## String theory |

In **string theory** is a

String theory is a broad and varied subject that attempts to address a number of deep questions of

String theory was first studied in the late 1960s as a theory of the

One of the challenges of string theory is that the full theory does not have a satisfactory definition in all circumstances. Another issue is that the theory is thought to describe an enormous

- fundamentals
- m-theory
- black holes
- ads/cft correspondence
- phenomenology
- connections to mathematics
- history
- criticism
- notes and references
- further reading
- external links

In the twentieth century, two theoretical frameworks emerged for formulating the laws of physics. The first is ^{[1]}

In spite of these successes, there are still many problems that remain to be solved. One of the deepest problems in modern physics is the problem of ^{[1]} The general theory of relativity is formulated within the framework of ^{[2]} In addition to the problem of developing a consistent theory of quantum gravity, there are many other fundamental problems in the physics of ^{[a]}

String theory is a ^{[3]}

One of the main developments of the past several decades in string theory was the discovery of certain "dualities", mathematical transformations that identify one physical theory with another. Physicists studying string theory have discovered a number of these dualities between different versions of string theory, and this has led to the conjecture that all consistent versions of string theory are subsumed in a single framework known as ^{[4]}

Studies of string theory have also yielded a number of results on the nature of black holes and the gravitational interaction. There are certain paradoxes that arise when one attempts to understand the quantum aspects of black holes, and work on string theory has attempted to clarify these issues. In late 1997 this line of work culminated in the discovery of the ^{[5]} This is a theoretical result which relates string theory to other physical theories which are better understood theoretically. The AdS/CFT correspondence has implications for the study of black holes and quantum gravity, and it has been applied to other subjects, including ^{[6]} and ^{[7]}^{[8]}

Since string theory incorporates all of the fundamental interactions, including gravity, many physicists hope that it will eventually^{[note 1]} fully describe our universe, making it a ^{[9]}

One of the challenges of string theory is that the full theory does not have a satisfactory definition in all circumstances. The scattering of strings is most straightforwardly defined using the techniques of ^{[10]} It is also not clear whether there is any principle by which string theory selects its ^{[11]} These problems have led some in the community to criticize these approaches to the unification of physics and question the value of continued research on these problems.^{[12]}

The application of quantum mechanics to physical objects such as the ^{[13]}

In quantum field theory, one typically computes the probabilities of various physical events using the techniques of ^{[13]}

The starting point for string theory is the idea that the point-like particles of quantum field theory can also be modeled as one-dimensional objects called strings.^{[14]} The interaction of strings is most straightforwardly defined by generalizing the perturbation theory used in ordinary quantum field theory. At the level of Feynman diagrams, this means replacing the one-dimensional diagram representing the path of a point particle by a two-dimensional surface representing the motion of a string.^{[15]} Unlike in quantum field theory, string theory does not have a full non-perturbative definition, so many of the theoretical questions that physicists would like to answer remain out of reach.^{[16]}

In theories of particle physics based on string theory, the characteristic length scale of strings is assumed to be on the order of the ^{−35} meters, the scale at which the effects of quantum gravity are believed to become significant.^{[15]} On much larger length scales, such as the scales visible in physics laboratories, such objects would be indistinguishable from zero-dimensional point particles, and the vibrational state of the string would determine the type of particle. One of the vibrational states of a string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force.^{[3]}

The original version of string theory was ^{[17]}

There are several versions of superstring theory: *SO*(32)*E*_{8}×*E*_{8}^{[18]}

In everyday life, there are three familiar dimensions of space: height, width and length. Einstein's general theory of relativity treats time as a dimension on par with the three spatial dimensions; in general relativity, space and time are not modeled as separate entities but are instead unified to a four-dimensional ^{[19]}

In spite of the fact that the universe is well described by four-dimensional spacetime, there are several reasons why physicists consider theories in other dimensions. In some cases, by modeling spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily.^{[b]} There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics.^{[20]} Finally, there exist scenarios in which there could actually be more than four dimensions of spacetime which have nonetheless managed to escape detection.^{[21]}

One notable feature of string theories is that these theories require ^{[22]}

^{[23]} In the limit where these curled up dimensions become very small, one obtains a theory in which spacetime has effectively a lower number of dimensions. A standard analogy for this is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling on the surface of the hose would move in two dimensions.^{[24]}

Compactification can be used to construct models in which spacetime is effectively four-dimensional. However, not every way of compactifying the extra dimensions produces a model with the right properties to describe nature. In a viable model of particle physics, the compact extra dimensions must be shaped like a ^{[23]} A Calabi–Yau manifold is a special ^{[25]}

Another approach to reducing the number of dimensions is the so-called ^{[26]}

One notable fact about string theory is that the different versions of the theory all turn out to be related in highly nontrivial ways. One of the relationships that can exist between different string theories is called *SO*(32) heterotic string theory. Similarly, type IIB string theory is related to itself in a nontrivial way by S-duality.^{[27]}

Another relationship between different string theories is *R* is equivalent to a string propagating around a circle of radius 1/*R* in the sense that all observable quantities in one description are identified with quantities in the dual description. For example, a string has *p* and winding number *n* in one description, it will have momentum *n* and winding number *p* in the dual description. For example, type IIA string theory is equivalent to type IIB string theory via T-duality, and the two versions of heterotic string theory are also related by T-duality.^{[27]}

In general, the term *duality* refers to a situation where two seemingly different *dual* to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.^{[28]}

In string theory and other related theories, a *p*, these are called *p*-branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane.^{[29]}

Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. A *p*-brane sweeps out a (*p*+1)-dimensional volume in spacetime called its *worldvolume*. Physicists often study ^{[29]}

In string theory, ^{[30]}

Branes are frequently studied from a purely mathematical point of view, and they are described as objects of certain ^{[31]} The connection between the physical notion of a brane and the mathematical notion of a category has led to important mathematical insights in the fields of ^{[32]} and ^{[33]}

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