View Full Version : String torsion constraints
Urs Schreiber
Oct1-04, 09:04 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>Uma Mahanta and collaborators had made some estimates on bounds on\n"propagating torsion" using muon (g-2) experiments\n(http://www.g-2.bnl.gov/index.shtml)\n\nP. Das & U. Mahanta:\nTorsion constraints from the recent precision measurement of the muon\nanomaly\nhep-ph/0211137\n\nas well as using LEP data (Mahanta&Raychudhuri, hep-ph/0307350).\n\nIn the introduction of hep-ph/0211137 it says that the authors want to\nconsider torsion as would follow from a non-vanishing H=dB field strength of\nthe string\'s Kalb-Ramond field. The action of that coupled to fermions\nshould schematically read like\n\nS = int (dB)^2 + \\bar psi D psi\n\nwhere D is the Dirac operator with torsion ~H, i.e. D = y^m d_m + H_lmn\ny^lmn up to inessential prefactors (I write "y" for the Clifford\ngenerators).\n\nBut Mahanta et al. instead use an action of the schematic form (for totally\nantisymmetric torsion)\n\nS = int H^2 + (d*H)^2 + fermion coupling .\n\nDoes anyone know what the justification of this action is?\n\nI have the impression that they are really thinking of the standard action\nof a massive 3 form, regarding the torsion 3-form as a propagating field\ninstead of as the field strength of a 2-form B.\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>Uma Mahanta and collaborators had made some estimates on bounds on
"propagating torsion" using muon (g-2) experiments
(http://www.g-2.bnl.gov/index.shtml)
P. Das & U. Mahanta:
Torsion constraints from the recent precision measurement of the muon
anomaly
http://www.arxiv.org/abs/hep-ph/0211137
as well as using LEP data (Mahanta&Raychudhuri, http://www.arxiv.org/abs/hep-ph/0307350).
In the introduction of http://www.arxiv.org/abs/hep-ph/0211137 it says that the authors want to
consider torsion as would follow from a non-vanishing H=dB field strength of
the string's Kalb-Ramond field. The action of that coupled to fermions
should schematically read like
S = \int (dB)^2 + \bar \psi D \psi
where D is the Dirac operator with torsion ~H, i.e. D = y^m d_m + H_{lmn}y^{lmn} up to inessential prefactors (I write "y" for the Clifford
generators).
But Mahanta et al. instead use an action of the schematic form (for totally
antisymmetric torsion)
S = \int H^2 + (d*H)^2 + fermion coupling .
Does anyone know what the justification of this action is?
I have the impression that they are really thinking of the standard action
of a massive 3 form, regarding the torsion 3-form as a propagating field
instead of as the field strength of a 2-form B.
Lubos Motl
Oct1-04, 10:45 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>Hi Urs,\n\nfirst of all - the word "justification" is probably not the best word as\nlong as you work with string theory. In string theory you can calculate\nall these things - at least the equations of motion, and up to a field\nredefinition. See e.g. page 114 of Joe\'s book volume 1, and pages 87, 91\nof Joe\'s book volume 2 for the actions in the maximal spacetime\ndimensions in bosonic string and superstring theories, respectively.\n\nSecond, these papers look confusing to me because they work with the\nB-field as torsion in four dimensions. The real physics of a 2-form\npotential in 4 dimensions is that you can take its 3-form field strength,\nHodge-dualize it, and obtain a one-form field strength of a dual 0-form\npotential. Therefore, physics of the B-field in 4 dimensions is equivalent\nto physics of a scalar. This scalar is called the axion - and there are\nmany types of axions that can appear in various realistic models.\n\n(Axions have been proposed as dark matter candidates, and especially as\nsolutions of the strong CP problem - why is the CP-violating theta-angle\nin QCD so small even though it does not have to be - Peccei-Quinn\nmechanism.)\n\n> But Mahanta et al. instead use an action of the schematic form (for totally\n> antisymmetric torsion)\n>\n> S = int H^2 + (d*H)^2 + fermion coupling .\n\nI\'ve seen this action neither in the paper you mentioned nor anywhere\nelse. d*H is roughly *Box(B). This term has a different dimension, and\nwould have to include a prefactor of order \\alpha\' - relatively to the\nmain kinetic term (H^2). I think it\'s plausible that it appears as an\n\\alpha\'-correction, but it is irrelevant at low energies. Why do you care\nabout it?\n\nBest\nLubos\n______________________________ ________________________________________________\n E-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)\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>Hi Urs,
first of all - the word "justification" is probably not the best word as
long as you work with string theory. In string theory you can calculate
all these things - at least the equations of motion, and up to a field
redefinition. See e.g. page 114 of Joe's book volume 1, and pages 87, 91
of Joe's book volume 2 for the actions in the maximal spacetime
dimensions in bosonic string and superstring theories, respectively.
