Discussion:
Background independence
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seldon
2005-10-29 19:03:16 UTC
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But if you look at the effective target space action of string theory
you'll note that it is precisely of the same "background free" form as
the Einstein-Hilbert action (no wonder, because it is just
Einstein-Hilbert plus dilaton/axion and higher order terms) and that the
metric indeed is dynamical, just as in GR. That's pretty obvious.
Can anyone please explain to me what this refers to? What is the
'effective target space action'? And how does the background metric of
the target space suddenly become dynamical? Isn't it a fixed input for
string theory?

I have only very basic knowledge of string theory (zwiebach and bits of
GSW part 1). Many thnx already!

Seldon
Lubos Motl
2005-10-29 19:18:21 UTC
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Post by seldon
Can anyone please explain to me what this refers to? What is the
'effective target space action'?
In field theory, target space is the configuration space of the scalar
fields; the set of all possible values that the scalar fields at one point
can take. On the worldsheet, there are scalar fields (with respect to the
worldsheet) X^m(sigma,tau) that describe the embedding of the worldsheet
to spacetime.

Consequently, the target space of the two-dimensional field theory
describing the worldsheet means nothing else than the spacetime.

Physics of string theory at low energy may be described by field theory
coupled to gravity. The effective spacetime (=target space) action is the
action that includes terms for all fields that describe dynamics at low
energies, such as the Yang-Mills action, Einstein-Hilbert action, and
other terms.
Post by seldon
And how does the background metric of the target space suddenly become
dynamical?
It "becomes" dynamical (well, it is always dynamical in reality) once we
look at the spectrum of the closed string and find a massless spin 2
excitation of it. The coherent states of closed strings in this mode are
physically equivalent to deformations of the "background" metric. In other
words, physical closed strings in this excitation mode are identical to
excitations of the gravitational field. One can show that all their
interactions etc. agree. See chapters 3 of Green+Schwarz+Witten and/or
Polchinski, among other good introductory texts about string theory.

The existence of these new modes of the string - or, equivalently,
"marginal operators" - implies that the same theory also includes
backgrounds with different geometries. Only the geometries that satisfy
the low-energy equations of motion (such as Einstein's equations or
generalized Maxwell's equations) may be used as a starting point to expand
string theory around.
Post by seldon
Isn't it a fixed input for string theory?
The background metric - much like the background values of all other
fields - only determines a point around which we expand physics. One may
imagine it is "fixed" for a particular calculation, but it is definitely
not fixed physically. Saying that the background is fixed is the same
mistake like saying that the Taylor expansion for the exponential

exp(x) = 1 + x + x^2/2 + x^3/6 + ...

implies that x must be fixed and x=0.
Post by seldon
I have only very basic knowledge of string theory (zwiebach and bits of
GSW part 1). Many thnx already!
It may be a good idea to study at least the first three chapters of GSW
systematically.

Hope that it helped.

All the best
Lubos
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seldon
2005-10-31 22:50:57 UTC
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Many thanks for your quick reply, i'll certainly study GSW more
systematically soon! To get things clear, is it correct then that
string theory is in a sense a pertubative approach to a theory of
quantum gravity? And is M-theory supposed to be the nonperturbative
theory in this sense?

I have one other question, not entirely related to the above. But i'll
ask it here anyway. In Zwiebach i read about a possible way to
construct the standard model by using intersecting branes. Do you know
of any review article that describes (almost) all currently known ways
to construct the standard model from string theory? Or could you give
me a (short) list of the possible ways that are known? Constructing the
standard model seems to me to be *the* primary task, or am i wrong
here?

Many thanks again!
Seldon
Lubos Motl
2005-10-31 23:16:52 UTC
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Post by seldon
Many thanks for your quick reply, i'll certainly study GSW more
systematically soon! To get things clear, is it correct then that
string theory is in a sense a pertubative approach to a theory of
quantum gravity?
Dear Seldon,

in some sense, yes. In the modern sense, no. String theory as people knew
it in the 1960s and 1970s and the 1980s was about the perturbative
calculations as Taylor expansions in "g_{string}", the stringy coupling
constant. People were not able to calculate much more and it was not just
because of technical problems with evaluating well-defined expressions; a
more complete definition or even clues what's happening at larger
"g_{string}" were missing.

That's not really true anymore. A great deal of insights is known about
the behavior of string theory at strong coupling. We still use the word
"string theory" for the whole theory, including physics at strong
coupling. Honestly, at strong coupling, the term "string theory" is a
misnomer because at stronger coupling, strings are not more fundamental
than other objects found in the theory.
Post by seldon
And is M-theory supposed to be the nonperturbative theory in this sense?
On the other hand, M-theory is definitely non-perturbative. There is no
dimensionless parameter in M-theory in 11 dimensions that could be chosen
small. Low-energy derivative expansion based on 11D supergravity is the
only perturbative expansion that M-theory in 11 dimensions admit.

