Prof. Washington Taylor, IV

Washington Taylor is primarily working on the problem of unifying quantum mechanics and gravity. String theory is currently the most promising candidate for a framework in which to understand quantum gravity. It is still not possible, however, to define string theory in a space-time background compatible with the physics we see around us, and string theory cannot yet be used to make specific predictions. Taylor's research focuses particularly on the problem of finding a nonperturbative and background-independent definition of string theory and M-theory, and on the related problem of analyzing solutions of this theory. The goals of this research are to understand the basic principles of quantum gravity and to understand the consequences of these principles for cosmology, the physics of the early universe, and high-energy particle physics.

Over the last decade, Taylor has worked on different approaches to finding a fundamental formulation of string theory and on understanding the physics of the new mathematical structures suggested by string theory. Taylor has made important contributions to our current understanding of the connection between gauge theories and string theories, as well as to D-brane physics, the matrix model of M-theory, and string field theory.

Currently Taylor is working on the string vacuum problem. As discussed below, the experimental observation of a positive cosmological constant and the apparent existence of a vast plethora of string vacuum solutions pose major challenges to the program of constructing a string vacuum compatible with observation and using such a vacuum to make physical predictions. Taylor's current work focuses both on the construction of new string vacua and on analyzing the space of known vacua for correlations which may lead to testable predictions.

What is string theory? -- String theory (and its alter ego M-theory) is currently the most viable candidate for a unified theory of physics which describes all forces of nature, encompassing the physics of gravity as well as quantum field theory. The traditional world-sheet approach to string theory gives a consistent local theory of quantum gravity, and allows for the computation of perturbative scattering processes for gravitons, gauge particles, and excited strings. While this approach shows that string theory is a good quantum theory of gravity locally, it requires that the global space-time background be put in by hand. This approach has several limitations: it cannot describe physics beyond perturbation theory, and cannot (yet) be defined in realistic space-time backgrounds (such as de Sitter space or string compactifications with fluxes). Recent nonperturbative approaches to string theory, such as the M(atrix) theory and AdS/CFT pictures, give more powerful nonperturbative descriptions of string theory and M-theory, but only in fixed asymptotic backgrounds with vanishing or negative cosmological constant. Since recent observations that the rate of expansion of the universe is accelerating indicate that there is a positive (but extraordinarily small) cosmological constant in the observable region of the universe, we are still lacking a description of string theory which may be applicable to the observed universe.

The string vacuum problem -- One remarkable feature of string theory is that the theory is only consistent in a space-time with 10 dimensions (11 for M-theory). Since we only observe three macroscopic spatial dimensions and one time dimension, string theory predicts 6 "extra" dimensions (7 for M-theory). An elegant way of reconciling this apparent disagreement is through the Kaluza-Klein mechanism: the extra six dimensions may be curled up into a tiny compact manifold, so small that it is unobservable to us. For a special class of 6-dimensional manifolds, called Calabi-Yau manifolds, the resulting macroscopic 4-dimensional physics is a supersymmetric theory of gravity with matter and gauge fields, similar in spirit to the field theory governing our patch of the universe. We can even define perturbative string theory in such a Calabi-Yau "compactification." There are some differences in the detailed physics of these models from what we observe, however. In particular, a) in these Calabi-Yau compactifications there are always massless scalar fields ("moduli") associated with free parameters in the choice of compactification, b) the 4D physics described by these models is supersymmetric, c) in these models the cosmological constant vanishes identically.

To match string theory to experimental observation, therefore, we must add further ingredients to the story. One very promising approach is to include generalized fluxes on the Calabi-Yau. This involves turning on topologically discretized field strengths which appear in string theory and which generalize the familiar magnetic flux of standard electromagnetism. Although string theory cannot be rigorously defined in backgrounds with these fluxes, consideration of the low-energy supersymmetric gravity fields in these backgrounds shows that in the presence of generalized fluxes, the free parameters (moduli) of the compactification are generically forced to take fixed values, and the cosmological constant may take a nonzero value. Supersymmetry can either be broken at this stage, or by including other types of effects.

This gives a plausible framework in which string theory may give rise to physics like that we see around us. Other related approaches come from compactifying different limits of string theory and M-theory on other kinds of spaces. At this point, however, we encounter a major challenge. It seems that the number of consistent ways in which the compactification manifold and associated fluxes can be chosen is enormous. In fact, the number of such possible vacua is infinite; but even after imposing some simple physical constraints to restrict to a finite number of vacua, the theory may still give rise to numbers of vacua like 101000 or more.

The appearance of this large number of apparent vacua, with no obvious selection mechanism to choose one over any other, has given rise to a substantial controversy in the theoretical physics community. It is clearly of central importance to understand how this large number of solutions may be understood in order to plausibly relate string theory to experimental physics. One possible scenario, which has attracted many adherents as well as many detractors, is the notion that the mechanism of eternal inflation may give rise to a truly expansive cosmos, in which different solutions of string theory are realized in different local pockets of the universe. In this scenario, the
cosmological constant would take different values in different regions of the "multiverse," and, as shown by Weinberg, only in regions where this constant is incredibly small such as our own, would structure such as galaxies form. While the cosmological constant has been measured to be 10(-120) in natural units, it seems that string theory has enough solutions in principle that, if this constant is reasonably uniformly distributed, there will still be many regions with the experimentally observed value. Though such an "environmental" determination of a fundamental constant of nature is objectionable to many scientists, until another plausible mechanism for generating a small cosmological constant is found, it seems we must take this scenario seriously. In any case, it is clearly of fundamental importance to understand the space of possible string vacua and their properties.

Taylor's current research is focused on understanding the space of string vacua and addressing questions relevant to this controversy and to the problem of relating string theory to experiment. Recent papers, mentioned below, suggest that the space of possible string vacua is even larger than previously believed. Ongoing work involves
studying special classes of these vacua to find correlations which may dictate observable physics.