String Theory
Quantum Field Theory and Standard Model
The research that started with Atom and Atomic Nucleus 100 years ago, has culminated in the Standard Model of High Energy Physics (SM of HEP). SM has been proved to be the correct theory of Nature valid down to centimeter. This size is times smaller than cm which is the size of an atom.
In SM, the three basic forces of Nature, electromagnetic, weak and strong interactions have been incorporated in the Yang-Mills theory which is a generalization of Maxwell equations describing electromagnetism.
Electromagnetic interactions occur through the exchange of photons which have zero mass and spin one. In SM, there are 12 particles of spin one, including photon, whose exchange is responsible for the electromagnetic, weak and strong forces. These are called gauge bosons.
This SM uses Quantum Field Theory which combines Special Theory of Relativity with Quantum Mechanics in a mathematically consistent way.
SM was created by theoretical physicists 40 years ago. In the next 40 years experimental physicists verified each ingredient of SM, except one, namely Higgs boson. Higgs boson was caught only in 2012 in the Large Hadron Collider (LHC) of CERN, Geneva. This was an important discovery.
Where do we go from here? SM is not the end of Physics. There are many things yet to be discovered. The most important thing left out of SM is gravitation. SM contains only electromagnetic, weak and strong forces. Gravitation which is the most important force has been left out in SM.
It is a surprising fact that the two great revolutions of the 20th century Relativity and Quantum Mechanics are not consistent with each other. Here what is referred to as Relativity is the General Theory of Relativity. Special Theory Relativity has already been combined with Quantum Mechanics and that is Quantum Field Theory which is the language of SM.
In Einstein's General Theory of Relativity, gravitation is nothing but the curvature of space-time and this refuses to join with Quantum Mechanics.
Therefore,
Quantum Gravity has become a fundamental challenge in Physics.
String Theory has been discovered to be the correct theory for Quantum Gravity. String theory has many other features apart from gravitation; it has the other three forces too. It contains SM also and thus appears to be the correct theory for all the four forces of Nature.
Indian scientists have made important contributions to String Theory. Many Indian students are attracted by this theory.
History of String Theory
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String Theory was born in the research on S-matrix which was used to describe the collisions of strongly interacting particles such as nucleon and pion that are called hadrons.
Veneziano discovered the correct formula for the S-matrix. Just when this research reached its pinnacle which is the Dual Model, Nambu discovered that the particles of the Dual Model are all vibrations of a String. So S-matrix theory was given up and research on Strings started.
Some milestones in the history of String Theory are given below:
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Veneziano 1968 Dual Model
Nambu 1969 Strings
Ramond and Nevue-Schwartz 1971 Fermions and Superstrings
Goddard and others 1971 26 dimensions
Gliozi and others 1977 10 dimensions
Nevue and Scherk 1972 Yang-Mills in string
Yoneya 1974 Gravity in string
Scherk and Shwartz 1974 Liberation of strings from hadronic world
Green and Schwartz 1984 Discovery of anomaly-free strings
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These were remarkable discoveries. While trying to construct the strings for fermions, Ramond and Nevue-Schwartz discovered Supersymmetry.
In order to construct string theory consistent with relativistic quantum mechanics, Goddard, Goldstone, Rebbi and Thorne discovered that 3+1=4 space-time is not sufficient, 25+1=26 dimensions are needed; Gliozi, Scherk and Olive found that for the supersymmetric string, 9+1=10 dimensions were needed.
In the context of the theory of hadrons, these discoveries, especially the higher dimensions were considered as bizarre. So, the popularity of strings started to wane.
Another reason for the strings losing favor was the discovery that Quantum Chromodynamics was discovered as the correct theory for hadrons.
At the same time, inspired by the connection of strings to Yang-Mills and gravity discovered by Neveu, Scherk and Yoneya, Scherk and Schwartz liberated String Theory from the hadronic world. That liberated string theory from all its difficulties. All they had to do was to raise the string tension from to .
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Thus was born the supersymmetric string living in 10-dimensional space-time.
Generally, both quantum field theories and string theory suffer from anomalies. In 1984, Green and Schwartz discovered that and
strings do not have anomalies. After this discovery, many physicists began to pay attention on Strings.
String Theory
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In String Theory, a point particle is replaced by a one-dimensional object called string. Its length is about cm, which is the fundamental scale of quantum gravity. The various vibrational modes of the string are the particles such as electron or photon.
String theory automatically contains gravity. This is the beauty of string theory. But this is bought at a high price. Strings live only in a 9-dimensional Universe. Including the dimension of time, it is 10-dimensional.
We are aware of only 3 space dimensions and time. Where are the extra 6 dimensions? They are all curved into cm. These curved dimensions and string's size will be revealed only if we reach cm. As we said already, in experimental physics we have reached down to a depth of cm only.
String can have its ends open or joined together. The former is called open string and the latter closed. Strings have ground state as well as excited states. The non-supersymmetric string (both closed and open) existing in 26 dimensions has a ground state with negative mass squared, called tachyonic. This is unstable and so must be rejected. We must consider only supersymmetric string living in 10 dimensions.
The open superstring has a ground state which has spin 1 and mass zero. This can be identified as the gauge boson of Yang-Mills theory. The ground state of the closed superstring has spin 2 and mass zero. This can be identified as graviton, the quantum of gravity.
Apart from these mass zero particles, all the excited states of the string will have masses of the of the order Gev which are not accessible at the low-energy experiments.
