## ghostly issues

<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>"Charlie Stromeyer Jr." &lt;cstromey@hotmail.com&gt; schrieb im Newsbeitrag\nnews:61773ed7.0405252052.3406eded-100000@posting.google.com...\n&gt; Urs Schreiber &lt;Urs.Schreiber@uni-essen.de&gt; wrote in message news:\n&gt;\n&gt; &gt; &gt; Yes, and for more clarification also see the earlier paper\n&gt; &gt; &gt; (hep-th/0405007).\n&gt; &gt;\n&gt; &gt; Ah, thanks. I haven\'t gone through the details (a science of its own, it\n&gt; &gt; seems)\n&gt;\n&gt; Is it still a science when you find either the Devil or God in the\n&gt; details ?-)\n\n\nOnly then!\n\n\n&gt; &gt; Hm. In section 5 the authors of the above paper do discuss worldsheet\n&gt; &gt; diffeos and the super diffeo ghosts it seems.\n&gt;\n&gt; Correct, but as you have already seen this paper is not strictly the\n&gt; original Berkovits\' approach but a modification of it.\n\n\nYes. It\'s hard to get an overview of all the techniques proposed and used.\nBut I gather from what I have seen that Berkovits\' SSFT formalism is very\npowerful and useful.\n\n\n&gt; This same paper\n&gt; also refers to another modification of the Berkovits\' approach which\n&gt; is a generalization called the EPS formailism (hep-th/0404141), but\n&gt; don\'t worry because the "B-ghosts" here are less scary than "Super\n&gt; Ghosts" :-)\n\nI guess that\'s why we have nice diagrams as (152) of that paper\n(hep-th/0405007)...\n\nWhat I find interesting about the B-s that are motivated in (136) and found\nin (142) is that they are not pure ghost at all but contain plenty of\nphysical fields.\n\nI guess this is related to a remark made by Davide Gaiotto in\n\nhttp://groups.google.de/groups?selm=302ccf73.0405241639.13c20041-100000%40posting.google.com,\n\nwhere he mentioned that in general CFTs we don\'t expect the Virasoro\ngenerators to be Q-exact. This seems to imply in particular that even when\nit is the Virasoro "potential" need not be a ghost. In hep-th/0405007 the\nauthors write above equation (136)\n\n"For gauged WZNW models there exist in general an operator B which makes T\nBRST-exact [...]"\n\nand this B is the baroque expression in (142).\n\nHm, I guess I have to familiarize myself with the notions discussed in\nsection 3 of that paper, where the idea of BRST operators that don\'t have\nthe form (151) seems to originate.\n\n\nWhat I like about the lambda-ghosts (what\'s a good name for them?) that\nappear in the pure spinor formalism as in\n\nQ = \\oint \\lambda \\cdot d\n\n(where d is the susy generator that comes from the second class constraints\nof the GS string)\n\nis that this BRST operator nicely fits into an old and propbably very naive\nidea which I once had, where I thought that it would "feel right" to somehow\nidentify the grading of the BRST operator with that of fermionic generators.\nIn my diploma thesis (\\approx master thesis) I had tried, among other\nthings, to do BRST theory for relativistic susy quantum mechanics governed\nby a generalized deRham Dirac operator\n\nD = d_{generalized} + d^\\dagger_{generalized}\n\non some manifold. (This appears for instance in the study of supersymmetric\nquantum cosmology, as I tried to demonstrate in\nhttp://www-stud.uni-essen.de/~sb0264/sqm.html .)\n\nSo the idea was to make use of the fact that D is already graded (Z2 at\nleast) and can hence be easily made nilpotent by appropriately multiplying\nwith the projector onto the top grade, for instance. Due to the simple case\nof one dimension this is in this simple case precisely the basic idea that\ngives rise to the form of the BRST operator in the pure spinor formalism -\nif you tweak your eyes sufficiently, at least. :-)\n\n&gt; &gt; &gt; You may also want to look at some of the techniques that have been\n&gt; &gt; &gt; used for Type 0 strings because these strings are described by N=1\n&gt; &gt; &gt; susy worldsheet theories (hep-th/0308123 and 0309028).\n&gt; &gt;\n&gt; &gt; Later. Maybe when I find a method to increase the number of hours in one\n&gt; &gt; day ;-)\n&gt;\n&gt; Have you considered GTR, or trying to capture your own mind as a known\n&gt; quantum state so that it cane be cloned? Otherwise, you will have to\n&gt; settle for a more approximate method of cloning :-)\n\nYou mean I should make somebody read it, understand it and write a nice\nsummary for us all to sci.physics.strings??\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Charlie Stromeyer Jr." <cstromey@hotmail.com> schrieb im Newsbeitrag
> Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:
>
> > > Yes, and for more clarification also see the earlier paper
> > > (http://www.arxiv.org/abs/hep-th/0405007).

