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View Full Version : [SOLVED] Re: BF-YM inspired string action


Lubos Motl
Apr18-04, 12:47 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>Hi Eric,\n\nI want to say that while I was reading again the "Japanese (IKKT) matrix\nmodel" paper\n\nhttp://arxiv.org/abs/hep-th/9612115\n\n- because it is now being studied by several people what its relation to\nthe quantum foam ideas might be - the authors forced me to realize that\nthe Schild gauge (see page 4 of that paper), which is the form in which\nthey obtain type IIB strings as the large N limit of their model, is\nactually the supersymmetrized version of your quartic term for the stringy\naction which is classically equivalent to the Polyakov or Nambu-Goto\nactions. Or at least, they are very similar.\n\nBest wishes\nLubos\n___________________________________ ___________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\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>Hi Eric,

I want to say that while I was reading again the "Japanese (IKKT) matrix
model" paper

http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/9612115

- because it is now being studied by several people what its relation to
the quantum foam ideas might be - the authors forced me to realize that
the Schild gauge (see page 4 of that paper), which is the form in which
they obtain type IIB strings as the large N limit of their model, is
actually the supersymmetrized version of your quartic term for the stringy
action which is classically equivalent to the Polyakov or Nambu-Goto
actions. Or at least, they are very similar.

Best wishes
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Urs Schreiber
Apr18-04, 01:05 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>On Sun, 18 Apr 2004, Lubos Motl wrote:\n\n&gt; http://arxiv.org/abs/hep-th/9612115\n&gt;\n&gt; - because it is now being studied by several people what its relation to\n&gt; the quantum foam ideas might be\n\nOh, so there is renewed interest in this model?\n\nAre you referring to Vafa\'s ideas about "quantum foam"?\n\n&gt; - the authors forced me to realize that\n&gt; the Schild gauge (see page 4 of that paper), which is the form in which\n&gt; they obtain type IIB strings as the large N limit of their model, is\n&gt; actually the supersymmetrized version of your quartic term for the stringy\n&gt; action which is classically equivalent to the Polyakov or Nambu-Goto\n&gt; actions. Or at least, they are very similar.\n\nClassically, if f is an isotonic function then the actions\n\nint a\n\nand\n\nint f(a)\n\nare equivalent, of course. So that\'s why you can use instead of the\nNG action\n\nint sqrt{g} d^d x\n\nthe version\n\nint f(sqrt(g)) d^d x .\n\nUsing in particular f(x) = x^2 for x &gt; 0 gives you the (bosonic) Schild\naction from the NG action.\n\nBut is this what Eric has been discussing?\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>On Sun, 18 Apr 2004, Lubos Motl wrote:

> http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/9612115
>
> - because it is now being studied by several people what its relation to
> the quantum foam ideas might be

Oh, so there is renewed interest in this model?

Are you referring to Vafa's ideas about "quantum foam"?

> - the authors forced me to realize that
> the Schild gauge (see page 4 of that paper), which is the form in which
> they obtain type IIB strings as the large N limit of their model, is
> actually the supersymmetrized version of your quartic term for the stringy
> action which is classically equivalent to the Polyakov or Nambu-Goto
> actions. Or at least, they are very similar.

Classically, if f is an isotonic function then the actions

\int a

and

\int f(a)

are equivalent, of course. So that's why you can use instead of the
NG action

\int \sqrt{g} d^d x

the version

\int f(\sqrt(g)) d^d x .

Using in particular f(x) = x^2 for x > gives you the (bosonic) Schild
action from the NG action.

But is this what Eric has been discussing?