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LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Sun May 08, 2005 11:21 am    Post subject: String theory - physics or formalism?

In string field theory, the string vertices satisfy a BV algebra, while
the string action satisfies the BV master equation. Indeed string field
theory was the first theory to make full use of the power of the BV
formalism.

On the other hand, as soon as we move to non-conformal backgrounds, the
interpretation of Feynman diagrams in terms of Riemann surfaces
disappears and all we are left with is the BV algebra, which is a
feature of all gauge theories.

Bearing in mind the background independence of string field theory.
where does the distinction between string theory and the rest of
physics then lie? Is it not then possible to describe any
BV-quantisable gauge theory as a string theory, and does this not mean
that string theory is nothing but formalism, and cannot hope to
describe new physics?

- Sabbir Rahman
Mike Amling
science forum Guru

Joined: 05 May 2005
Posts: 525

Posted: Sun May 08, 2005 1:30 pm    Post subject: Re: String theory - physics or formalism?

"LEJ Brouwer" <intuitionist1@yahoo.com> wrote in message
 Quote: In string field theory, the string vertices satisfy a BV algebra, while the string action satisfies the BV master equation. Indeed string field theory was the first theory to make full use of the power of the BV formalism. On the other hand, as soon as we move to non-conformal backgrounds, the interpretation of Feynman diagrams in terms of Riemann surfaces disappears and all we are left with is the BV algebra, which is a feature of all gauge theories. Bearing in mind the background independence of string field theory. where does the distinction between string theory and the rest of physics then lie? Is it not then possible to describe any BV-quantisable gauge theory as a string theory, and does this not mean that string theory is nothing but formalism, and cannot hope to describe new physics?

All any scientific theory has to do to be able to lead to "new science" is
to make testable predictions that some other theory doesn't make. Unless all
"BV-quantisable gauge" theories make exactly the same set of predictions,
why would you assume that there can be no "new physics" due to what you say
above?
Urs Schreiber
science forum Guru Wannabe

Joined: 04 May 2005
Posts: 127

Posted: Sun May 08, 2005 4:21 pm    Post subject: Re: String theory - physics or formalism?

On Sun, 8 May 2005, it was written:

 Quote: An aside question: What's the BV formalism?

The Batalin-Vilkovisky (BV) formalism is a general formalism for
quantizing theories with gauge invariances. It is described for instance
in the textbook

M. Henneaux & C. Teitelboim
Quantization of gauge systems
Princeton (1992)

or in the lectures

M. Henneaux
Lectures on the antifield-BRST formalism for gauge theories
proceedings of the XX GIFT meeting

and goes back to

I. Batalin & G. Vilkovisky
Quantization of gauge theories with linearly dependent generators
Phys. Rev. D 28 (1983) 2567

By suitably doubling the field content of a gauge theory it is possible to
encode its dynamics and gauge invariances in conceptually very simple equations
called the "BV master equation" and the "BV master transformation". The
BRST formalism is reobtained as a special case.

In string field theory this BV formalsim has proved to be very useful. In
fact, as Barton Zwiebach writes:

"The closed string field theory is apparently the first field theory for
which the most sophisticated machinery for quantization, the
Batalin-Vikovisky (BV) field-antifield formalism, is necessary and useful
in its full form."

This quote is taken from p. 2 of

B. Zwiebach
Closed string field theory: quantum action and the B-V master equation
hep-th/9206084

In section 3.3 (pp. 26) of that text you can find the basics of the BV
formalism briefly reviewed and applied to closed string field theory.

In section 4.3 (pp. 37) the master action of closed SFT is given first for
the classical (genus = 0) case (p. 37) and then for the full quantum
action (p. 42).

The master transformation for closed SFT is on the bottom of p 45 and the
relation to the BRST formalism on p. 46

The BV formalism has been used to study the background-independence of
string field theory, for instance in

E. Witten
On Background independent open-string field theory
hep-th/9208027

Concerning the original question in this thread, whether the formulation
of SFT in terms of the BV formalism makes SFT obsolete, the answer is: No.

The BV formalism is a book-keeping tool for dealing with gauge theories.
The formalism alone does not encode the dynamics of a given gauge theory.
That dynamics is instead encoded in the "master action". Different
"master actions" give rise to different "theories". The action of string
field theory reduces in certain limits to that of ordinary gauge (and
gravity) theories, but it is much richer.
Aaron Bergman

Joined: 24 Mar 2005
Posts: 94

Posted: Sun May 08, 2005 4:21 pm    Post subject: Re: String theory - physics or formalism?

 Quote: An aside question: Whats the BV formalism?