Second, these papers look confusing to me because they work with the
B-field as torsion in four dimensions. The real physics of a 2-form
potential in 4 dimensions is that you can take its 3-form field strength,
Hodge-dualize it, and obtain a one-form field strength of a dual 0-form
potential. Therefore, physics of the B-field in 4 dimensions is equivalent
to physics of a scalar. This scalar is called the axion - and there are
many types of axions that can appear in various realistic models.
(Axions have been proposed as dark matter candidates, and especially as
solutions of the strong CP problem - why is the CP-violating \theta-angle
in QCD so small even though it does not have to be - Peccei-Quinn
mechanism.)
> But Mahanta et al. instead use an action of the schematic form (for totally
> antisymmetric torsion)
>
> S = \int H^2 + (d*H)^2 + fermion coupling .
I've seen this action neither in the paper you mentioned nor anywhere
else. d*H is roughly *Box(B). This term has a different dimension, and
would have to include a prefactor of order \alpha' - relatively to the
main kinetic term (H^2). I think it's plausible that it appears as an
\alpha'-correction, but it is irrelevant at low energies. Why do you care
about it?
Best
Lubos
__{_______________________________________________ _____________________________}
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)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Urs Schreiber
Oct1-04, 11:35 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 Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag\nnews:Pine.LNX.4.31.0410011136200.2291 0-100000@feynman.harvard.edu...\n\n> first of all - the word "justification" is probably not the best word as\n> long as you work with string theory. In string theory you can calculate\n> all these things - at least the equations of motion, and up to a field\n> redefinition. See e.g. page 114 of Joe\'s book volume 1, and pages 87, 91\n> of Joe\'s book volume 2 for the actions in the maximal spacetime\n> dimensions in bosonic string and superstring theories, respectively.\n\n\nYup. And because these authors use something different I was wondering what\nthey thought should be the justification for doing so.\n\n\n> Second, these papers look confusing to me because they work with the\n> B-field as torsion in four dimensions. The real physics of a 2-form\n> potential in 4 dimensions is that you can take its 3-form field strength,\n> Hodge-dualize it, and obtain a one-form field strength of a dual 0-form\n> potential. Therefore, physics of the B-field in 4 dimensions is equivalent\n> to physics of a scalar. This scalar is called the axion - and there are\n> many types of axions that can appear in various realistic models.\n\n\nI know that you dualize to get the axion. But that\'s just rewriting. It does\nnot change the fact that the fermions see a torsion, whether you write that\nas d B or as * d chi\n\n\n> > S = int H^2 + (d*H)^2 + fermion coupling .\n>\n> I\'ve seen this action neither in the paper you mentioned nor anywhere\n> else.\n\nTheir S^mu is *H and their S^mu nu is d * H.\n\n> Why do you care about it?\n\nBecause I am wondering about phenomenological consequences of torsion\neffects on fermions. I am not the only one. There are a couple of paper on\nthat, but none of them that I have seen so far seem to correctly deal with\nthe string theory formalism.\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 Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag
news:Pine.LNX.4.31.0410011136200.22910-100000@feynman.harvard.edu...
> first of all - the word "justification" is probably not the best word as
> long as you work with string theory. In string theory you can calculate
> all these things - at least the equations of motion, and up to a field
> redefinition. See e.g. page 114 of Joe's book volume 1, and pages 87, 91
> of Joe's book volume 2 for the actions in the maximal spacetime
> dimensions in bosonic string and superstring theories, respectively.
Yup. And because these authors use something different I was wondering what
they thought should be the justification for doing so.
> Second, these papers look confusing to me because they work with the
> B-field as torsion in four dimensions. The real physics of a 2-form
> potential in 4 dimensions is that you can take its 3-form field strength,
> Hodge-dualize it, and obtain a one-form field strength of a dual 0-form
> potential. Therefore, physics of the B-field in 4 dimensions is equivalent
> to physics of a scalar. This scalar is called the axion - and there are
> many types of axions that can appear in various realistic models.
I know that you dualize to get the axion. But that's just rewriting. It does
not change the fact that the fermions see a torsion, whether you write that
as d B or as * d \chi
> > S = \int H^2 + (d*H)^2 + fermion coupling .
>
> I've seen this action neither in the paper you mentioned nor anywhere
> else.
Their S^\mu is *H and their S^\mu \nu is d * H.
> Why do you care about it?
Because I am wondering about phenomenological consequences of torsion
effects on fermions. I am not the only one. There are a couple of paper on
that, but none of them that I have seen so far seem to correctly deal with
the string theory formalism.
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