Superstring Theory: Stringing Together All the Forces of Physics

May 19, 2010

Five theorists at KEK are Superstring theory: stringing at the leading edge of superstring theory. From left: together all the forces of physics Dr. Shun’ya Mizoguchi, [Superstring Theory, IKKT Matrix Model, Black Hole, Extra Dimension] Prof. Jun Nishimura, KEK scientists developed the IKKT matrix model the leader of the superstring group that is used to make predictions from the Type IIB Prof. Yoshihisa Kitazawa, superstring theory. Read here about the Prof. Satoshi Iso, contributions of KEK’s superstring theorists in and Dr. Makoto Natsuume. the field, and how superstring theory, the possible Theory of Everything, is starting to make

“The answer to the Ultimate anyway. Luckily, physicists on the planet Earth theory and Einstein’s theory of general may have known more sensible questions to relativity. This hypothetical theory is popularly Question of Life, the Universe, and ask, such as, Is there an ultimate theory that referred to as the theory of quantum gravity. Everything is” probably not forty-two. The governs our universe, and if so, what is it? The two current central theories have been vastly successful, surviving many experimental supercomputer Deep Thought created by For the past half-century, physicists have tried and observational tests across vast distance hyperintelligent pandimensional philosophers to ﬁnd a theory that unites the two central scales. However, these two theories cannot be in Douglas Adams’ the Hitchhiker’s Guide to theories of modern physics: quantum ﬁeld easily reconciled as their fundamental notions the Galaxy didn’t know what the question was

[1] dimensions of spacetime. In this original form, string theory could only explain the force mediating particles, the bosons, and could not explain the other particle family, the fermions. As fermions are the particles from which matter is constructed this was a problem. Physicists incorporated fermions into the theory by adding a property called supersymmetry. According to supersymmetry, every boson has a fermionic superpartner, and every fermion has a bosonic superpartner. The string theory that includes supersymmetry is known as superstring theory. Superstring is consistent in 10 dimensional spacetime.

With further study, physicists found that there are five distinct superstring theories which are consistent with our current knowledge of the universe. Individual strings could be open (a line String theory was originally formulated to describe the strong interaction. with two ends) or closed (a loop). A closed loop However, the theory of quantum chromodynamics (QCD) soon took its place. could be ‘orientable’ or ‘unorientable’ Although temporarily abandoned, string theory later became the most depending on whether there was a defined promising candidate for a theory of quantum gravity. direction along the length of the loop. In a racetrack in which cars can move in forward or backward direction, if the car can tell which of spacetime differ. At microscopic scales, the Tamiaki Yoneya found that string theory direction it’s moving then the racetrack is uncertainty principle of quantum field theory predicted the existence of a graviton—a orientable, while if the car cannot distinguish the states that every point in space is subject to hypothetical elementary particle that mediates direction it’s moving, the racetrack is said riotous quantum fluctuations, in which gravity. This was the beginning of a unified field unorientable. An orientable closed string could elementary particles and antiparticles are theory, a single theory that could describe the also differentiate the left moving or right moving continuously created and destroyed. This functioning of all four fundamental forces. waves along the string. The superstring theory seething sea of vacuum cannot be reconciled of open and closed strings is called Type I. The with the smooth curves of spacetime described Kitazawa relates gravity and the gauge theory theories of closed orientable superstrings are by general relativity. using superstring theory. In this theory, the called Type IIA and Type IIB where the former is gravitational interaction is an exchange of a left-right symmetric, while the latter is left-right On the one hand, general relativity explains string loop called graviton. When a loop is asymmetric. The hybrid of left moving gravity by means of curvature of spacetime. On tossed, the trajectory of it would be cylindrical superstring and right moving bosonic string the other hand, quantum field theory explains tube, so that the gravitational interaction takes gives rise to two other superstring theories the other three forces—strong, electromagnetic, the form of a cylinder in spacetime. There are called heterotic strings. All five of these are and weak—as the result of interactions among two ways to look at the tube. One is a loop supersymmetric, ten-dimensional, string fundamental particles using something called traveling through time, and the other is an open theories. gauge theory. “We need a theory that can straight string going around in a circle. A closed explain both gravity and gauge interactions,” string is a graviton and an open string is a The theory of particular interest here is the Type says Prof. Yoshihisa Kitazawa of KEK, the leader gauge particle—such as photon, so the tube IIB superstring theory. The Type IIA strings turns of the superstring group at the KEK Theory represents both gravity and gauge particles. out to produce a universe which is too Center. “One promising candidate is superstring “They are just two different ways to look at the symmetric. Our universe is filled with theory.” same thing.” handedness. Neutrinos, for example, are left- handed. Type IIB superstring predicts an String theory proposes that the elementary Five superstring theories asymmetric universe, just like the one we live in. constituents of matter are one-dimensional String theory, when initially discovered, made strings, rather than zero-dimensional particles. mathematical sense only if there were 26 Further developments These strings may be either open or closed, and may vibrate at different frequencies. The shape of the string and the frequency of the vibration determine the type of the particle. “Consider Newton’s law of gravitation. As you move closer and closer to a point mass, the gravitational force between you and the mass becomes infinitely large,” explains Kitazawa. This creates a problem because a singularity— divergence to infinity at zero radius—is a discontinuity in spacetime. “The extension of particles to strings is the simplest way to avoid the singularities in spacetime that are inherent in the point particle picture.”

