[SOLVED] Sliver, butterfly, etc. [Archive]

Urs Schreiber

May14-04, 06:52 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>Unfortunately I have lots of other things to do currently,\nbut when I find the time I am still trying to better understand\nopen string field theory.\n\nRight now I am looking at section 8.4 of\n\nTaylor & Zwiebach: D-Branes, Tachyons, and String Field Theory,\nhep-th/0311017\n\nwhere "projector" string fields are discussed.\n\nIs there some heuristic way to understand why the sliver state,\nthe "identity" state and the butterfly state all consist of\nthe worldsheet vacuum and its Virasoro descendants?\n\nI assume that this must be understood physically from the\nfact that these descendants are spurious and hence merging\nthem with other other states (e.g. in the case of the identity\nstate) does not really change the original state, somehow.\n\nIn terms of multiplication of wedge states it is easily understood\nthat the wedge with 0 and with infinite angle act as projectors,\nsimply because 0 and oo are "projectors" under addition.\n\nHave similar projectors been constructed for some flavor of\nsuperSFT?\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>Unfortunately I have lots of other things to do currently,
but when I find the time I am still trying to better understand
open string field theory.

Right now I am looking at section 8.4 of

Taylor & Zwiebach: D-Branes, Tachyons, and String Field Theory,
http://www.arxiv.org/abs/hep-th/0311017

where "projector" string fields are discussed.

Is there some heuristic way to understand why the sliver state,
the "identity" state and the butterfly state all consist of
the worldsheet vacuum and its Virasoro descendants?

I assume that this must be understood physically from the
fact that these descendants are spurious and hence merging
them with other other states (e.g. in the case of the identity
state) does not really change the original state, somehow.

In terms of multiplication of wedge states it is easily understood
that the wedge with and with infinite angle act as projectors,
simply because and oo are "projectors" under addition.

Have similar projectors been constructed for some flavor of
superSFT?

Charlie Stromeyer Jr.

May14-04, 05:20 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>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:<Pine.LNX.4.31.0405140632340.12546-100000@feynman.harvard.edu>...\n\n> Right now I am looking at section 8.4 of\n>\n> Taylor & Zwiebach: D-Branes, Tachyons, and String Field Theory,\n> hep-th/0311017\n>\n> where "projector" string fields are discussed. [...]\n\n> Have similar projectors been constructed for some flavor of\n> superSFT?\n\nHi Urs, I do not have time to read such a long paper but there are\nanswers to your questions including your last question above. Consider\nthis from [1]:\n\n"The subject of most of the references mentioned above are surface\nstate projectors [32, 33]. These are projectors with field\nconfigurations arising from path integrations over fixed Riemann\nsurfaces whose boundary consists of a parametrized open string and a\npiece with open string boundary conditions. A very fundamental result\nin this realm [17] was that all such surfaces\nwith the property that their boundaries touch the midpoint of the open\nstring lead to projector functionals in the star algebra. Although\nthis class of projectors is quite large, it is advantageous to look\nfor projectors without these singular property which could eventually\nlead to D-brane solutions\nwith finite energy densities.\n\nThis is the motivation for the present paper. We study projectors of a\nfermionic first order system of weights (1, 0). It is shown that\nprojectors of this system give rise to bosonic projectors."\n\nAlso, do you or anyone else know what ever became of B. Zwiebach\'s\nthinking about the role of operads and PROP in CFT? This was once\ninteresting to me because I prefer to think about string theory in\nterms of mathematical patterns rather than in terms of what the\nphysics involved might have to mean, and thus not having to worry too\nmuch about the pesky requirements of Nature\'s empirical reality :-)\n\nRoughly put, operads have multiple inputs but only one output, whereas\nPROP has both multiple inputs and multiple outputs. Partial operads\nseemed like a nice and fairly simple method for describing CFT at tree\nlevel, but the PROPs were needed for higher genus.\n\n\n[1] http://arxiv.org/abs/hep-th/0312314\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> wrote in message news:<Pine.LNX.4.31.0405140632340.12546-100000@feynman.harvard.edu>...

> Right now I am looking at section 8.4 of
>
> Taylor & Zwiebach: D-Branes, Tachyons, and String Field Theory,
> http://www.arxiv.org/abs/hep-th/0311017
>
> where "projector" string fields are discussed. [...]

> Have similar projectors been constructed for some flavor of
> superSFT?

Hi Urs, I do not have time to read such a long paper but there are
answers to your questions including your last question above. Consider
this from [1]:

"The subject of most of the references mentioned above are surface
state projectors [32, 33]. These are projectors with field
configurations arising from path integrations over fixed Riemann
surfaces whose boundary consists of a parametrized open string and a
piece with open string boundary conditions. A very fundamental result
in this realm [17] was that all such surfaces
with the property that their boundaries touch the midpoint of the open
string lead to projector functionals in the star algebra. Although
this class of projectors is quite large, it is advantageous to look
for projectors without these singular property which could eventually
lead to D-brane solutions
with finite energy densities.

This is the motivation for the present paper. We study projectors of a
fermionic first order system of weights (1, 0). It is shown that
projectors of this system give rise to bosonic projectors."

Also, do you or anyone else know what ever became of B. Zwiebach's
thinking about the role of operads and PROP in CFT? This was once
interesting to me because I prefer to think about string theory in
terms of mathematical patterns rather than in terms of what the
physics involved might have to mean, and thus not having to worry too
much about the pesky requirements of Nature's empirical reality :-)

Roughly put, operads have multiple inputs but only one output, whereas
PROP has both multiple inputs and multiple outputs. Partial operads
seemed like a nice and fairly simple method for describing CFT at tree
level, but the PROPs were needed for higher genus.

[1] http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0312314

Urs Schreiber

May18-04, 01:45 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 Fri, 14 May 2004, Charlie Stromeyer Jr. wrote:\n\n> Hi Urs, I do not have time to read such a long paper but there are\n> answers to your questions including your last question above. Consider\n> this from [1]:\n[...]\n> [1] http://arxiv.org/abs/hep-th/0312314\n\nInteresting. I have only skimmed this paper, but it seems that the\npoint is that for the fermionic system a certain class of projectors\ncan be easily classified, since the general ansatz in equation (3.5)\nonly contains a couple of free parameters which can explicitly be solved\nfor, but that at the same time these solutions are in correspondence\nwith bosonic analogs of projectors (p.14). Is that a reasonable summary?\n\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 Fri, 14 May 2004, Charlie Stromeyer Jr. wrote:

> Hi Urs, I do not have time to read such a long paper but there are
> answers to your questions including your last question above. Consider
> this from [1]:
[...]
> [1] http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0312314

Interesting. I have only skimmed this paper, but it seems that the
point is that for the fermionic system a certain class of projectors
can be easily classified, since the general ansatz in equation (3.5)
only contains a couple of free parameters which can explicitly be solved
for, but that at the same time these solutions are in correspondence
with bosonic analogs of projectors (p.14). Is that a reasonable summary?