## Chaudhuri on the Hagedorn "myth"

<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>http://motls.blogspot.com/2005/06/chaudhuri-on-hagedorn-myth.html\n\nThis short note is closely related to a previous article about the work of\nDienes and Lennek. Tonight, it is Shyamoli Chaudhuri who is "dispelling\nthe Hagedorn myth" (incidentally, it was already in 1965 when Hagedorn\nsuggested that at high enough temperatures, open strings merge into a gas\nof chaotic long closed strings):\n\nhep-th/0506143\n\nShe calculates the thermal free energy - apparently in a different way\nthan we are used to (from Atick and Witten and related works) - to\nconclude that the exponential growth of the states with the energy does\nnot exist. In section 2.1 she argues that the growth of the number of\nstates with the level does not imply the same growth of free energy as a\nfunction of temperature (or the density of states with the total energy).\nThe true growth is slower, she says, making the full expression\nconvergent. Nevertheless, she finds a first order phase transition at the\nT-self-dual temperature.\n\nHer basic argument is the same as in the Dienes and Lennek\'s paper: the\ncorrect one-loop torus path integral only goes over the fundamental region\nof the modular group which removes the dangerous region with small\n"Im(tau)" and makes, according to her beliefs, the integral convergent for\nany temperature.\n\nI encourage everyone for whose research and thinking the Hagedorn behavior\nis important to decide about the fate of the transition without any\nprejudices. After checking various things, I personally believe that the\nHagedorn "folklore" will survive and both of the recent anti-Hagedorn\npapers are misled. (Chaudhuri is more radical because she seems to believe\nthat the transition would be absent even in type 0 and other strings.)\n\nThe integral over the fundamental region combined with the summation over\nthe two winding numbers that count how both circles of the worldsheet\ntorus wind around the thermal circle in spacetime may be replaced by a\nfull integral over the upper "tau" half-plane, which re-introduces the\ndangerous region with small "Im(tau)" and revives the "Hagedorn myth".\n\nTechnically, I think that her error is the step from (15) to (16) in her\npaper where she uses the Hardy-Ramanujan formula, assuming that the\nexcitation of the string is very large, which removes by hand the actual\ndivergence that would, in this calculational procedure, emerge from the\nthermal tachyon (the ground state of the winding sector "w=1" around the\nthermal circle in spacetime - in this sector the GSO projection is\nreversed) - a contribution that she neglects because the Hardy-Ramanujan\nformula is definitely not applicable for low-lying states such as this\nthermal tachyon.\n\nNote that once you admit that the relevant CFT has a thermal tachyon, the\ndiscussion simply ends. With a thermal tachyon, the Hagedorn divergence\narises from the region with large values of "Im(tau)", not small ones. And\nthis "infrared" region is definitely not removed in string theory. To\nsummarize, I now believe that if one defines the thermal stringy\namplitudes in the most obvious stringy extension of the thermal\npath-integral rules of QFT, one finds the thermally wound tachyon whose\nmass determines the Hagedorn temperature, and the new critical papers\nfail.\n\nFeel free to disagree.\n____________________________________________________________ __________________\nE-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)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\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>http://motls.blogspot.com/2005/06/ch...dorn-myth.html

This short note is closely related to a previous article about the work of
Dienes and Lennek. Tonight, it is Shyamoli Chaudhuri who is "dispelling
the Hagedorn myth" (incidentally, it was already in 1965 when Hagedorn
suggested that at high enough temperatures, open strings merge into a gas
of chaotic long closed strings):

http://www.arxiv.org/abs/hep-th/0506143

She calculates the thermal free energy - apparently in a different way
than we are used to (from Atick and Witten and related works) - to
conclude that the exponential growth of the states with the energy does
not exist. In section 2.1 she argues that the growth of the number of
states with the level does not imply the same growth of free energy as a
function of temperature (or the density of states with the total energy).
The true growth is slower, she says, making the full expression
convergent. Nevertheless, she finds a first order phase transition at the
T-self-dual temperature.

Her basic argument is the same as in the Dienes and Lennek's paper: the
correct one-loop torus path integral only goes over the fundamental region
of the modular group which removes the dangerous region with small
"$Im(\tau)$" and makes, according to her beliefs, the integral convergent for
any temperature.

I encourage everyone for whose research and thinking the Hagedorn behavior
is important to decide about the fate of the transition without any
prejudices. After checking various things, I personally believe that the
Hagedorn "folklore" will survive and both of the recent anti-Hagedorn
papers are misled. (Chaudhuri is more radical because she seems to believe
that the transition would be absent even in type and other strings.)

The integral over the fundamental region combined with the summation over
the two winding numbers that count how both circles of the worldsheet
torus wind around the thermal circle in spacetime may be replaced by a
full integral over the upper "$\tau$" half-plane, which re-introduces the
dangerous region with small "$Im(\tau)$" and revives the "Hagedorn myth".

Technically, I think that her error is the step from (15) to (16) in her
paper where she uses the Hardy-Ramanujan formula, assuming that the
excitation of the string is very large, which removes by hand the actual
divergence that would, in this calculational procedure, emerge from the
thermal tachyon (the ground state of the winding sector "w=1" around the
thermal circle in spacetime - in this sector the GSO projection is
reversed) - a contribution that she neglects because the Hardy-Ramanujan
formula is definitely not applicable for low-lying states such as this
thermal tachyon.

Note that once you admit that the relevant CFT has a thermal tachyon, the
discussion simply ends. With a thermal tachyon, the Hagedorn divergence
arises from the region with large values of "$Im(\tau)$", not small ones. And
this "infrared" region is definitely not removed in string theory. To
summarize, I now believe that if one defines the thermal stringy
amplitudes in the most obvious stringy extension of the thermal
path-integral rules of QFT, one finds the thermally wound tachyon whose
mass determines the Hagedorn temperature, and the new critical papers
fail.

Feel free to disagree.
__{____________________________________________________________________ ________}
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)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^
 PhysOrg.com physics news on PhysOrg.com >> Kenneth Wilson, Nobel winner for physics, dies>> Two collider research teams find evidence of new particle Zc(3900)>> Scientists make first direct images of topological insulator's edge currents


I believe that the error is in (25), which is the first equation that differs from the standard understanding, by the unmotivated introduction of the phase factor $e^{i \pi w}$. This manifestly destroys modular invariance, as it breaks the symmetry between w and the Poisson resummation variable m. Similar equations appeared in several earlier and now-withdrawn preprints by this author, in each case with the assertion that it was the unique modular-invariant partition function. In fact, the unique modular-invariant partition function is the usual one, with Hagedorn divergence. Legitimately Anonymous Physicist

 Similar discussions for: Chaudhuri on the Hagedorn "myth" Thread Forum Replies Calculus & Beyond Homework 9 Biology 13