> >
> > Ah, thanks. I haven't gone through the details (a science of its own, it
> > seems)

>
> Is it still a science when you find either the Devil or God in the
> details ?-)

Only then!

> > Hm. In section 5 the authors of the above paper do discuss worldsheet
> > diffeos and the super diffeo ghosts it seems.

>
> Correct, but as you have already seen this paper is not strictly the
> original Berkovits' approach but a modification of it.

Yes. It's hard to get an overview of all the techniques proposed and used.
But I gather from what I have seen that Berkovits' SSFT formalism is very
powerful and useful.

> This same paper
> also refers to another modification of the Berkovits' approach which
> is a generalization called the EPS formailism (http://www.arxiv.org/abs/hep-th/0404141), but
> don't worry because the "B-ghosts" here are less scary than "Super
> Ghosts" :-)

I guess that's why we have nice diagrams as (152) of that paper
(http://www.arxiv.org/abs/hep-th/0405007)...

What I find interesting about the B-s that are motivated in (136) and found
in (142) is that they are not pure ghost at all but contain plenty of
physical fields.

I guess this is related to a remark made by Davide Gaiotto in

where he mentioned that in general CFTs we don't expect the Virasoro
generators to be Q-exact. This seems to imply in particular that even when
it is the Virasoro "potential" need not be a ghost. In http://www.arxiv.org/abs/hep-th/0405007 the
authors write above equation (136)

"For gauged WZNW models there exist in general an operator B which makes T
BRST-exact [...]"

and this B is the baroque expression in (142).

Hm, I guess I have to familiarize myself with the notions discussed in
section 3 of that paper, where the idea of BRST operators that don't have
the form (151) seems to originate.

What I like about the $\lambda-ghosts$ (what's a good name for them?) that
appear in the pure spinor formalism $as inQ = \oint \lambda \cdot d$

(where d is the susy generator that comes from the second class constraints
of the GS string)

is that this BRST operator nicely fits into an old and propbably very naive
idea which I once had, where I thought that it would "feel right" to somehow
identify the grading of the BRST operator with that of fermionic generators.
In my diploma thesis $(\approx$ master thesis) I had tried, among other
things, to do BRST theory for relativistic susy quantum mechanics governed
by a generalized deRham Dirac operator

$$D = d_{generalized} + d^\dagger_{generalized}$$

on some manifold. (This appears for instance in the study of supersymmetric
quantum cosmology, as I tried to demonstrate in
http://www-stud.uni-essen.de/~sb0264/sqm.html .)

So the idea was to make use of the fact that D is already graded (Z2 at
least) and can hence be easily made nilpotent by appropriately multiplying
with the projector onto the top grade, for instance. Due to the simple case
of one dimension this is in this simple case precisely the basic idea that
gives rise to the form of the BRST operator in the pure spinor formalism -
if you tweak your eyes sufficiently, at least. :-)

> > > You may also want to look at some of the techniques that have been
> > > used for Type strings because these strings are described by N=1
> > > susy worldsheet theories (http://www.arxiv.org/abs/hep-th/0308123 and 0309028).

