[SOLVED] Landscape averages - paper of the day - Kumar+Wells [Archive]

Lubos Motl

Sep23-04, 09:59 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!\n\nToday the paper that seems rather interesting to me is one by Jason Kumar\nand James Wells,\n\nhttp://www.arxiv.org/abs/hep-th/0409218\n\nThey try to estimate the average *rank* of the gauge group in rather\ngeneric type IIB flux compactifications on Calabi-Yau three-folds of the\ncurrently popular type - which means that they count the number of\nD3-branes in it, roughly speaking. The paradigm of "Susskind\'s" landscape\naverages was initiated by Michael Douglas.\n\nFor a given topology of a Calabi-Yau three-fold, they look at the tadpole\ncancellation condition and apply rather complicated and specific formulae\n- well, they even look too specific to me ;-) - to compute the "ensemble\naverage" of the rank of the gauge group.\n\nRecall that the Standard Model gauge group\'s rank is four (2 from SU(3), 1\nfrom SU(2), 1 from U(1)). To entertain, they of course obtain average\nranks close to four for rather simple Calabi-Yau manifolds (orbifold\nT^6/Z_2), which may sastisfy *some* readers. ;-) To make things even more\nfunny, they also consider the average rank among the vacua with a small\ncosmological constant, and their result is slightly higher - namely\nexactly four for T^6/Z_2, as required for the Standard Model. This will\nsatisfy even more readers :-), but not all of them - and of course, the\nauthors realize (and explain) very well that these averages are not real\npredictions - and in fact, their favorite answer of the total rank is not\nfour anyway, as we will see below.\n\nI would say that they are very careful about possible non-scientific\ninterpretations, and very careful not to irritate the readers who don\'t\nlike the anthropic principle. Their description of "what the landscape\naverages are good for" looks at least psychologically promising to me,\nand it is more or less the opposite to what is usually said.\n\nWhat do I mean? Many landscape supporters give up the vacuum selection\nprinciple - they give up the quest for the specific model that would allow\nus to make arbitrarily good predictions. Instead, they want to see that\nsome features of those vacua that admit life are rather generic, and they\nagree with reality. One is then supposed to be rather satisfied because we\nobtain a semi-quantitative statistical agreement between our theory and\nexperiment.\n\nKumar and Wells\' approach and motivation is just the opposite one, and I\nlike it. They don\'t give up the task to find the right vacuum. In fact,\nthey still consider it to be the ultimate goal, and are open-minded about\nthe possible ways how can we eventually get the right one. Therefore, they\nwant to focus on *very non-generic* properties of the real vacuum that are\n*not easily* reproduced in an otherwise realistic subclass of stringy\ncompactifications. This strategy is trying, of course, to find the right\nvacuum most quickly, by getting the maximal possible information about the\nright compactification in every step.\n\n....\n\nWell, let me return to the bulk of the paper. After they compute the\naverage group ranks, they look at the subset of the models that can\nrealistically suppress the proton decay. They use some rough arguments and\ncommon wisdom about what is necessary to suppress the proton decay in\nMSSM-like theories, and argue that the realistic candidates need higher\nrank.\n\nI have not quite understood the statistical treatment of this point - do\nthey want to eliminate the vacua with rapid proton decay by hand, or\nderive that they\'re unlikely? At any rate, it seems to me that they at\nleast believe that they have a *statistical* argument that the\nstringy-natural mechanisms to suppress the proton decay start with a\nbigger gauge group - in other words, the discrete symmetries (such as Z_2\nR-parity) may not be the solution recommended by string theory.\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\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!

Today the paper that seems rather interesting to me is one by Jason Kumar
and James Wells,

http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0409218

They try to estimate the average *rank* of the gauge group in rather
generic type IIB flux compactifications on Calabi-Yau three-folds of the
currently popular type - which means that they count the number of
D3-branes in it, roughly speaking. The paradigm of "Susskind's" landscape
averages was initiated by Michael Douglas.

For a given topology of a Calabi-Yau three-fold, they look at the tadpole
cancellation condition and apply rather complicated and specific formulae
- well, they even look too specific to me ;-) - to compute the "ensemble
average" of the rank of the gauge group.

