String theory and its verification

It should be said at the outset that, as of yet, there has been no experimental verification of string theory. In order to have experimental verification one needs a sharp prediction. It has been difficult to obtain such a prediction. String theory is still at an early stage of development, and it is not so easy to make predictions with a theory that is not well understood. Still, some interesting possibilities have emerged.

As we mentioned earlier, superstring theory requires a ten-dimensional spacetime: one dimension of time and nine of space. If string theory is correct, extra spatial dimensions must exist, even if we have not seen them yet. Can we test the existence of these extra dimensions? If the extra dimensions are the size of the Planck length l P (the length scale associated with four-dimensional gravity), they will remain beyond direct detection, perhaps forever. Indeed, l P∼ 10−33cm, and this distance is many orders of magnitude smaller than 10 −16 cm, which is roughly the smallest distance that has been explored with particle accelerators. This scenario was deemed to be most likely. It was assumed that in string theory the length scale l s coincides with the Planck length, in which case extra dimensions would be of Planck length, as well. It turns out, however, that string theory allows extra dimensions that are as large as a tenth of a millimeter! Surprisingly, extra dimensions that large may have gone undetected. To make this work out, the string length l s is taken to be of the order of 10 −18 cm. Moreover, our three-dimensional space emerges as a hypersurface embedded inside the nine-dimensional space. The hypersurface, or higher-dimensional membrane, is called a D-brane. D-branes are real, physical objects in string theory. In this setup, the presence of large extra dimensions can only be tested by gravitational experiments. If large extra dimensions are detected, this would be strong evidence for string theory. The direct detection of strings could even be possible.

Another possibility has to do with supersymmetry. If we start with a ten-dimensional superstring theory and compactify the six extra dimensions, the resulting four-dimensional theory is, in many cases, supersymmetric. No unique predictions have emerged for the specific details of the four-dimensional theory, but supersymmetry may be a rather generic feature. An experimental discovery of supersymmetry in future accelerators would suggest very strongly that string theory is on the right track.

Leaving aside predictions of new phenomena, we must ask whether the Standard Model emerges from string theory. It should, since string theory is supposed to be a unified theory of all interactions, and it must therefore reduce to the Standard Model for sufficiently low energies. While string theory certainly has room to include all known particles and interactions, and this is very good news indeed, no one has yet been able to show that they actually emerge in fine detail. In Chapter 15 we will study some models which use D-branes and have an uncanny resemblance to the world as we know it. In these models the particle content is in fact precisely that of the Standard Model (the particles are obtained with zero mass, however, and it is not clear whether the process that gives them mass can work out correctly). Our four-dimensional world is part of the D-branes, but these D-branes happen to have more than three spatial directions. The additional D-brane dimensions are wrapped on the compact space (we will learn how to imagine such configurations!). The gauge bosons and the matter particles in the model arise from vibrations of open strings that stretch between D-branes. As we will learn, the endpoints of open strings must remain attached to the D-branes. If you wish, the musical analogy for strings is improved. Just as the strings of a violin are held stretched by pegs, the D-branes hold fixed the endpoints of the open strings whose lowest vibrational modes could represent the particles of the Standard Model!

String theory shares with Einstein?s gravity a problematic feature. Einstein?s equations of gravitation admit many cosmological solutions. Each solution represents a consistent universe, but only one of them represents our observable universe. It is not easy to explain what selects the physical solution, but in cosmology this is done using arguments based on initial conditions, symmetry, and simplicity. The smaller the number of solutions a theory has, the more predictive it is. If the set of solutions is characterized by continuous parameters, selecting a solution is equivalent to adjusting the values of the parameters.

In this way, a theory whose formulation requires no adjustable parameters may generate adjustable parameters through its solutions! It seems clear that in string theory the set of solutions (string models) is characterized by both discrete and continuous parameters. In this light we can wonder what are the possible outcomes of the search for a realistic string model. In order to reproduce the Standard Model it seems clear that the string model must not have continuous parameters; such parameters imply the existence of massless fields that have not been observed. One possible outcome (the worst one) is that no string model reproduces the Standard Model. This would rule out string theory. Another possible outcome (the best one) is that one string model reproduces the Standard Model.

Moreover, the model represents a well isolated point in the space of all string solutions. The parameters of the Standard Model are thus predicted. The number of string models may be so large that a strange possibility emerges: many string models with almost identical properties all of which are consistent with the Standard Model to the accuracy that it is presently known. In this possibility there is a loss of predictive power. Other outcomes may be possible. String theorists sometimes say that string theory has already made at least one successful prediction: it predicted gravity! (I heard this from John Schwarz.) There is a bit of jest in saying so ? after all, gravity is the oldest known force in nature. I believe, however, that there is a very substantial point to be made here. String theory is the quantum mechanics of a relativistic string. In no sense whatsoever is gravity put into string theory by hand. It is a complete surprise that gravity emerges in string theory. Indeed, none of the vibrations of the classical relativistic string correspond to the particle of gravity. It is a truly remarkable fact that we find the particle of gravity among the quantum vibrations of the relativistic string. The striking quantum emergence of gravitation in string theory has the full flavor of a prediction.

String theory has been a very stimulating and active area of research ever since Michael Green and John Schwarz showed in 1984 that superstrings are not afflicted with fatal inconsistencies that threaten similar particle theories in ten dimensions. Much progress has been made since then.

String theory has provided new and powerful tools for the understanding of conventional particle physics theories, gauge theories in particular. These are the kinds of theories that are used to formulate the Standard Model. Close cousins of these gauge theories arise on string theory D-branes.

String theory has also made good strides towards a statistical mechanics interpretation of black hole entropy. We know from the pioneering work of Jacob Bekenstein and Stephen Hawking that black holes have both entropy and temperature. In statistical mechanics these properties arise if a system can be constructed in many degenerate ways using its basic constituents. Such an interpretation is not available in Einstein?s gravitation, where black holes seem to have few, if any, constituents. In string theory, however, certain black holes can be built by assembling together various types of D-branes and strings in a controlled manner. For such black holes, the predicted Bekenstein entropy is obtained by counting the ways in which they can be built with their constituent D-branes and strings.

As a theory of quantum gravity, string theory will be needed to study cosmology of the Very Early Universe. The deepest mysteries of the universe seem to lie hidden in a regime where classical general relativity breaks down. String theory should allow us to peer into this unknown realm. Some day, we may be able to understand the nature of the Big Bang, and know whether there is a pre Big Bang cosmology.

Most likely, answering such questions will require a mastery of string theory that goes beyond our present abilities. String theory is in fact an unfinished theory. Much has been learned about it, but in reality we have no complete formulation of the theory. A comparison with Einstein?s theory is illuminating. Einstein?s equations for general relativity are elegant and geometrical. They embody the conceptual foundation of the theory and feel completely up to the task of describing gravitation. No similar equations are known for string theory, and the conceptual foundation of the theory remains largely unknown. String theory is an exciting research area because the central ideas remain to be found.

Describing nature and formulating the theory ? those are the present-day challenges of string theory. If surmounted, we will have a theory of all interactions, allowing us to understand the fate of spacetime and the mysteries of a quantum mechanical universe. With such high stakes, physicists are likely to investigate string theory until definite answers are found.

Date: 2016-06-12; view: 214