String TheoryBasic Properties

Nambu-Goto

The Nambu-Goto action is used for 1 x 1 dimensional flat targets

The Nambu-Goto action is not the primary action that physicists use when they develop quantized versions of string theory.

The Polyakov action is more easily quantized than the Nambu-Goto action because it is linear and it is therefore used more often.

There are two actions used to describe how the strings move through space and time. They predict where the strings are located on the world sheet which describes the embedding of the string in spacetime.

Polyakov

Characteristics of the stringsThe strings oscillate because of tension and

kinetic energyThe quantum mechanics of strings states that

these oscillations take on vibrational modes.These modes behave differently from

particles. The String’s mass, spin, and charge is

determined by the string’s dynamics.

Characteristics of the stringsIn a guitar string, the different notes that sound when

the string is plucked are a result of the properties of the string: tension, length, thickness.

The notes coming out of the guitar are excitation modes of the string.

The particles that are observed in particle accelerators can be thought of as musical notes, or excitations modes of strings.

Different excitation modes make the strings appear as electrons, photons, and so on.

Strings have a miniscule length that is known as the Planck length. The Planck length is about 10-33

centimeters

Levels of magnification:1. Macroscopic level - Matter2. Molecular level3. Atomic level - Protons, neutrons, and electrons4. Subatomic level - Electron5. Subatomic level - Quarks6. String level

Worldsheets…Graphs are used to describe the position of

point-like particle’s motion. These graphs depict the worldline of the

particleThe worldline represents the particles history

in spacetime: where it has been positioned.Worldsheets can be used to reflect when

strings split or connect.This picture represents

worldsheets of closed strings spitting or connecting.

How many string theories are there?Theorist can build string theories by setting different

characteristics.Start with a tiny stringIt is either an open string or a closed stringIt can have only bosons (particles that transmit forces)

or it can also have fermions (particles that make up matter)

If there are only bosons, the theorist will have a bosonic string theory

If there are also fermions, then they will need supersymmetry (equal number of bosons and fermions: equal amount of forces and matter.

This supersymmetry leaves the theorist with a superstring theory.

A Brief Table of String TheoriesType

SpacetimeDimensions

Details

Bosonic 26Only bosons, no fermions means only forces, no matter, with both open and closed strings. Major flaw: a particle with imaginary mass, called the tachyon

I 10 Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO(32)

IIA 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions spin both ways (nonchiral)

IIB 10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions only spin one way (chiral)

HO 10Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry isSO(32)

HE 10Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E8x E8