> >
> > Later. Maybe when I find a method to increase the number of hours in one
> > day ;-)

>
> Have you considered GTR, or trying to capture your own mind as a known
> quantum state so that it cane be cloned? Otherwise, you will have to
> settle for a more approximate method of cloning :-)

You mean I should make somebody read it, understand it and write a nice
summary for us all to sci.physics.strings??



Urs Schreiber wrote in message news: > I guess this is related to a remark made by Davide Gaiotto in > > http://groups.google.de/groups?selm=...ng.google.com, > > where he mentioned that in general CFTs we don't expect the Virasoro > generators to be Q-exact. This seems to imply in particular that even when > it is the Virasoro "potential" need not be a ghost. So do you mean e.g. that the cohomology of any ghost number of the BRST operator near the tachyon vacuum vanishes? So that after the tachyon condenses there would be only a closed string vacuum, i.e. there are no more open string degrees of freedom but only closed string dynamics? > So the idea was to make use of the fact that D is already graded (Z2 at > least) and can hence be easily made nilpotent by appropriately multiplying > with the projector onto the top grade, for instance. Did you also examine branes-antibranes which are Z2-graded? > > Have you considered GTR, or trying to capture your own mind as a known > > quantum state so that it can be cloned? Otherwise, you will have to > > settle for a more approximate method of cloning :-) > > You mean I should make somebody read it, understand it and write a nice > summary for us all to sci.physics.strings?? Or you could try to summon the ghosts of great scientists to help you. However, if you conjure forth the ghosts of female scientists such as Meitner, Curie or Noether your girlfriend may get jealous and then start singing the classic song "I don't stand a ghost of a chance with you" :-)



On Fri, 28 May 2004, Charlie Stromeyer Jr. wrote: > So do you mean e.g. that the cohomology of any ghost number of the > BRST operator near the tachyon vacuum vanishes? So that after the > tachyon condenses there would be only a closed string vacuum, i.e. > there are no more open string degrees of freedom but only closed > string dynamics? I didn't mean that in particular, but of course that's probably the most famous example. Yes, indeed the BRST operator which describes the tachyon vacuum (which is nothing but an insertion of the c-ghost $at z=\pm i)$ has trivial cohomology. This is interpreted as corresponding to the fact that all the open strings have disappeared as the brane has decayed so that one should not expect to find any non-trivial physical states. BUT, of course the open strings have not just disappeared without a trace, but must have become closed strings. How do we see the closed strings in the vacuum OSFT? I had some papers addressing this point somewhere here on my desk, but finding them right now will be a task more difficult than just making the internet search again. :-) As far as I could see there are some very interesting ideas how the closed string degrees of freedom might manifest themselves, but the problem is far from being solved. But actually my original question concerned a far less drastic situation: Assume we are looking at bosonic OSFT in some background where the D25 brane is not yet decayed. Do we expect that of all possible such backgrounds (corresponding for instance to massive excitations of the open string) $many/some$ (none?) will have non-Q-exact worldsheet Virasoro generators? Frankly, I currently don't understand why (with the usual BRST formalism for open bosonic strings, not some exotic reformulation of the BRST cohomology of the superstring, as we have discussed lately) we would expect the Virasoros of some background not to be Q-exact. What I also sort of understand is that if in the context of the superstring we could manage to get hold of a BRST operator describing an RR background (as for instance using the methods described in that paper which we discussed) that then Q-exactness of the Virasoro generators is not to be expected, due to the branch cuts in the spin field OPEs, which prevent us from performing the necessary commutator and lead to some non-local features on the worldsheet. Probably non-local worldsheet effects might in general be the reason for non-Q-exactness of the Vir generators? > > So the idea was to make use of the fact that D is already graded (Z2 at > > least) and can hence be easily made nilpotent by appropriately multiplying > > with the projector onto the top grade, for instance. > > Did you also examine branes-antibranes which are Z2-graded? No, no. What I wrote had nothiing to do with particualrities of specific physical configurations, I was just talking about the grading in a Hilbert space which supports spinors $or/and$ differential forms of some sort, like the gradings considered in Connes' noncommutative geometry, for instance. > Or you could try to summon the ghosts of great scientists to help you. Better yet, I'll invent the worldsheet Goblin field and study Ghost'n'Goblins CFTs.

