How many dimensions are there in string theory
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Dimensions in String Theory: An Overview
Introduction to String Theory Dimensions
String theory, a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects known as strings, fundamentally alters our understanding of the universe's dimensions. Unlike traditional physics, which operates within the familiar three spatial dimensions and one time dimension, string theory posits the existence of additional dimensions.
Ten-Dimensional String Theory
The most commonly discussed version of string theory operates in ten dimensions. This includes the four familiar dimensions plus six additional spatial dimensions that are compactified, meaning they are curled up in such a way that they are not observable at macroscopic scales. This ten-dimensional framework is essential for the consistency of the theory, particularly in the context of anomaly cancellation and supersymmetry2 7.
Eleven-Dimensional M-Theory
An extension of string theory known as M-theory suggests that the universe may actually have eleven dimensions. M-theory unifies the five different string theories and eleven-dimensional supergravity, proposing that the additional dimension becomes apparent at strong coupling limits of the ten-dimensional string theories3 7. This eleventh dimension is crucial for understanding the dynamics and dualities between different string theories.
Six-Dimensional Compactifications
In some scenarios, string theory is studied in six dimensions, particularly in the context of compactifications on K3 surfaces. These six-dimensional models are significant for understanding anomaly cancellation and the matter content of heterotic and type I compactifications1. Such studies help in exploring the possible realizations of string theory in lower dimensions and their implications for supergravity theories.
Higher-Dimensional Theories
There are also explorations into string theories in dimensions higher than ten. For instance, some research has proposed the existence of string theories in more than ten dimensions through mechanisms like closed-string tachyon condensation, which can lead to dynamical transitions between different dimensional frameworks8. These higher-dimensional theories often involve complex adjustments in the string-frame metric and dilaton gradient.
Critical Dimensions and Compactification
The critical dimension for string theories, particularly in curved spaces, is often derived based on the background metric and the presence of Wess-Zumino terms associated with compactified dimensions. This critical dimension is essential for constructing consistent string theories and is typically quantized in units of the string tension9.
Conclusion
In summary, string theory primarily operates within a ten-dimensional framework, with extensions to eleven dimensions in M-theory. There are also significant studies in six-dimensional compactifications and explorations into higher-dimensional theories. These dimensions are crucial for the consistency and unification of the various string theories, providing a deeper understanding of the fundamental structure of the universe.
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Most relevant research papers on this topic
String universality in six dimensions
All consistent six-dimensional supergravity theories can be realized in string theory, potentially demonstrating string universality as a concrete conjecture.
Highly CitedString universality in ten dimensions.
In ten dimensions, all supersymmetric theories of gravity without known inconsistencies can be realized in string theory, as all anomalies can be cancelled without compromising supersymmetry and Abelian gauge invariance.
Highly CitedString theory dynamics in various dimensions
This study suggests that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring, and a duality between heterotic string and Type IIA superstrings controls strong coupling dynamics in five, six, and seven dimensions.
Highly CitedRETRACTED: STRING theorem from one dimension to high dimension
This paper proposes a STRING theorem from one dimension to high dimension, demonstrating its validity and revealing the energy density conversion rule in string theory.
Highly CitedE‐String Theory on Riemann Surfaces
Compactifications of 6d E-string theory to four dimensions reveal emergent symmetries and new predictions for 4D exceptional dualities and symmetries.
Highly CitedEffective string theory.
Effective string theory demonstrates compatibility between contradictory features and long-distance dynamics of string solutions in four dimensions, such as Nielsen-Olesen vortex or QCD strings.
Highly CitedDevelopments in string cosmology
The second string revolution, which began around 1995, has significantly altered our understanding of the universe by extending 10-dimensional string theory to 11-dimensional M-theory, revealing a more complex universe than previously imagined.
Highly CitedDimension-changing exact solutions of string theory
This paper presents new solutions for string theory, allowing dynamic transitions between different dimensions, with different degrees of stability and supersymmetry, and also allowing solutions to bypass the critical dimension and proceed directly to spacelike linear dilaton theories in dimensions greater than or equal to two.
Critical dimension of string theories in curved space.
A consistent string theory can be constructed only in the presence of a Wess-Zumino term, with the compactified radius quantized in units of string tension.
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