callan & Larus Thorlacius: Worldsheet Dynamics of String Junctions,
> > http://www.arxiv.org/abs/hep-th/9803097.
>
> Right, this is also junctions. It's hard to see how these things can
> create BPS states for fivebranes.
There is the notion of a (p,q) web of 5-branes, which looks like it is
just what is needed here. It is described in
Aharony, Hanany & Kol:
Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid
Diagrams,
http://www.arxiv.org/abs/hep-th/9710116
and expanded on for instance in
Kol & Rahmfeld:
BPS Spectrum of 5 Dimensional Field Theories, (p,q) Webs and Curve
Counting,
http://www.arxiv.org/abs/hep-th/9801067
A string network of (p,q) branes may end on a "web" of (p,q) 5-branes,
where (1,0) 5-branes are D5s, whjile (0,1) 5-branes are NS5s.
If the 5-branes wrap circles in IIB, this entire (p,q) string network
ending on a (p,q) 5-brane web configuration lifts to a network of M2s
ending on (1-cycles in) M5s (wrapping (p,q) cycles on a T^2), which is
essentially what we are looking for.
> I thought that the pants diagrams relevant for fivebranes should already
> exist in the infinite space, and the circles arising as the boundaries of
> the pants membrane within the fivebranes should be closed, but
> topologically trivial. Incidentally, it seems likely that some extra
> physics inside the fivebrane would have to protect the circle from
> shrinking.
The 5-brane must wrap cycles as must the boundary of the membranes
ending on them in the above context. But if this is how it is, would
it make these configurations less relevant or interesting for the
speculation that the ~n^3 degrees of freedom are given by membrane
"pants"?
Urs Schreiber
Nov25-04, 04:20 AM
<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>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> schrieb im Newsbeitrag\nnews:206f2305.0411221203.3a1f27f0-100000@posting.google.com...\n\n> Ok, but if it (n^3 scaling via pant-like membranes) works in this\n> case, wouldn\'t it already be interesting?\n\nBy private email I was pointed to the old paper\n\nD. Berenstein & R. Leigh:\nString Junctions and Bound States of Intersecting Branes,\nhep-th/9812142\n\nThe authors begin by reviewing how a black hole in 4D is obtained from\nwrapping M5s on internal cycles, how there are three different wrapping\n"types" and how the entropy of the resulting black hole scales as the\nproduct N1 N2 N3 of the number of these three types of branes.\n\nSince such an ~N^3 scaling cannot be accounted for (not directly at least)\nby states of strings stretched between these branes, they argue that it\ncomes from the 3-string junctions that we talked about in this thread, i.e.\nin the M-theory picture from M2 pants with certain wrapping numbers\nconnecting three 5-branes.\n\nThey also give a U-dual description of the same situation in terms of\ntwisted string states sitting at an orbifold singularity. This sounds like\nit should be related to the fractional strings that Lubos said Nima Arkani\nHamed is talking of\n(http://golem.ph.utexas.edu/string/archives/000461.html#c001684).\n\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>"Urs Schreiber" <Urs.Schreiber@uni-essen.de> schrieb im Newsbeitrag
news:206f2305.0411221203.3a1f27f0-100000@posting.google.com...
> Ok, but if it (n^3 scaling via pant-like membranes) works in this
> case, wouldn't it already be interesting?
By private email I was pointed to the old paper
D. Berenstein & R. Leigh:
String Junctions and Bound States of Intersecting Branes,
http://www.arxiv.org/abs/hep-th/9812142
The authors begin by reviewing how a black hole in 4D is obtained from
wrapping M5s on internal cycles, how there are three different wrapping
"types" and how the entropy of the resulting black hole scales as the
product N1 N2 N3 of the number of these three types of branes.
Since such an ~N^3 scaling cannot be accounted for (not directly at least)
by states of strings stretched between these branes, they argue that it
comes from the 3-string junctions that we talked about in this thread, i.e.
in the M-theory picture from M2 pants with certain wrapping numbers
connecting three 5-branes.
They also give a U-dual description of the same situation in terms of
twisted string states sitting at an orbifold singularity. This sounds like
it should be related to the fractional strings that Lubos said Nima Arkani
Hamed is talking of
(http://golem.ph.utexas.edu/string/archives/000461.html#c001684).
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