The String Theories

The strings are vibrating in a spacetime, and the spacetime is a result of weaving together the strings. But what are the concepts of space and time fail to have meaning until innumerable strings weave together to produce them. We would need a fully spaceless and timeless formulation of string theory, in which spacetime emerges from the collective behavior of strings. Background-independent theory.


1 Early History of String Theory

The history of the string theory is rater interesting. In 1968 G. Veneziano discover that Euler beta function matched data on strong nuclear forces. In 1970, Susskind et. al. show that the behavior may be due to tiny strings connecting the particles (their paper was rejected.) Quantum chromodynamics was flourishing, and string theory almost died. In 1974, John Schwarz and Joel Scherk identified the massless and spin-2 particle in quantum mechanical equation of string theory with graviton. Therefore, the string theory became the first quantum theory of the gravitational force. There were many anomalies, but in 1984, Green and Schwarz showed that all anomalies cancel out. This started the first String Theory. The strings are the most elementary ingredient in the universe.


1.1 A Unified Theory of Matter and Forces

At this time, fundamental particles are electron/muon/tau, electron neutrino/muon neutrino/Tau-neutrino, Up-quark/Charm quark/Top-quark, Down-quark/Strange-quark/Bottom-quark. This called the Standard Model. The Standard Model is able to explain essentially all data produced by the world�s atom smashers, but requires particles and their properties as inputs. In the standard model, a Higgs field takes on a non-zero value through all space, and the mass of a particle depends on how much drag force it experiences as it wades through the Higgs ocean.


In the string theory, there is only one fundamental ingredient � the string � and the different particles reflect the different vibrational patterns of a string. The messenger particles Gluon/Photon/W&Z/graviton also are vibrating strings. Therefore, the string theory was recognized as a unified theory for all matter and forces!


1.2 Why it works

It works because strings are not point particles. String theory limits how violent the jitters of the gravitational field become � and the limit is just big enough to avoid the catastrophic clash between quantum mechanics and general relativity.


1.3 Particles and the String

The string has zero mass � the lowest-energy. The mass of a particle is the energy of its vibrating string. The vibrational patterns arose in pairs whose spin value differs by half a unit. This becomes the supersymmetry string theory (1984).


1.4 Unification in Higher Dimensions (Ten-Dimensional Space-Time Universe)

In 1919, Theodor Kaluza proposed a four-dimensional space to unify Einstein�s general theory of relativity and Maxwell equation for electromagnetic field. In 1926, Oskar Klein suggested that the additional dimension might be hidden, as curled-up dimension. String Theory predicted the number of space dimensions as nine.

The size and shape of extra dimensions play a pivotal role in determining particle properties. The string theory version of the Higgs field/ocean is made of strings; the drag force (mass of the vibrational patterns) is due to interactions between strings, so cane be calculated.


5 M-Theory (The Second Superstring Revolution)

There are five distinct versions of string theory developed, with closed strings, open strings, etc. In 1995, Edward Witten a hidden unity that tied all five string theories together, showing that the five theories are actually just five ways of mathematically analyzing a single theory. The unifying master theory is the M-theory. Each string theory may provide simpler answers to certain set of questions. Witten�s work revealed that the universe has ten space dimensions, to unify all string theories.

In the M-theory, there are also objects with p-spatial dimensions called p-branes (as membranes). All p-branes are significantly heavier than strings. The endpoints of open strings are restricted to move within some p-dimensional region of space, occupied by a p-brane (by Polchinski). The analysis of these higher-dimensional objects (p-branes) may be through analysis of strings.


1.5.1 Our Universe as a Brane

A brane is where the strings are attached to as a background. If our universe is a three-brane (i.e., a three-dimensional brane), then our familiar four-dimensional spacetime is due to a real physical entity that is a three-brane. We are immersed in the three-brane � like a Higgs Ocean filled with dark energy and myriad quantum field fluctuations. The extra dimensions in the string theory may be small and hidden or they are just outside our three-brane universe that we have no way of detecting them.


1.5.2 String Theories are Isomorphic

Each string theory gives a correct description of the universe with a particular geometrical representation of the strings in the large dimensions, and the small dimensions are hidden with a special geometrical configuration. The five string theories are isomorphic � they can be transformed completely into each other. This is the ads/CFT Correspondence.

The dictionary that translates questions posed in one string theory into questions posed in another string theory also translates the geometry of the extra dimensions in the first theory into a different extra-dimensional geometry in the second theory.
Every observation you describe within one string theory has an alternative and equally viable description within the other string theory, even though the language of each theory and the interpretation it gives may differ.


1.5.3 M-theory and the adS/CFT correspondence

The adS/CFT correspondence is a type of duality, which states that two apparently distinct physical theories are actually equivalent. On one side of this duality is the physics of gravity in a spacetime known as anti-de Sitter space (adS).
Five-dimensional anti-de Sitter space has a boundary which is four-dimensional, and in a certain limit looks like flat spacetime with one time and three space directions. The adS/CFT correspondence states that the physics of gravity in five-dimensional anti-de Sitter space, is equivalent to a certain supersymmetric Yang-Mills theory which is defined on the boundary of adS. This Yang-Mills theory is thus a `hologram' of the physics which is happening in five dimensions.


3 Reference


1. Jacob D. Bekenstein, Information in the Holographic Universe -- Theoretical results about black holes suggest that the universe could be like a gigantic hologram, Scientific American, August 2003, p. 59.
2. Retrieved from http://en.wikipedia.org/wiki/Holographic_principle
3. Greene, Brian, �The Fabric of the Cosmos,� Random House, 2004


© Wayne L. Wang 2004