Basic 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. Polyakov

Characteristics of the strings The strings oscillate because of tension and kinetic energy The 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 strings In 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 centimeters

Levels of magnification: 1. Macroscopic level - Matter 2. Molecular level 3. Atomic level - Protons, neutrons, and electrons 4. Subatomic level - Electron 5. Subatomic level - Quarks 6. String level

Worldsheets… Graphs are used to describe the position of point-like particle’s motion. These graphs depict the worldline of the particle The 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 string It is either an open string or a closed string It 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 Theories Type Spacetime Dimensions Details Bosonic26 Only bosons, no fermions means only forces, no matter, with both open and closed strings. Major flaw: a particle with imaginary mass, called the tachyon I10 Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO(32) IIA10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions spin both ways (nonchiral) IIB10 Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions only spin one way (chiral) HO10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry isSO(32) HE10 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E 8 x E 8