Note that the term ``M-theory'' is used in two different meanings which
were incorrectly thought to be equivalent: one of them is a description of
vacua of "string theory" (in the broad sense) that involve 11-dimensional
spacetime. This is M-theory in the narrow sense. The other meaning is the
most general framework that includes all insights from string theory in
all backgrounds and all values of couplings. It's M-theory in the broad
sense.

When physics of the 11D M-theory looked completely mysterious, people
believed that once they find how 11-dimensional physics works (at higher
energies), everything would be clear about all of string theory. Almost no
one believes this anymore. 11-dimensional spacetime is just another
background of "string theory" in the broad sense, much like the vacua
that admit perturbative expansions.
Post by seldon
I have one other question, not entirely related to the above. But i'll
ask it here anyway. In Zwiebach i read about a possible way to
construct the standard model by using intersecting branes. Do you know
of any review article that describes (almost) all currently known ways
to construct the standard model from string theory?
I am personally not aware of such a complete and up-to-date review. Let me
sketch the basic list of scenarios:

1. Conventional models

This includes the models that revolutionized particle physics in 1985.
They are based on heterotic string theory on a six-dimensional Calabi-Yau
three-fold with E8 x E8 gauge symmetry to start with. One of the E8 groups
is hidden and usually responsible for supersymmetry breaking via gaugino
condensation.

The other E8 group is ours, and it is typically broken to a Grand Unified
group such as E6 or SO(10) or SU(5) by a bundle or Wilson lines. This
predicts a high-energy GUT scale at 10^{16} GeV, neutrino masses around a
fraction of electronvolt (confirmed experimentally), and typically also
low-energy supersymmetry around a TeV visible at the LHC.

This class of models is arguably the most successful one in reproducing
the details of the particle physics spectrum and interactions. It is less
clear how the cosmological constant may remain small here.

(In some of these models, the Calabi-Yau manifold is an orbifold that can
also be fermionized to a fermionic CFT etc. These cute, non-geometric
models are much less popular today because it is not quite clear how they
fit to the duality network.)

2. Horava-Witten models

At stronger coupling, a new, 11-th dimension whose shape is a line
interval appears, in the previous setup of E8 x E8 heterotic string
theory. It was explained by Horava and Witten in 1995. People also use the
term Heterotic M-theory for a description of the previous picture that
includes an 11-dimensional spacetime with two domain walls at the end.

3. G2 holonomy manifolds

M-theory in 11 dimensions can also be compactified on 7-dimensional
manifolds of G2 holonomy to obtain N=1 supersymmetric physics in four
dimensions - a scenario most popular around 2000. To match the left-right
asymmetric spectrum of physics, the G2 manifold must be singular. The
Standard Model lives at this singularity and some explicit works have
been done about the details of phenomenology.

4. Type IIA brane vacua

These G2-holonomy singularities can also be interpreted as a dual
M-theoretical description of type IIA vacua with intersecting D6-branes
(usually combined with O6 orientifold planes) that you read about in
Barton's book. Some of them have also been shown to give a
Standard-Model-like physics.

5. F-theory on four-folds and flux vacua

Finally, there are also type IIB vacua. More generally, you may interpret
them as 12-dimensional "F-theory" on an eight-dimensional Calabi-Yau
"four-fold". People typically include many generalized magnetic fluxes
etc. with some consistency conditions. This class of vacua is, compared to
the rest of the list, the least developed one if you want to obtain the
details of the Standard Model physics, the right spectrum, and
interactions.

On the other hand, it is the most popular context in which the
Randall-Sundrum warped geometry ideas are embedded into string theory. It
is also popular because there are googols of vacua like that; it is really
this class that is still believed to form the majority of the "anthropic
landscape" that assumes a large "multiverse" in which we are the random
ones. The highly controversial idea of the anthropic principle is probably
the most widely accepted possible solution of the cosmological constant
problem. All these things occur in this class - although there have been
recent proposals how to generalize this class of vacua to non-geometric
ones.
Post by seldon
Constructing the standard model seems to me to be *the* primary task, or
am i wrong here?
String theorists have partially solved this task, with irresistable hints
that it must be correct, and a complete solution - the second draft, using
words of Prof. Witten - seems to be surprisingly difficult and it is
questionable whether a direct attack, before some insights about other
things are revealed, is a good strategy. But many of us would agree with
you; getting the Standard Model right is a key task.

Recently, new progress has been done in the group of Burt Ovrut et al. to
get these things straight from a particular vacuum in the category 1.

All the best
Lubos
______________________________________________________________________________
E-mail: ***@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/
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