String theory was originally developed to explain strong interactions, but was replaced by the successful theory of quantum chromodynamics (QCD). It was not until 1969 that Yoichiro Nambu and others independently formulated string theory as quantum mechanics of one dimensionally extended String theory says that gauge particles such as photons, gluons, and W/Z object. In the mid 70s, Japanese physicist bosons are open strings, but that the graviton is a closed string.

[2] theory. This questions that need to be answered. Why four, A gravitational interaction matrix model and not some other number? Neither general between two D-branes. is called the relativity nor quantum field theory can predict The graviton is the open IKKT model, the dimensionality of spacetime. These red cylinder, while the D- and it in theories require the number of dimensions be branes are blue sheets. principle input as an empirical value. String theory, on The cylindrical spacetime allows string the other hand, has ability to predict path of the graviton theorists to dimensionality. Although superstring theory could be created either solve the predicts ten dimensions, the extra dimensions Type IIB can be curled up in so small a volume that by a loop travelling superstring humans cannot perceive them, so that for all parallel to the axis of the exactly to practical purposes, spacetime is four- cylinder (tossed produce a dimensional. This is called compactification of loop ,red), or by a description dimensions. longitudinal line moving of tangentially around the spacetime. When Kitazawa and Prof. Satoshi Iso of KEK circumference of the apply the analytical approach to a matrix cylinder (green). “The matrix superstring model, it is by assuming solvable model has conditions of fields in spacetime. In that, they many choose specific assumptions in order to make degrees of the calculation feasible. They have solved the in superstrings freedom. In part, this means that the matrix, for instance, assuming very low density spacetime described by a matrix model is of discrete spacetime points. Then they Superstring physicists spent long years fuzzy,” explains Kitazawa. “That may sound a examine if the result would look like the pondering, wondering which one of the five little odd at first, but it is a fundamental spacetime we live in. “From the calculation of superstring theories would be the ultimate property of quantum mechanics. For example, the simple case emerged a spacetime in which theory that they had been looking for. Then, in the position and momentum of an electron four-dimension is infinitely probable.” Because 1995, Edward Witten presented a unified string cannot both be determined precisely at the of the low spacetime point density they theory. He showed that all five superstring same time because of the uncertainty assumed, the space emerged as a very bumpy theories are different ways of looking at a principle.” space, rather than a smooth one. They are bigger entity including an eleven dimensional looking for a new tool that allows them to theory called M-theory. The ‘M’ is said to In quantum field theory, parameters are further investigate the dimensionality of stand for many things: ‘mother’, ‘mystery’, and defined at every point in spacetime to describe spacetime. ‘matrix’, among others. quantum fluctuations. This means that the