## ghostly issues

<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 &lt;Urs.Schreiber@uni-essen.de&gt; wrote in message news:\n\n&gt; But actually my original question concerned a far less drastic situation:\n&gt; Assume we are looking at bosonic OSFT in some background where the D25\n&gt; brane is not yet decayed. Do we expect that of all possible such\n&gt; backgrounds (corresponding for instance to massive excitations of the\n&gt; open string) many/some (none?) will have non-Q-exact worldsheet Virasoro\n&gt; generators?\n&gt;\n&gt; Frankly, I currently don\'t understand why (with the usual BRST formalism\n&gt; for open bosonic strings, not some exotic reformulation of the BRST\n&gt; cohomology of the superstring, as we have discussed lately) we would\n&gt; expect the Virasoros of some background not to be Q-exact. [...]\n\n&gt; Probably non-local worldsheet effects might in general be the reason for\n&gt; non-Q-exactness of the Vir generators?\n\nWithin the level truncation approximation (called "LT" in paper [1]),\nthere is an inherent lack of commutativity between L_0 and the\nnon-perturbative BRS operator because L_0 is not a derivative of the\nstar product. This is explained in Section 2 of [1], and also see [2].\n\n\n[1] http://arxiv.org/abs/hep-th/0309164\n\n[2] http://arxiv.org/abs/hep-th/0009105 and\n\nhttp://arxiv.org/abs/hep-th/0105024\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote in message news:

> But actually my original question concerned a far less drastic situation:
> Assume we are looking at bosonic OSFT in some background where the D25
> brane is not yet decayed. Do we expect that of all possible such
> backgrounds (corresponding for instance to massive excitations of the
> open string) $many/some$ (none?) will have non-Q-exact worldsheet Virasoro
> generators?
>
> Frankly, I currently don't understand why (with the usual BRST formalism
> for open bosonic strings, not some exotic reformulation of the BRST
> cohomology of the superstring, as we have discussed lately) we would
> expect the Virasoros of some background not to be Q-exact. [...]

> Probably non-local worldsheet effects might in general be the reason for
> non-Q-exactness of the Vir generators?

Within the level truncation approximation (called "LT" in paper [1]),
there is an inherent lack of commutativity between $L_0$ and the
non-perturbative BRS operator because $L_0$ is not a derivative of the
star product. This is explained in Section 2 of [1], and also see [2].

[1] http://arxiv.org/abs/http://www.arxi...hep-th/0309164

[2] http://arxiv.org/abs/http://www.arxi...hep-th/0009105 and

http://arxiv.org/abs/http://www.arxi...hep-th/0105024



Urs Schreiber wrote in message news: > But actually my original question concerned a far less drastic situation: > Assume we are looking at bosonic OSFT in some background where the D25 > brane is not yet decayed. Do we expect that of all possible such > backgrounds (corresponding for instance to massive excitations of the > open string) $many/some$ (none?) will have non-Q-exact worldsheet Virasoro > generators? > > Frankly, I currently don't understand why (with the usual BRST formalism > for open bosonic strings, not some exotic reformulation of the BRST > cohomology of the superstring, as we have discussed lately) we would > expect the Virasoros of some background not to be Q-exact. [...] > Probably non-local worldsheet effects might in general be the reason for > non-Q-exactness of the Vir generators? Within the level truncation approximation (called "LT" in paper [1]), there is an inherent lack of commutativity between $L_0$ and the non-perturbative BRS operator because $L_0$ is not a derivative of the star product. This is explained in Section 2 of [1], and also see [2]. [1] http://arxiv.org/abs/http://www.arxi...hep-th/0309164 [2] http://arxiv.org/abs/http://www.arxi...hep-th/0009105 and http://arxiv.org/abs/http://www.arxi...hep-th/0105024 [This posting was re-posted again after the Harvard FAS newsserver problems on June 2nd. LM]