Recall that the Standard Model gauge group's rank is four (2 from SU(3), 1
from SU(2), 1 from U(1)). To entertain, they of course obtain average
ranks close to four for rather simple Calabi-Yau manifolds (orbifold
T^6/Z_2), which may sastisfy *some* readers. ;-) To make things even more
funny, they also consider the average rank among the vacua with a small
cosmological constant, and their result is slightly higher - namely
exactly four for T^6/Z_2, as required for the Standard Model. This will
satisfy even more readers :-), but not all of them - and of course, the
authors realize (and explain) very well that these averages are not real
predictions - and in fact, their favorite answer of the total rank is not
four anyway, as we will see below.

I would say that they are very careful about possible non-scientific
interpretations, and very careful not to irritate the readers who don't
like the anthropic principle. Their description of "what the landscape
averages are good for" looks at least psychologically promising to me,
and it is more or less the opposite to what is usually said.

What do I mean? Many landscape supporters give up the vacuum selection
principle - they give up the quest for the specific model that would allow
us to make arbitrarily good predictions. Instead, they want to see that
some features of those vacua that admit life are rather generic, and they
agree with reality. One is then supposed to be rather satisfied because we
obtain a semi-quantitative statistical agreement between our theory and
experiment.

Kumar and Wells' approach and motivation is just the opposite one, and I
like it. They don't give up the task to find the right vacuum. In fact,
they still consider it to be the ultimate goal, and are open-minded about
the possible ways how can we eventually get the right one. Therefore, they
want to focus on *very non-generic* properties of the real vacuum that are
*not easily* reproduced in an otherwise realistic subclass of stringy
compactifications. This strategy is trying, of course, to find the right
vacuum most quickly, by getting the maximal possible information about the
right compactification in every step.

....

Well, let me return to the bulk of the paper. After they compute the
average group ranks, they look at the subset of the models that can
realistically suppress the proton decay. They use some rough arguments and
common wisdom about what is necessary to suppress the proton decay in
MSSM-like theories, and argue that the realistic candidates need higher
rank.

I have not quite understood the statistical treatment of this point - do
they want to eliminate the vacua with rapid proton decay by hand, or
derive that they're unlikely? At any rate, it seems to me that they at
least believe that they have a *statistical* argument that the
stringy-natural mechanisms to suppress the proton decay start with a
bigger gauge group - in other words, the discrete symmetries (such as Z_2
R-parity) may not be the solution recommended by string theory.

All the 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)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Michael R. Douglas

Sep30-04, 04:26 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>It\'s a nice paper as it makes a definite claim: the distribution of\nthe rank N of the gauge group in string compactifications goes as\nexp -N/N_{avg} for some relatively small N_{avg}.\n\nWhile I think the argument Kumar and Wells give is sensible and\ninteresting, it depends on unjustified assumptions, which makes the\nclaim rather preliminary (as admittedly are all claims in this area at\nthis point). Of course one of these is the idea that the number of D3\nbranes dominates the rank of the gauge group or is distributed the\nsame way, as there are many other types of D-branes with different\nmatter content etc.\n\nHowever the main point left out is that theories with gauge sectors\ntend to have a larger multiplicity of vacua, because their matter must\nbe stabilized and this will lead to many vacua. In the case of D3\'s\nthis at least includes their position moduli on the CY, which by\narguments given in my 0303194, for N D3\'s would be expected to have of\norder \\chi(Sym_N M), the Euler character of the N-fold symmetric\nproduct of the CY M. For most CY\'s this is a pretty large factor\nwhich dominates at low N and pushes the peak of the distribution up,\nthough the large N tail would still be exponential.\n\nI am somewhat suspicious of the large N behavior being exponential, on\nempirical grounds: there are known to be F theory compactifications to\nfour dimensions with N=1 supersymmetry with gauge group ranks of\norder 100000 (Candelas et al), which is pretty unlikely to come out of\nthe distribution exp -N/N_{avg} with small N_{avg}. I suspect the\nnumber of vacua is more likely to fall off as a power of N, but do not\nyet have a good argument for this.\n\nFinally, I would like to say that the idea of a "landscape average" is\nNOT mine and does not describe my work. First, as a minor point, I\ndon\'t usually use the term "landscape" -- but this is just my own\ntaste, landscape is a good term which just emphasizes other aspects of\nthe problem, such as the structure of the potential and barriers\nbetween vacua, than the ones I have been working on.\n\nMore importantly, as explained in 0303194, my recent 0409207, etc., I\nthink it is meaningless to average over different vacua, because we\nonly observe one vacuum. Rather, the goal of my own work, and what I\nadvocate doing, is to characterize the distribution of vacua well\nenough to estimate the number N_SM of different vacua which satisfy\nthe many existing observational constraints (standard model,\ncosmological, etc.) as well as possible future constraints (this might\nlead to "predictions" as discussed in 0409207). Based on this\ninformation, we can decide whether we should continue the search for\nthe right vacuum directly (appropriate if N_SM <= a few), look for\nadditional principles to cut down the number (if N_SM is large), or\ngive up and start making anthropic arguments or whatever (if N_SM is\nridiculously large). These works describe many other ways to use this\ninformation, for example to know which properties are common in\nstring/M theory (so less interesting) or rare (so more interesting and\nmore selective).\n\nSo for me, a quantity like the average rank of the gauge group, while\nwell defined, is not directly physically meaningful, and not to be\nconsidered as a preferred value (just as the actual height of any\nsingle human is unlikely to be equal to the average height of a\nhuman). It is useful, but just as a way of characterizing the\ndistribution (as in the exp -N/N_{avg} above).\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>It's a nice paper as it makes a definite claim: the distribution of
the rank N of the gauge group in string compactifications goes as
\exp -N/N_{avg} for some relatively small N_{avg}.

