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ULTIMATE SYMMETRY:

Fractal Complex-Time and Quantum Gravity

by Mohamed Haj Yousef



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II.3.2 Super Symmetry in Strings Theory and Extra Dimensions


In the 1960s, Geoffrey Chew (b. 1924) and Steven Frautschi (b. 1933) discovered that the mesons make families called Regge trajectories with masses related to spins in a way that was later understood, by Yoichiro Nambu (1921-2015), Holger Nielsen (b. 1941) and Leonard Susskind (b. 1940), to be the relationship expected from rotating strings. Chew advocated making a theory for the interactions of these trajectories that did not presume that they were composed of any fundamental particles, but would construct their interactions from self-consistency conditions on the S-matrix, which was started by Werner Heisenberg in the 1940s as a way of constructing a theory that did not rely on the local notions of space and time, which Heisenberg believed that they should break down at the nuclear scales. While the scale was off by many orders of magnitude, the approach he advocated was ideally suited for a theory of Quantum Gravity.

In 1969-70, Nambu, Nielsen, and Susskind recognized that the theory could be given a description in space and time in terms of strings. The scattering amplitudes were derived systematically from the action principle, giving a space-time picture to the vertex operators. In 1971, Pierre Ramond (b. 1943) added fermions to the model, which led him to formulate a two-dimensional super symmetry to cancel the wrong-sign states. In the fermion theories, the critical dimension was 10, but Stanley Mandelstam (1928-2016) formulated a world sheet conformal theory for both the Bose and Fermi case, giving a two-dimensional field theoretic path-integral to generate the operator formalism, while Michio Kaku (b. 1947) and Keiji Kikkawa (1935-2013) gave a different formulation of the bosonic string, as a string field theory, with infinitely many particle types and with fields taking values not on points, but on loops and curves.

In 1974, Tamiaki Yoneya (b. 1947) discovered that all the known string theories included a massless spin-two particle that obeyed the correct Ward identities to be a graviton. John Schwarz (b. 1941) and Joel Scherk (1946-1980) came to the same conclusion and made the bold leap to suggest that Strings Theory was a theory of Gravity, not a theory of Hadrons. They reintroduced Kaluza-Klein theory as a way of making sense of the extra dimensions. At the same time, Quantum Chromodynamics was recognized as the correct theory of hadrons.

In the early 1980s, Edward Witten (b. 1951) discovered that most theories of Quantum Gravity could not accommodate chiral fermions, like the neutrino. This led to study violations of the conservation laws in gravity theories with anomalies, with hundreds of physicists started to work in this field, which was called the first super string revolution. The second super string revolution started in 1995, when Witten united the five string theories that existed at the time, giving birth to a new 11-dimensional theory called M-theory that was later formulated with holographic description, which was the first definition of Strings Theory that was fully non-perturbative and a concrete mathematical realization of the holographic principle. It is an example of a gauge-gravity duality and is now understood to be a special case of the AdS/CFT correspondence.

In 1997, Juan Maldacena (b. 1968 ) noted that the low energy excitations of a theory near a black hole consist of objects close to the horizon, which for extreme charged black holes looks like an anti-de Sitter space. He noted that in this limit the gauge theory describes the string excitations near the branes. So he hypothesized that Strings Theory on a near-horizon extreme-charged black-hole geometry, an anti-de Sitter space times a sphere with flux, is equally well described by the low-energy limiting gauge theory, the  super symmetric Yang-Mills theory. This hypothesis, which is called the AdS/CFT correspondence, is now well-accepted as a concrete realization of the holographic principle, which has far-reaching implications for black holes, locality and information in physics, as well as the nature of the gravitational interaction.

Through this relationship, Strings Theory has been shown to be related to gauge theories like Quantum Chromodynamics and this has led to more quantitative understanding of the behavior of hadrons, bringing Strings Theory back to its roots developed in 1960s.

To construct models of particle physics based on Strings Theory, physicists typically begin by specifying a shape for the extra dimensions of space-time. Each of these different shapes corresponds to a different possible Universe, or vacuum state, with a different collection of particles and forces. String theory as it is currently understood has an enormous number of vacuum states, typically estimated to be around , and these might be sufficiently diverse to accommodate almost any phenomena that might be observed at low energies.

Some physicists believe this large number of solutions is actually a virtue because it may allow a natural anthropic explanation of the observed values of physical constants, in particular the small value of the cosmological constant. The anthropic principle is the idea that some of the numbers appearing in the laws of physics are not fixed by any fundamental principle but must be compatible with the evolution of intelligent life.