In every supersymmetric theory, there will exist a fermion corresponding to the boson. So, in the superstring theory, fermions such as electrons also will exist.
We said that the mass zero spin 1 boson is the gauge boson and the mass zero spin 2 boson is the graviton. So String theory incorporates Standard Model and Quantum Gravity.
String interactions
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Two open strings can join at the ends and become one open string. One string can split and become two open strings.
The two ends of an open string can join to make a single closed string. So, open strings alone cannot exist as a consistent theory. Open strings necessarily make closed strings. Since, as we already said, open string correspond to Standard Model and closed string gives gravity, we see that consistent string theory automatically contains gravity. This is in stark contrast to (local) quantum field theory which can describe strong, weak and electromagnetic interactions but is incapable of dealing with gravity.
This shows how important string theory is for Quantum Gravity.
Heterotic Strings
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In point particle theory, there is the beautiful Kaluza-Klein idea in which 4-dimensional Yang-Mills theory and 4-dimensional gravitation can be obtained from a higher (>4) dimensional gravity theory by compactifying the extra dimensions. There is a similar idea in string theory. this is called heterotic string theory. This was discovered by Gross, harvey, Martinec and Rhom in 1985.
In the heterotic string, from higher dimensional closed string, by compactifying some dimensions, open strings and closed strings can be obtained. These open strings have precisely the or gauge forces, that had been proved to be anomaly-free.
Consistent String theories
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The following five have been proved to be the only consistent string theories:
1. Type I superstring with : open and closed strings living in 10 dimensions
2. Type IIA superstring: closed string alone living in 10 dimensions with nonchiral fermions.
3. Type IIB superstring: closed string alone living in 10 dimensions with chiral fermions.
4. Heterotic : Closed string which after compactification becomes gauge forces and gravity
5. Heterotic : Closed string which after compactification becomes gauge forces and gravity
Miracles of string Theory
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Let us summarize whatever we said so far, through the miracles of string theory.
1. For string theory, higher dimensions and supersymmetry are necessary.
2. String theory works only if gravity is included.
3. Quantum anomalies are not present in and strings
4. There is a Kaluza-Klein type of string theory, called heterotic string theory.
5. The infinities that are present in quantum field theory are absent in string theory.
The miracles stop here. All these miracles occur in 10 dimensions. How do we go to the 4-dimensional world from 10-dimensional world. One choice for the compact 6-dimensional manifold is the Calabi-Yao manifold.
Two important developments of more recent times:
1. Polkinsky discovered that String Theory contains not only one-dimensional string but also 2-dimensional membrane and extended objects of all dimensions up to nine. So string theory is the relativistic quantum mechanics of all objects up to nine dimensions and so it involves mind-boggling mathematics!
2.It has been discovered that the five consistent string theories are just different faces of a single theory. Ashok Sen played a major role in this discovery.
A challenge in Fundamental Physics
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It is apparent that String Theory is the correct theory for Quantum Gravity. So after the successful Standard Model, String Theory has become the next frontier of research.
If String Theory is the solution for the problem of Quantum Gravity, how can we be sure of that? What is the experimental proof of String Theory?
It took 40 years to prove the Standard Model. It required the construction of particle accelerators of higher and higher energies which ultimately led to the construction of the Large Hadron Collider (LHC) of eV.
LHC is a behemoth. It is a circle of 28 kilometer circumference and it took 20,000 scientists and engineers who worked for 20 years to build it.
In relativistic quantum mechanics, a length and the energy needed to probe that length are in inverse proportion to each other. When the length is small, energy becomes high. We have come to the length of cm. The energy needed to experimentally probe that length is eV which is the energy of LHC. To probe the length scale of string theory or quantum gravity which is cm, we will need times more energy. .
This is called Planck energy. Most of the scientists believe it is impossible to build such an accelerator.
This is the challenge in Fundamental Physics.
Actually, situation is not that bad. There is no limit to the ability of the human mind. It has the capability to cross this obstacle.
Instead of increasing the size of the accelerator, new ways of particle acceleration must be discovered.
If new principles of acceleration are not found, in about 2040, basic physics research will stop! This has nothing to do with quantum gravity or Planck energy. The accelerator technology used so far cannot take us beyond about eV.
In the last 80 years, accelerator energies have grown enormously. Every years, energy has increased ten-fold. This is a good sign for the future of fundamental physics. If such a growth continues, -fold energy will be achieved in 16x6 = 96 years. Some may consider this as too long. That is wrong. Even to test the Standard Model it took forty years.
But the above growth will be possible only if new technologies and new methods of particle acceleration are continuously discovered. The earlier growth was possible only because of the discovery of new principles of particle acceleration.
For many years, I have been talking about this and emphasizing that our country must start research on new new technologies of particle acceleration.
What are these new ways? I will mention one of them.
Laser-Plasma accelerators
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In the last 30 years, many ideas about about Laser-Plasma Acceleration (LPA) have been discovered. Using the plasma wake fields, they have accelerated electrons to eV in a distance of 1 cm. Ordinary accelerators need 1 kilometer to get such energies.
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Therefore, table-top accelerators will be possible and such a progress will help to discover newer methods. LPA alone may not lead to Planck energy, but it will be an important step to reach that goal.
Our country must launch LPA research. I have been discussing this with many experts in lasers and plasma physics.
Two steps must be taken immediately:
1. A task force to plan LPA activities must be formed.
2. A Centre for LPA must be created.
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This is about a major aim. It is a big dream.
Only through such dreams,
our country's Science will advance.
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