1. One obviously expects a unique Holy Grail unified theory (if it exists at all) rather than five (the so-called embarrassing riches problem). There are two possible solutions to this puzzle. One possibility is that these five superstring theories are actually equivalent even though they look quite different in appearance. The other is that even though each of the five superstring theories unifies quantum mechanics with general relativity, none of them is the final theory but merely a special aspect of a fundamental and yet-unknown big theory. Establishing either of the above possibilities requires going beyond the perturbative region of superstring theory.
   
2. Each of these perturbative string theories requires 10 space-time dimensions and space-time supersymmetry. In the foreseeable future, we don't expect to build an accelerator with energy around 10^{19}GeV to test these theories directly. So the minimum test is to require that at least some of these string theories produce our four-dimensional observable physics, for example, the Standard Model. In spite of many people's efforts, we have been unable to achieve this. The failure of our efforts indicates that our real world may reside intrinsically in the non-perturbative region of string theory if superstring indeed has its role in describing nature.
   
3. The other natural question is: can an asymptotic theory be theory of everything? As a TOE, one expects that the only possible input are the fundamental constants such as the speed of light, the Planck constant, and string tension, plus possible initial data (boundary conditions). The rest should be derivable. In particular, the vacua should be determined dynamically. However, for each of the five perturbative superstrings, we assume, from the outset, the space-time to be flat and the string coupling, which is related to the vacuum expectation value of dilaton (a massless particle in the spectrum), to be small to validate the perturbative expansion. This is against the very nature of TOE. Whether the string coupling is small or not should be determined dynamically. In other words, a perturbative theory can be used to calculate relevant processes but cannot be used to determine the underlying vacuum structure. Therefore, a TOE cannot be a perturbative theory. Our experience in field theory also supports the above. For example, the Higgs mechanism in Standard Model is non-perturbative and cannot be understood from the corresponding perturbative expansion. The quark confinement in QCD cannot be understood from the perturbative QCD. So a TOE, if it exists at all, must be non-perturbative in nature.
   
4. From the view of perturbative strings, the 11-dimensional supergravity seemingly has no role to play. We know that each of the five 10-dimensional superstrings gives the corresponding supergravity in the respective low-energy limit. The lower dimensional supergravities are the low energy limits of the corresponding compactified superstrings. If the 10-dimensional superstrings are the whole story, we cannot explain the origin of the 11-dimensional supergravity which is equally good as any other supergravities on the supergravity level. Further 11-dimensional supergravity is related to type IIA 10-dimensional supergravity upon dimensional reduction on a tiny circle. Once again, we need to study non-perturbative region of string theory to understand the above supergravity connection.

We therefore conclude that the aforementioned puzzles can only be answered in the non-perturbative region of string theory. This clearly indicates that if superstrings have anything to do with nature, the non-perturbative superstrings are mostly relevant. Perturbative strings, even though they have technical advantage, play minor roles, most likely, in describing the real world. With this in mind, it is natural for us to investigate the non-perturbative properties of string theory.

Just as in quantum field theory, we have very limited knowledge of non-perturbative methods in string theory. The simplest, though quite non-trivial, is to seek possible non-perturbative states of string theory. This investigation can spell out the most useful degrees of freedom, i.e., the lightest ones, and tell us the role of string itself. During the period of 1990-93, Callan, Harvey, and Strominger as one group and Duff and myself as the other group started such a journey. We found, in terms of today’s terminology, supersymmetric BPS NS5-brane and Dp-branes from the low-energy limits of various superstrings. It turns out that the mass scales associated with these branes are equal to or less than that of a fundamental string if the dimensionless string coupling is equal to or greater than one. In other words, in the strong coupling region, NS5-branes and Dp-branes play at least equally important role as the fundamental strings. We therefore must include the dynamics of these branes into consideration. This further implies the existence of a big unknown unified theory which takes the five known perturbative superstrings and the once isolated 11-dimensional supergravity as special limits if these known theories are indeed related to the real world. This big theory is just the not-yet-constructed M-theory.

Finding the complete formulation of this theory is the current effort in the string/M theory community. We have learned many lessons from such an endeavor. For example, space-time may not be a fundamental concept and gravity may not be a fundamental interaction, either. I have no doubt that there are many conceptual revolutions in the course of finding such a theory.

Jian-Xin Lu, Ph.D.
University of Michigan
Department of Physics
Ann Arbor, Michigan, USA