Susskind argued that Strings Theory provides a natural anthropic explanation of the small value of the cosmological constant, since the different vacuum states of Strings Theory might be realized as different Universes within a larger multiverse. The fact that the observed Universe has a small cosmological constant is just a tautological consequence of the fact that a small value is required for life to exist.

One of the main criticisms of Strings Theory from early on is that it is not manifestly background independent. In Strings Theory, one must typically specify a fixed reference geometry for space-time, and all other possible geometries are described as perturbations of this fixed one. This is unlike General Relativity which is background independent because does not privilege any particular space-time geometry. Lee Smolin (b. 1955) claims that this is the principal weakness of Strings Theory as a theory of Quantum Gravity, saying that it has failed to incorporate this important insight from General Relativity.

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

Since Strings Theory incorporates all of the fundamental interactions, including gravity, many physicists hope that it fully describes our Universe, making it a theory of everything. One of the goals of current research in Strings Theory is to find a solution of the theory that reproduces the observed spectrum of elementary particles, with a small cosmological constant, containing dark matter and a plausible mechanism for cosmic inflation. While there has been progress toward these goals, it is not known to what extent Strings Theory describes the real world or how much freedom the theory allows to choose the details.

One of the relationships that can exist between different string theories is called S-duality. This is a relationship which says that a collection of strongly interacting particles in one theory can, in some cases, be viewed as a collection of weakly interacting particles in a completely different theory. Roughly speaking, a collection of particles is said to be strongly interacting if they combine and decay often and weakly interacting if they do so infrequently. Type I Strings Theory turns out to be equivalent by S-duality to the  heterotic Strings Theory. Similarly, type IIB Strings Theory is related to itself in a nontrivial way by S-duality.

Another relationship between different string theories is T-duality. Here one considers strings propagating around a circular extra dimension. T-duality states that a string propagating around a circle of radius 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 momentum as it propagates around a circle, and it can also wind around the circle one or more times. The number of times the string winds around a circle is called the winding number. If a string has momentum 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 Strings Theory is equivalent to type IIB Strings Theory via T-duality, and the two versions of heterotic Strings Theory are also related by T-duality.

The discovery of the AdS/CFT correspondence was a major advance in physicists understanding of Strings Theory and Quantum Gravity. One reason for this is that the correspondence provides a formulation of Strings Theory in terms of Quantum Field Theory, which is well understood by comparison. Another reason is that it provides a general framework in which physicists can study and attempt to resolve the paradoxes of black holes.

In 1975, Stephen Hawking published a calculation which suggested that black holes are not completely black but emit a dim radiation due to quantum effects near the event horizon. At first, Hawking s result posed a problem for theorists because it suggested that black holes destroy information. More precisely, Hawking s calculation seemed to conflict with one of the basic postulates of quantum mechanics, which states that physical systems evolve in time according to the Schroedinger equation. This property is usually referred to as unitarity of time evolution. The apparent contradiction between Hawking s calculation and the unitarity postulate of quantum mechanics came to be known as the black hole information paradox.

The AdS/CFT correspondence resolves the black hole information paradox, at least to some extent, because it shows how a black hole can evolve in a manner consistent with quantum mechanics in some contexts. Indeed, one can consider black holes in the context of the AdS/CFT correspondence, and any such black hole corresponds to a configuration of particles on the boundary of anti-de Sitter space. These particles obey the usual rules of quantum mechanics and in particular evolve in a unitary fashion, so the black hole must also evolve in a unitary fashion, respecting the principles of quantum mechanics. In 2005, Hawking announced that the paradox had been settled in favor of information conservation by the AdS/CFT correspondence, and he suggested a concrete mechanism by which black holes might preserve information.

Super symmetry is part of Super-strings Theory, a string theory of Quantum Gravity, although it could in theory be a component of other Quantum Gravity theories as well, such as Loop Quantum Gravity. For Super-string Theory to be consistent, super symmetry seems to be required at some level (although it may be a strongly broken symmetry). If experimental evidence confirms super symmetry in the form of super symmetric particles such as the neutralino that is often believed to be the lightest super partner, some people believe this would be a major boost to Super-string Theory. Since super symmetry is a required component of Super-strings, any discovered super symmetry would be consistent with Super-strings. If the Large Hadron Collider and other major particle physics experiments fail to detect super symmetric partners, many versions of Super-strings Theory which had predicted certain low mass super partners to existing particles may need to be significantly revised.

 



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The time of anything is its presence; but I am not in time, and You are not in time; so I am Your time, and You are my time!
Ibn al-Arabi [The Meccan Revelations: III.546.16 - tans. Mohamed Haj Yousef]
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