Batalin-Vilkovisky. See Weinbeg vol II.

Aaron
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Mon May 09, 2005 6:07 am    Post subject: Re: String theory - physics or formalism?

Hi Urs,

(I haven't figured out how to get Google to insert quotes, but
anyway...). You mention that,

 Quote: The action of string field theory reduces in certain limits to that of ordinary gauge (and gravity) theories, but it is much richer.

but that is not my understanding. All gauge theories are BV-quantisable
theories, and (unless I am hugely mistaken) all string theories are, in
principle, BV-quantisable. So I am not sure how they can be 'much
richer' than BV-quantisable theories. In any case, my point is that the
'richer' string theory gets, the better it is as a formalism for
describing new theories, and the worse it is in terms of predicting
anything meaningful about our universe. The problem with the
overflowing abundance of possible string vacua is an indication of
this.

I did not mean to suggest in any way that SFT was obsolete - in fact
quite the contrary - if you are going to do string theory then that is
(IMO, anyway) the best way to do it. My point was more to do with our
overzealous expectations of string theory as a possible unified theory
of everything. In particular, what SFT in the BV formalism appears to
teach us (about string theory as a whole, not just SFT) is that string
theory is not really a theory, but rather a mathematical formalism.
(Sorry if I am repeating myself here - it is not intentional).

Best wishes,

Sabbir.
Urs Schreiber
science forum Guru Wannabe

Joined: 04 May 2005
Posts: 127

Posted: Mon May 09, 2005 6:23 am    Post subject: Re: String theory - physics or formalism?

On Mon, 9 May 2005, LEJ Brouwer wrote:

 Quote: The action of string field theory reduces in certain limits to that of ordinary gauge (and gravity) theories, but it is much richer. but that is not my understanding. All gauge theories are BV-quantisable theories, and (unless I am hugely mistaken) all string theories are, in principle, BV-quantisable. So I am not sure how they can be 'much richer' than BV-quantisable theories.

Because they have a richer (master) action.

I might be missing your point, but it seems to me that what you are
arguing for is similar to saying that all theories which can be treated by
Lagrangian formalism are equivalent, just because the formalism is the
same for all of them. But they are not. While the abstract form of the
Euler-Lagrange equations is the same (delta L = 0), the Lagrange
functional (L) itself differs from theory to theory and hence the concrete
form of the Euler-Lagrange equations differs.

Saying that a theory can be written in BV form doesn't tell you anything
about the particulars of the theory (almost nothing, at least).

Personally, what I feel is much deeper than the fact that SFT can be
written in BV form is the (of course not totally unrelated) fact that
closed SFT action is a sum over all brackets of an L_oo algebra. These
brackets specify an omega-category with a semistrict Lie bracket
omega-functor (i.e. a semistrict Lie omega-algebra). I would love to
understand what this *means* for the nature of the SFT action.
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

 Posted: Tue May 10, 2005 6:20 am    Post subject: Re: String theory - physics or formalism? Hi Urs, You are right, I just got a little confused! Local background independence of SFT means that infinitesimal background definitions correspond merely to field redefinitions in the BV formalism which happen to lead to the same physical observables. However there exist finite background deformations (string dualities), which although still the same theory, have fields expanded about different vacua, of which they are many. The problem is that there are so many possible vacua it appears that you can describe almost any theory you want with them in some limit. This of course does not mean that the space of string vacua is the same as the space of gauge theories (sorry for the red herring), but it does mean that it is hard to imagine string theory making positive predictions about observable physics, and in that sense is more of a mathematical formalism than physics. Admittedly I started losing interest in string theory as a possible unified theory (of course it is, but which one to choose, and why?), but remained interested in the mathematical structure of theory space, which I felt could be generalised to the space of gauge theories. Best wishes, Sabbir.
Urs Schreiber
science forum Guru Wannabe

Joined: 04 May 2005
Posts: 127

Posted: Wed May 11, 2005 5:04 pm    Post subject: Re: String theory - physics or formalism?

Let me make some provocative remarks:

On Tue, 10 May 2005, LEJ Brouwer wrote:

 Quote: You are right, I just got a little confused! Local background independence of SFT means that infinitesimal background definitions correspond merely to field redefinitions in the BV formalism which happen to lead to the same physical observables.

I don't want to be obnoxious but I would like to point out again that in
my opinion the question whether or not and which gauge theories appear as
certain limits of string theory has nothing to do with whether or not
string field theory is or can be treated using BV formalism.

 Quote: they are many. The problem is that there are so many possible vacua it appears that you can describe almost any theory you want with them in some limit.