theory is background dependent, that the In addition to predicting the dimensionality of At this same time, the matrix theory of details of the physics at a particular time and spacetime, superstring theory may also be superstrings emerged. Up to this point, string location are dependent on time and location. able to predict other fundamental parameters physicists had been using a perturbative The physics of general relativity, on the other such as the number of free constants and the approach, a mathematical method to hand, is independent of background. A unified number of generations of particles in the approximate to the solution of a problem that theory is expected to be independent of Standard Model. Iso says that, “superstring could not be solved exactly. Unfortunately, this coordinate, so the dependence of field theory theory is deeply mathematical in nature. What wasn’t working well, as the perturbed terms on coordinates has long been troubling to distinguishes it from the empirical approach to diverged to infinity. Therefore, physicists were theorists. According to Kitazawa, the physical problems is that we want to ‘explain’ looking for non-perturbative approach. This remarkable thing about “the matrix superstring numbers rather than putting them in a theory came in the form of the matrix model. model is that it is independent of coordinates.” by hand.” By ‘explain,’ Iso means he hopes to derive values for fundamental physical In the early 90s, Joseph Polchinski discovered Using the matrix model, physicists are trying to constants from first principles. In short, he that the superstring requires more extended find a low-energy approximation to superstring hopes to, “find the deeper mechanisms at objects called D-branes. This revolutionary theory, which they can then compare to the work behind the current theory.” idea was proved to be vastly successful, Standard Model. There are two ways to do explaining microscopic structure of black- this. First, one can use the traditional analytical holes. According to Kitazawa, “It was Good news about black holes approach, constructing the math and solving it conjectured D-branes be written by matrix Prof. Jun Nishimura recently announced some by hand. Second, one can use the new models, which was a revolution in the field of exciting news produced by computation of numerical approach, and take advantage of string matrix model.” black hole thermodynamic properties using the the power of modern supercomputers. matrix model. “I wanted to find something IKKT matrix model specific that could show that superstring Why four dimensions? theory is an accurate model of our reality,” In 1996, four theorists at KEK, Ishibashi, We live in four-dimensional spacetime. For says Nishimura. “Black holes, which are a Kawai, Kitazawa, and Tsuchiya developed a physicists, the dimensionality is one of many matrix model for the Type IIB superstring

The IKKT matrix model, discovered by KEK’s Ishibashi, Kawai, Kitazawa, and Tsuchiya, is equivalent to the Type IIB superstring theory. The discovery allows exact calculation of the theory.

[3] Scientists thought it was impossible to compute the Nishimura’s numerical calculation of the properties conditions inside a black hole until Prof. Jun Nishimura of of a black hole required the use of this KEK succeeded using a matrix superstring model. supercomputer at the KEK’s computing center. manifestation of gravity, made this reality check spacetime is equivalent to a black hole in five- has many aspects,” says Iso. For Natsuume, possible.” dimensional spacetime. superstring theory is an intellectual exercise, the theory is, “like a toy box, stuffed with many Using general relativity and quantum field “This was the first time that string theory has interesting theories, stimulating and fun.” theory, Steven Hawking predicted that a black ever been mentioned in an announcement of a hole emits radiation called Hawking radiation. major experiment,” says Dr. Makoto Natsuume Dr. Shun’ya Mizoguchi, who studies The detailed calculation of the dynamics inside who studies the quark-gluon plasma using reconstruction of the Standard Model from a black hole was thought impossible a decade black holes. “The gap between the predictions superstring theory, says he would likes to see ago, because general relativity could not be of superstring theory and the reality observed in where the beauty of the theory and the reality applied to the center of black hole, where the experiment is smaller than many of us had merge. “String theory is now different from when spacetime curvature diverges to infinity. expected.” The experiment also gave strong it started twenty years ago as the Theory of Nishimura, who had been working on matrix evidence that superstring theory can accurately Everything. It has experienced several theory computation for a long time, saw an explain the strong interaction. Iso says: mathematical revolutions. Now that the Large opportunity. The result was dazzling: a perfect “Superstring theory is not just the ultimate Hadron Collider at CERN has started operation, match with the prediction by Hawking. theory, but it also has the ability to make it may be the right time to come back to where testable predictions for complex systems.” we started: particle physics.” “I would have been happy just to be able to show that the computation was possible,” says The theory of Nishimura. “Not only was I able to do that, but I was also able to reproduce the inner workings particles, the of black holes using a superstring matrix universe, and model.” The result was published in Physical Review Letters. His next challenge is to apply everything the similar calculation techniques to answer the As the world center of question of four-dimensionality in the IKKT study of Type IIB matrix matrix model. theory, contributions of KEK’s superstring group Not just the ultimate theory to the worldwide superstring community Others have investigated additional ways to are many. The individual validate superstring theory. In 2005, an interests of the group’s intriguing result came out of Brookhaven’s members are also very quark-gluon plasma experiment. The viscosity diverse. “Aside from the of the quark-gluon plasma in the experiment mathematical was found to be surprisingly close to the value significance, superstring predicted by the superstring black hole theory plays a role as the calculation. According to the superstring theory, theory that unifies all A collision event in quark-gluon plasma. (Photo: Courtesy the quark-gluon plasma in four-dimensional theories of physics, and of Brookhaven National Laboratory)

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