Where are we in extra dimensions?

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First, I must say that this very question is obsolete if it is phrased in this way.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.

Higher-dimensional vacua

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
  • M-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?

Black holes and pulsars could reveal extra dimensions

We discuss the observable effects of enhanced black hole mass loss in a black hole-neutron star (BH-NS) binary, due to the presence of a warped extra spatial dimension of curvature radius L in the braneworld scenario. For some masses and orbital parameters in the expected ranges the binary components would outspiral—the opposite of the behavior due to energy loss from gravitational radiation alone. If the NS is a pulsar, observations of the rate of change of the orbital period with a precision obtained for the binary pulsar B1913+16 could easily detect the effect of mass loss. For M BH = 7 M sunM NS = 1.4 M sun, eccentricity e = 0.1, andL = 10 μm, the critical orbital period dividing systems that inspiral from systems that outspiral is P ≈ 6.5 hr, which is within the range of expected orbital periods; this value drops to P ≈ 4.2 hr for M BH = 5 M sun. Observations of a BH-pulsar system could set considerably better limits on L in these braneworld models than could be determined by torsion-balance gravity experiments in the foreseeable future….. arxiv.org

MAKING a black hole let go of anything is a tall order. But their grip may slowly weaken if the universe has extra dimensions, something that pulsars could help us to test.

String theory, which attempts to unify all the known forces, calls for extra spatial dimensions beyond the three we experience. Testing the theory has proved difficult, however.

Now John Simonetti of Virginia Tech in Blacksburg and colleagues say black holes orbited by neutron stars called pulsars could do just that – if cosmic surveys can locate such pairings. “The universe contains ‘experimental’ setups we cannot produce on Earth,” he says.

Black holes are predicted to fritter away their mass over time by emitting particles, a phenomenon called Hawking radiation. Without extra dimensions, this process is predicted to be agonisingly slow for run-of-the-mill black holes weighing a few times as much as the sun, making it impossible to measure.

Extra dimensions would give the particles more ways to escape, speeding up the process. This rapid weight loss would loosen a black hole’s gravitational grip on any orbiting objects, causing them to spiral outwards by a few metres per year, the team calculates (The Astrophysical Journal, DOI: 10.1088/2041-8205/737/2/l28 and arxiv.org).
A pulsar orbiting a black hole could reveal this distancing. That’s because the lighthouse-like pulses of radiation they emit would vary slightly depending on the size of the star’s orbit.
http://www.newscientist.com
Read also: This Week’s Hype, Part II