Are you also worried about the fact that there are so many effective field
theories that you can describe almost any low energy theory you want using
field theory?

 Quote: but it does mean that it is hard to imagine string theory making positive predictions about observable physics,

Does the fact that you cannot derive the content of the standard model
from field theory mean that it is hard to imagine field theory making
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Urs Schreiber
science forum Guru Wannabe

Joined: 04 May 2005
Posts: 127

Posted: Thu May 12, 2005 6:50 am    Post subject: Re: String theory - physics or formalism?

"LEJ Brouwer" <intuitionist1@yahoo.com> schrieb im Newsbeitrag

 Quote: string theory really strikes me as overkill - it is just far too complex,

I believe this is precisely the reason why many people find string theory
attractive: You start with a very simple principle, 2D SCFTs with c=0, and
you _find_ that this opens the door to a universe of structures that haven't
been put in by hand. It's the large ration of output over input that is
usually the sign that something interesting is going on.

 Quote: The right answer should be nice and neat,

The principle behing the answer should, but the answer itself may be messy.
Newton's mechanics is nice and neat. But finding in it the "vacuum" (i.e.
the solution) that reproduces the origin of the solar system is much messier
than the once expected simple answer that the earth is at the center of the
universe with everything rotating around it on heavenly shells.

 Quote: On a more fundamental note, I never could bring myself to believe in quantum mechanics (and hence QFT and hence even SFT). [...] I understand that you were once interested in Nelson's stochastic formulation of quantum mechanics. I believe that that is where you will find some of the answers really lie.

I am still latently interested in this general question, but it does not
seem that much progress can be expected by explicitly thinking about it. It
seems more likely that one day, after other things have been better
understood, like holography maybe, the answer to the question will appear by
itself or else the question will diappear by itself.

though:

http://golem.ph.utexas.edu/string/archives/000400.html .
LEJ Brouwer
science forum Guru Wannabe

Joined: 07 May 2005
Posts: 120

Posted: Thu May 12, 2005 11:45 am    Post subject: Re: String theory - physics or formalism?

Hi Urs,

 Quote: I believe this is precisely the reason why many people find string theory attractive: You start with a very simple principle, 2D SCFTs with c=0, and you _find_ that this opens the door to a universe of structures that haven't been put in by hand. It's the large ration of output over input that is usually the sign that something interesting is going on.

But the same thing can also be said about the Mandelbrot set - which
brings me back to my original question. While we give lip service to the
fact that string theory is a potential theory of everything, the real
day-to-day reason that we are attracted to, and do research in, string
theory is because of its inherent mathematical beauty.

Maybe it will, one day, lead to a theory of everything, but right now,
do most string theorists really care? Is it really more a branch of pure
mathematics than physics?
After all, the number of string theorists genuinely concerned with
phenomenology is relatively small, and my impression is that they are even
looked down upon as they are considered to be engaging in a foregone
exercise - of course we can derive the standard model - we can even do it
in an infinite number of ways, with an infinite number of different
predictions for our universe!

 Quote: The principle behing the answer should, but the answer itself may be messy. Newton's mechanics is nice and neat. But finding in it the "vacuum" (i.e. the solution) that reproduces the origin of the solar system is much messier than the once expected simple answer that the earth is at the center of the universe with everything rotating around it on heavenly shells.

starting with a huge amount of dust left to self-gravitate, that stellar,
galactic and planetary structures are reproduced (and my understanding is
that Newtonian gravity is indeed used with significant success in that
field), then Newtonian mechanics is nice and neat, and extremely powerful.
The same thing cannot be said about string theory.
Yes it based on simple principles, but the nature of its consequences are
really quite different. There is even an enormous range of possibilities
as initial conditions for string cosmology, which again has to be tuned in
an arbitrary fashion by hand. String theory simply does not
seem to predict anything in a unique way about the universe, and
everything has to be chosen by hand to fit observations.

 Quote: I am still latently interested in this general question, but it does not seem that much progress can be expected by explicitly thinking about it. It seems more likely that one day, after other things have been better understood, like holography maybe, the answer to the question will appear by itself or else the question will diappear by itself. People like t'Hooft and Adler are actively thinking about this stuff, though:

I have been dabbling in it myself (and the reason I raised the matter
is because you may want to take a look at my recent paper and the thread
"Quantum theory from gravity?" on s.p.r., assuming you have not already
done so). If nothing else, I think it does make the point that with such a
huge concentration of theoretical physicists concentrating their efforts
on string theory, alternative, simpler, and perhaps even more promising,
ideas get left by the wayside.

Best wishes,

Sabbir.

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