Superstring theory dimensions
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Superstring Theory Dimensions: An Overview
Introduction to Superstring Theory Dimensions
Superstring theory, a pivotal framework in theoretical physics, posits that the fundamental constituents of the universe are not point particles but one-dimensional "strings." These strings vibrate at specific frequencies, giving rise to various particles. A critical aspect of superstring theory is its requirement for additional spatial dimensions beyond the familiar three.
Ten-Dimensional Space-Time in Superstring Theory
The consistency of superstring theory necessitates a ten-dimensional space-time, comprising nine spatial dimensions and one temporal dimension. This requirement was established early in the development of the theory. In 1972, it was demonstrated that the theory required ten dimensions for its consistency, which was a significant departure from the four-dimensional space-time of general relativity3. This ten-dimensional framework allows for the incorporation of both bosonic and fermionic strings, leading to a ghost-free interacting theory3.
Expanding Universe in (9+1) Dimensions
Recent studies have explored the dynamics of a (9+1)-dimensional universe within the context of superstring theory. One such study reconsidered the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. The researchers introduced infrared cutoffs in both spatial and temporal directions to regularize the Lorentzian model. Their Monte Carlo studies revealed that three out of nine spatial dimensions start to expand at a critical time, resulting in a space with SO(3) symmetry instead of SO(9)1.
Eleven-Dimensional Extensions
While ten dimensions are standard in superstring theory, there have been propositions for extending the theory to eleven dimensions. One approach suggests a super Poincaré invariant action for the superstring in eleven dimensions, which could exist in any spacetime dimensions at the classical level4. Another study proposed covariant actions for classical superstrings in eleven dimensions using simple Chern-Simons terms5. These extensions aim to explore the potential of superstring theory beyond the conventional ten-dimensional framework.
Superstrings in Higher Dimensions
Further research has explored superstring theories in dimensions beyond ten. For instance, a study constructed superstring theories that obey a new supersymmetry algebra in (9,2) and (10,2) dimensions. These theories involve systems with superparticles and superstrings, each behaving effectively as if they have a single timelike dimension due to gauge symmetries and associated constraints8.
Conclusion
Superstring theory's requirement for additional dimensions is a cornerstone of its framework, with ten dimensions being the standard for consistency. However, ongoing research continues to explore the potential of superstring theory in higher dimensions, such as eleven or even (10,2) dimensions. These studies aim to deepen our understanding of the universe's fundamental structure and the role of extra dimensions in theoretical physics.
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Most relevant research papers on this topic
Expanding (3+1)-dimensional universe from a lorentzian matrix model for superstring theory in (9+1) dimensions.
The Lorentzian matrix model for superstring theory in (9+1) dimensions can be regularized by infrared cutoffs, leading to a theory with only one scale parameter and three out of nine spatial directions expanding at critical time.
Highly CitedChern-Simons Origin of Superstring Integrability.
The AdS_5S5 Green-Schwarz superstring is derived from four-dimensional Beltrami-Chern-Simons theory, offering a simple geometric origin for its Lax connection and spectral parameter, enabling integrable holography investigations using traditional field theory methods
Superstrings–An Overview a
Superstrings offer a fundamental theory of elementary particles and quantum gravity, offering a potential unification of quantum physics and hadronic physics.
Possible generalization of the superstring action to eleven dimensions
Superstring action can exist in any spacetime dimensions, allowing reexamination of the known brane scan.
Are there any superstrings in eleven dimensions?
Superstrings can be constructed in eleven dimensions using Chern-Simons terms and local world-sheet variables.
Quantum 3D Superstrings
Quantum 3D superstrings exist for spacetime dimensions D = 3,4,6,10, with the spectrum being parity-invariant and containing anyons of irrational spin.
An Effective superstring spectral action
Superstring partition function is a valid spectral action for string mode fluctuations, enabling effective noncommutative geometry in supersymmetric theories.
Superstrings with new supersymmetry in (9,2) and (10,2) dimensions
Superstring theories with new supersymmetry in (9,2) and (10,2) dimensions can effectively behave as if they have a single timelike dimension due to gauge symmetries and constraints.
Superstrings from 26 dimensions
Superstring theories in ten dimensions can be viewed as special dimensional reductions on 16-tori from non-supersymmetric Veneziano-Nambu-Goto strings in 26 dimensions, with Fermions appearing as solitons of the two-dimensional string field theory.
Highly CitedSuperstrings and topological strings at large N
Large N superstrings and topological strings exhibit duality, with superstrings propagating on noncompact Calabi-Yau manifolds and topologically distinct Calabi-Yau systems at large N.
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