*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

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