String theory

Open and closed strings

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World lines and world sheet

Compactification example

Calabi yau

Dualities in String Theory

D3-brane et D2-brane

String theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects known as strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string appears as an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force. Thus, string theory is a theory of quantum gravity.

String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. It has been a leading candidate for a unified theory of all the fundamental forces of nature, including gravity, electromagnetism, strong nuclear force, and weak nuclear force. It is also a richly mathematical theory, with connections to various areas of mathematics, such as algebraic geometry, topology, and differential geometry.

History

The origins of string theory are in the late 1960s and early 1970s, when it was proposed as a theory of the strong nuclear force, before being abandoned in favor of quantum chromodynamics. The theory was revived in the mid-1980s with the discovery of the so-called "first superstring revolution", which showed that string theory could be a viable candidate for a unified theory of all fundamental interactions.

Fundamental Concepts

Strings and Branes

In string theory, the basic objects are not point particles but rather strings, which can be open (having two endpoints) or closed (forming a loop). These strings can vibrate at different frequencies, and the vibrational modes correspond to different particles. Higher-dimensional objects called branes also play a crucial role in many versions of the theory.

Extra Dimensions

String theory requires the existence of extra spatial dimensions beyond the three that are observed. In most versions of the theory, there are a total of 10 or 11 dimensions. The extra dimensions are compactified on very small scales, which is why they are not observed in everyday life or in experiments at current particle accelerators.

Supersymmetry

Most formulations of string theory incorporate a principle called supersymmetry, a theoretical symmetry between bosons and fermions. Supersymmetry has not yet been observed experimentally, but it solves several theoretical problems and is a crucial feature of string theory.

Versions of String Theory

There are five major consistent versions of string theory:

• Type I string theory
• Type IIA string theory
• Type IIB string theory
• Heterotic SO(32) string theory
• Heterotic E8xE8 string theory

These theories are related by various dualities, which suggest that they may be different limits of a single underlying theory, often referred to as M-theory.

Implications and Applications

String theory has led to many insights in theoretical physics and mathematics, but it has not yet been confirmed by experimental evidence. It offers potential explanations for the nature of black holes and the structure of the universe, and it has inspired numerous developments in pure mathematics.

Challenges and Criticisms

Despite its mathematical elegance and its potential to unify the forces of nature, string theory faces significant challenges. It requires extra dimensions and predicts new particles (such as the graviton) that have not yet been observed. Additionally, the theory has a vast number of possible vacuum states, known as the "landscape", making it difficult to make specific predictions.

Conclusion

String theory remains one of the most fascinating and complex areas of modern theoretical physics. Its development has led to a deeper understanding of quantum gravity and has provided a rich interplay between physics and mathematics. However, its ultimate validity as a theory of everything remains to be seen, pending experimental verification and further theoretical advancements.