I did this paper to finish off my 2002 physics class; I worked on it March to June :) It's on string theories, and I think took me a couple of weeks to finish (I procrastinate a lot...). Hope you like it ^_^




Introduction to String theories
By Dwyn

0.1 Note
There's quite a few string-theory advances that aren't covered in this paper, such as black hole entropy.

1.1 Origin of the theory
Gabrielle Veneziano, an Italian physicist, put forward the original string theory in 1968 in an effort to describe the force between hadrons and bosons, which include the proton and neutron. When Quantum Chromodynamics (which introduced the color parameter) proved a better theory for that goal, string theory was dropped. Later, in the mid-70's, John Schwarz and J๖el Scherk found the theory, and discovered that the strings, the base of the theory, described gravity in terms of quantum mechanics – something no theory had been able to do successfully before. One of the things the theory predicted was a particle with zero mass and a spin of two; parameters the same as for the long-theorized 'graviton' particle for quantum gravity.

2.1 The Basic Idea of String Theory
The underlying idea in all superstring theories is that particles are not quite like their classic representation of spheres; instead, they're (extremely) small strings. Depending on the theory, these particle-strings can be curled into loops – closed strings – or be lines that wiggle around, not unlike earthworms – open strings. And note that while open strings can join ends and become closed (and possibly break loose again), the strings in closed string theories cannot break apart.

The way strings work as a particle is comparable to a guitar's string. Depending on the tension in a guitar string, different notes will sound when the string is plucked. Different 'tensions' on string theory-strings result in different particles.

2.2 Theories
There are two primary types of string theory – bosonic string theory, and superstring theory. There are other points in constructing a string theory, including defining whether the theory uses open or closed strings and whether orientation is a factor (orientation asks if you can tell which direction you're going on a string – called left and right handedness).

Bosonic string theory is related to the original theory; it only describes the force-carrying particles (bosons, hence the name of the theory group). It requires 25 space and 1 time dimension to be mathematically consistent. How could there be 25 space dimensions when we only perceive three? I'll get to that later.
The biggest failing of the bosonic string theories is that they require the tachyon, a particle with a less-than-zero mass when at rest and a speed faster than light (it gets around the negative rest mass by not being able to slow to the speed of light or lower). Also, many people find the idea of 26 spacetime dimensions too weird to be real.

The four possible bosonic string theories are:

String Type:	Oriented?
Open and closed	Yes
Open and closed	No
Closed	Yes
Closed	No

All bosonic string theories have only bosons (force particles), and no fermions (mass particles). Individual theories have special effects and particles, including massless antisymmetric tensor, graviton, and dilaton.

Superstring theory includes both bosons and fermions, the particles that make up matter, and it requires supersymmetry, in which each matter particle has a force particle counterpart; for example, neutron and neutrino. These theories need only 10 dimensions to work (and in fact may not work with more than 11). No superstring theory uses the theoretical tachyon particle, and they all have the graviton particle.

The biggest failing (if it can be called that) of superstring theories is that they require the supersymmetry theory, which has yet to be proven.

Type	Open or Closed?	Orientation?	N	Details
I	Open + closed	No	1	Gauge symmetry is SO(32); charges are attached to the ends of the strings.
IIA	Closed	No	2	Gauge symmetry is U(1). A non-chiral theory, meaning every fermion particle has both left- and right-handed versions. Neutrinos are only left-handed in reality, so the theory fails in this part of reality.
IIB	Closed	Yes	2	No gauge symmetry, so forces other than gravity can't be added to the theory. Chiral.
Heterotic E8XE8	Closed	Yes	1	E8XE8 gauge symmetry. Heterotic theory; has a bosonic string theory when you look one way down a string and a superstring theory looking the opposite direction on the same string.
Heterotic SO(32)	Closed	Yes	1	SO(32) gauge symmetry. Heterotic theory.

น
N is the number of spacetime supersymmetry charges, which is derived from the massless particle spectrum, and requires very complex and scary math to explain, so I won't get into that here.

