Basic scenarios of string theory
Gordon has assured me that (almost) no non-expert has understood advanced basics of string phenomenology, despite dozens if not hundreds of blog entries about these topics that have been written on this blog during the years.
So I would like to be a little bit (but not too much) more comprehensible and address this text to some of the readers who have never studied any string theory at a technical level but who have some idea about quantum field theory and the concept of extra dimensions. I will review the basic vacua of string/M-theory in 10-11 spacetime dimensions and their basic relationships.
It turns out that almost each of them may give rise to a particular, idiosyncratic class of realistic universes with 3+1 large dimensions that we may inhabit.
So what kinds of string theory are there?
First, I must say that this very question is obsolete if it is phrased in this way. In the 1980s, people would be talking about “different string theories” (and non-experts are doing so even today). But in the mid 1990s, string theorists have understood that all the “different string theories” are actually just environments in a single theory.
You should imagine that string/M-theory is a single theory with many “fields” and similar objects and if you tune these fields (think about scalar fields) to various values, you will obtain a universe with properties that are described by what used to be called “a particular string theory”. And string theory dictates how these points in the configuration space or “landscape” are connected, too. For example, the number and types of low-energy fields depend on the point in the configuration space, too.
Since the 1990s, we know that there is just one string theory and not many.
Fine. But we may still use the vocabulary of the 1980s for a little while. What string theories do we have if we don’t allow any compactification? There are six of them: all of them live in spacetime whose dimension is either 10 (string theory) or 11 (M-theory).
String theory was originally born in the late 1960s and within a few years, people understood that the right spacetime had 26 dimensions. But this was a different, older, not quite healthy string theory, the so-called “bosonic string theory”. This theory predicted that there were no fermions which is a bad starting point to describe our reality with lots of fermions. Even more seriously, bosonic string theory did include a (bosonic) tachyon, a particle that naively moves faster than light (but it’s surely not a neutrino) and that makes the spacetime of bosonic theory unstable (much like the “h=0” point of the Higgs field is unstable).
So I will not treat bosonic string theory as a part of the genuine, fully consistent string theory (although there are interesting papers that describe hypothetical dynamical processes that may change a 26-dimensional spacetime to a 10-dimensional one or vice versa). We will only focus on the string theories in 10-11 dimensions and assume that the 26-dimensional “theory” is just a toy model, not a fully consistent one, to learn the actual theory that matters and works, namely superstring/M-theory.
The six theories in the maximum dimension
The list of uncompactified string theories is short: it only contains 6 entries:
- type I string theory with spin(32)/Z_2 gauge group
- type IIA string theory
- type IIB string theory
- heterotic E_8 x E_8 string theory
- heterotic spin(32)/Z_2 string theory
The first five entries should be called “string theory” because vibrating 1-dimensional strings are the most important objects they contain. All of the string theories contain closed strings (e.g. the graviton is always a closed string); type I string theory is the only one on the list whose strings are unorientable and that also contains open strings. The last entry in my list is eleven-dimensional M-theory and contains no strings; instead, it has other extended objects, namely M2-branes and M5-branes. The numerals in the brane nomenclature count the number of spatial dimensions; so strings in string theories are also known as F1-branes (“F” stands for “fundamental”); they may also be obtained as M-theory’s M2-branes with one dimension wrapped around the compact dimension of the M-theory spacetime…… Continue reading Where are we in extra dimensions?