Fractional Supersymmetry [Archive]

Sep4-04, 03:06 AM

In my research on supersymmetric string theory I have dervied the following formula relating the number of worldsheet supersymmetries, N, to the critical dimension, d, of the target space:

d = 26 - 11N + 11/2*N^2 - 1/2*N^3

I have checked this for the examples I know of (N=0,1 and 2) and my formula agrees with the values in the literature. I'm not sure whether this has been done for higher values of N, but I assume my formula will still work. For example, has anyone computed the critical dimension for N=3 or N=4?

I have been looking at some work on fractional supersymmetry (in particular hep-th/9506177) and it appears that the number N=5/3 plays an important role. Plugging this in to my formula gives a prediction of d=3.96, which is very close to the observed value of d=4. Perhaps quantum corrections (or maybe non-perturbative effects) will alter the value 5/3 so the critical dimesnion is exactly 4. Does anyone know anything about quantum corrections of fractional supersymmetry?

GM :biggrin:

Mark Palenik

Sep9-04, 03:55 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>"GM" <giantmuntjac@hotmail.com> wrote in message\nnews:GM.1bzcjb@physicsforums.com...\n> In my research on supersymmetric string theory I have dervied the\n> following formula relating the number of worldsheet supersymmetries, N,\n> to the critical dimension, d, of the target space:\n>\n> d = 26 - 11N + 11/2*N^2 - 1/2*N^3\n>\n> I have checked this for the examples I know of (N=0,1 and 2) and my\n> formula agrees with the values in the literature. I\'m not sure whether\n> this has been done for higher values of N, but I assume my formula will\n> still work. For example, has anyone computed the critical dimension for\n> N=3 or N=4?\n>\n> I have been looking at some work on fractional supersymmetry (in\n> particular hep-th/9506177) and it appears that the number N=5/3 plays\n> an important role. Plugging this in to my formula gives a prediction of\n> d=3.96, which is very close to the observed value of d=4. Perhaps\n> quantum corrections (or maybe non-perturbative effects) will alter the\n> value 5/3 so the critical dimesnion is exactly 4. Does anyone know\n> anything about quantum corrections of fractional supersymmetry?\n>\n> GM :biggrin:\n>\n\nI actually know nothing about this, so I can\'t really tell you whether that\nformula means anything or not, but it looks kind of like a taylor expansion\nfor something. Is it possible that it is part of an infinite series? That\ncould *possibly* explain the 3.96. Of course, does 3.96 even make sense?\nMaybe if it\'s that close to 4, you can just round.\n\nHow did you derive the formula? From principles of physics, or just by\ntrying to fit numbers from literature to a function?\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>"GM" <giantmuntjac@hotmail.com> wrote in message
news:GM.1bzcjb@physicsforums.com...
> In my research on supersymmetric string theory I have dervied the
> following formula relating the number of worldsheet supersymmetries, N,
> to the critical dimension, d, of the target space:
>
> d = 26 - 11N + 11/2*N^2 - 1/2*N^3
>
> I have checked this for the examples I know of (N=0,1 and 2) and my
> formula agrees with the values in the literature. I'm not sure whether
> this has been done for higher values of N, but I assume my formula will
> still work. For example, has anyone computed the critical dimension for
> N=3 or N=4?
>
> I have been looking at some work on fractional supersymmetry (in
> particular http://www.arxiv.org/abs/hep-th/9506177) and it appears that the number N=5/3 plays
> an important role. Plugging this in to my formula gives a prediction of
> d=3.96, which is very close to the observed value of d=4. Perhaps
> quantum corrections (or maybe non-perturbative effects) will alter the
> value 5/3 so the critical dimesnion is exactly 4. Does anyone know
> anything about quantum corrections of fractional supersymmetry?
>
> GM :biggrin:
>

I actually know nothing about this, so I can't really tell you whether that
formula means anything or not, but it looks kind of like a taylor expansion
for something. Is it possible that it is part of an infinite series? That
could *possibly* explain the 3.96. Of course, does 3.96 even make sense?
Maybe if it's that close to 4, you can just round.

How did you derive the formula? From principles of physics, or just by
trying to fit numbers from literature to a function?