And as for the rightmost column...

2.3 Gauge Symmetries and Handedness
Gauge symmetries are abstract symmetries (as opposed to geometric symmetries, which are relatively easy to observe) that regulate assorted forces, including electrical voltage. It is a function added to a field equation to balance the equation and make it, well, equal, without actually changing the observable results. Gauge symmetries are very important in binding forces together in theories.

Handedness is the property of a molecule, crystal, or other object that distinguishes it from its mirror image. For example, a cat with a black patch on the left side of its face has handedness; its mirror image would have a black patch on the right side of its face, and it would be clear that they are not the same animal. An all white cat, however, would not have handedness; its mirror image would look the same as the original.

2.4 Extra Dimensions
26 spacetime dimensions is a lot. It would make for a very interesting perspective of the world, for sure, but most people agree that we only perceive four – three dimensions of space and one of time. But regardless of that, string theories require more than four dimensions in order to be mathematically consistent. How can we have 10 or 26 dimensions, and only have four noticeable? By having the extras curled up! If they were small enough, we of the macroscopic world would never notice them.
The extra dimensions are even beneficial – the degrees of freedom they offer could be very helpful in a Theory of Everything. Movement of the curled dimensions could make effects like electric charge of an electron arise!

The view of these curled dimensions is usually simplified as being wrapped up on six circles; for realistic results, they are treated as being wrapped up on mathematical elaborations known as Calabi-Yau Manifolds and Orbifolds.ฒ

3.1 The Second String Revolution
Within the past decade, tools were developed that allowed scientists to study the consistent superstring theories – all five of them – to a greater extent. Their studies revealed that all five theories were actually facets of each other, and of a larger theory!

This larger theory, often called M-theory (not to be confused with the 11-dimensional supergravity theory of the same name), uses all of the consistent ten-dimensional string theories as aspects of itself. By looking at different points in the theory or in the universe, it can look like any one of five (or more!) theories.
For an example of the aspects, take a dog and make five clones of her. Each clone will look different (because cloned animals need not look the same as the original), but it is still essentially the same animal. There are six theories, which are essentially the same but look different if you don't examine them closely.

That is one of the most interesting aspects of M-theory; even though its five component string theories are 10-dimensional, there's another theory that is 11-dimensional. How can one theory have eleven dimensions and five others ten, and have it all work? Aspects are again the answer; M-theory can be an 11-dimensional theory that looked like 10 dimensional at some points in its parameters.น Something else of note is if there is an 11-dimensional theory, the fundamental object could be a two-dimensional membrane, not a string. Similar to a drinking straw seen at a distance, the membranes would look like strings when the eleventh dimension is curled into a small "circle."ฒ

4.1 What do these theories make possible, or are good for?
Well... It is unknown if a successful theory would open up possibilities that are profitable (in an economic sense). A complete, or near-complete, knowledge of how the universe works and can work could open up new lines of innovation. Perhaps newly discovered subatomic particles or loopholes in the laws of physics could aid the design of nanobots, or of super-fast spaceships. No one knows.

But while technological and/or domestic advance is a worthy pursuit, one shouldn't study physics for that reason alone. To quote professor of physics Amanda Peet, "We don't study string theory because it's going to build us a better CD player. This is basic science, which stimulates applied research. I justify my existence by satisfying human curiosity about the universe."


น "The Official String Theory Website"
ฒ "M-Theory, the theory formerly known as Strings"

Bibliography
http://209.120.177.24/~worda1/report.htm
http://www.superstringtheory.fanspace.com/index.html
EDGE Magazine : Research and Discovery at the University of Toronto
Fundamental Forces
M-Theory, the theory formerly known as Strings
"The New Shorter Oxford English Dictionary"
         Edited by Lesley Brown; published by Clarendon Press
The Official String Theory Web Site
"Superstrings: A Theory of Everything?"
         By P.C.W. Davies and J. Brown, printed by Cambridge University Press




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