While I think the argument Kumar and Wells give is sensible and
interesting, it depends on unjustified assumptions, which makes the
claim rather preliminary (as admittedly are all claims in this area at
this point). Of course one of these is the idea that the number of D3
branes dominates the rank of the gauge group or is distributed the
same way, as there are many other types of D-branes with different
matter content etc.

However the main point left out is that theories with gauge sectors
tend to have a larger multiplicity of vacua, because their matter must
be stabilized and this will lead to many vacua. In the case of D3's
this at least includes their position moduli on the CY, which by
arguments given in my 0303194, for N D3's would be expected to have of
order \chi(Sym_N M), the Euler character of the N-fold symmetric
product of the CY M. For most CY's this is a pretty large factor
which dominates at low N and pushes the peak of the distribution up,
though the large N tail would still be exponential.

I am somewhat suspicious of the large N behavior being exponential, on
empirical grounds: there are known to be F theory compactifications to
four dimensions with N=1 supersymmetry with gauge group ranks of
order 100000 (Candelas et al), which is pretty unlikely to come out of
the distribution \exp -N/N_{avg} with small N_{avg}. I suspect the
number of vacua is more likely to fall off as a power of N, but do not
yet have a good argument for this.

Finally, I would like to say that the idea of a "landscape average" is
NOT mine and does not describe my work. First, as a minor point, I
don't usually use the term "landscape" -- but this is just my own
taste, landscape is a good term which just emphasizes other aspects of
the problem, such as the structure of the potential and barriers
between vacua, than the ones I have been working on.

More importantly, as explained in 0303194, my recent 0409207, etc., I
think it is meaningless to average over different vacua, because we
only observe one vacuum. Rather, the goal of my own work, and what I
advocate doing, is to characterize the distribution of vacua well
enough to estimate the number N_{SM} of different vacua which satisfy
the many existing observational constraints (standard model,
cosmological, etc.) as well as possible future constraints (this might
lead to "predictions" as discussed in 0409207). Based on this
information, we can decide whether we should continue the search for
the right vacuum directly (appropriate if N_{SM} <= a few), look for
additional principles to cut down the number (if N_{SM} is large), or
give up and start making anthropic arguments or whatever (if N_{SM} is
ridiculously large). These works describe many other ways to use this
information, for example to know which properties are common in
string/M theory (so less interesting) or rare (so more interesting and
more selective).

So for me, a quantity like the average rank of the gauge group, while
well defined, is not directly physically meaningful, and not to be
considered as a preferred value (just as the actual height of any
single human is unlikely to be equal to the average height of a
human). It is useful, but just as a way of characterizing the
distribution (as in the \exp -N/N_{avg} above).