Last updated 1/2/2018
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Taylor's research is focused on basic questions of fundamental physics: How can we describe quantum physics and gravity in a unified framework? And how does the observed standard model of particle physics fit into such a unifying framework for quantum gravity?
The "Standard Model" of particle physics is a quantum field theory that gives incredibly precise predictions for virtually all aspects of fundamental physics that can be observed experimentally and do not involve gravity (dark matter being a notable exception). Unfortunately, however, the methods of quantum field theory do not work with the gravitational force as described by Einstein's general theory of relativity, and physicists have struggled over the last century to find a theory that unifies quantum physics and gravity.
"String theory" refers to a collection of ideas and methodologies for describing a large class of quantum theories of gravity. While there is not yet a complete mathematically coherent formulation of string theory that captures all branches of the theory, there are several distinct consistent approaches that describe "patches" of what appears to be a single unifying framework. Furthermore, due in part to the work of Taylor and collaborators (see here) it is known that when enough symmetry is imposed, the set of quantum gravity theories is strongly constrained, and all consistent quantum theories of gravity are realized in string theory. These results, along with many other clues, suggest that there exists a unique unifying framework for quantum gravity, and that the tools of string theory allow us to describe many solutions of this theory.
There are many distinct "vacuum solutions" of string theory, corresponding to physical theories in a variety of space-time dimensions, with different forces like electromagnetism and the strong and weak nuclear forces, and with a variety of different types of matter. Perturbatively, each of these vacuum solutions looks like a distinct theory of quantum gravity, but these solutions are connected non-perturbatively at a more fundamental level and it is perhaps better to think of each vacuum solution as a distinct phase of a single theory. Some of these theories, or phases, have a structure very close to that of the standard model, and others are quite different. Because string theory has so many different solutions, some scientists have expressed concern that it may be difficult for string theory to make specific predictions. String theory does, however, place constraints on the kinds of forces, matter, and interactions that can appear in any of its solutions. One of the main goals of Taylor's research program is to elucidate these constraints, and to understand how the observed structure of the standard model, and observed cosmological features of the large-scale universe, fit with the structure of string theory vacuum solutions.
The vacuum solutions that are best understood are those that have supersymmetry. Supersymmetry is a symmetry not yet observed in nature, which relates particles with different quantum spins: supersymmetry relates fermions, such as the electron, which have half integer quantum spin, with bosons, such as the photon, which have integer quantum spin. Supersymmetry is not a symmetry of observed low-energy physics; a number of clues, such as dark matter, and the relatively light mass of the Higgs particle, suggest that supersymmetry may be restored at experimentally accessible energy scales, though there are no hints yet of supersymmetry from the Large Hadron collider, or other current experiments. Nonetheless, supersymmetry is a powerful theoretical tool, and like symmetries in many other physical systems, provides a considerable simplification for analytic approaches to theories with quantum gravity. Supersymmetry is therefore useful in theoretical analysis of the structure of quantum gravity, even if it is not realized at experimentally accessible energies in nature.
Taylor's research program in recent years has focused on developing a global understanding of the space of supersymmetric string vacua and supergravity theories.
The big picture goals of this research program are:
While these may appear to be very general and ambitious goals, in higher dimensions and with supersymmetry, the symmetries of the problem are sufficiently strong that analysis is mathematically tractable and substantial progress has been made. The challenge is to use insight from the analysis of theories with more symmetry to develop tools for studying quantum gravity theories in four dimensions with a minimal amount of supersymmetry.
More generally, Taylor has worked on a variety of problems in the area of quantum gravity in string theory, including fundamental formulations of string theory such as string field theory, matrix models and M-theory, nonperturbative physics of string theory such as D-brane dynamics, and connections between string theory, quantum field theory, and cosmology. Taylor has also worked on other problems, including an early paper on using quantum computers to simulate quantum systems.
In theories with many space-time dimensions, supersymmetry strongly constrains the set of possible theories, so that the set of quantum consistent theories of gravity with supersymmetry matches closely with the set of possible string theory vacua. Studying these higher-dimensional theories has given tools for the global characterization of the set of theories.
In 11 and 10 dimensions, the constraints of relativistic (Poincare) symmetry and supersymmetry are sufficient that there are only 5 distinct massless spectra associated with supersymmetric theories of quantum gravity without anomalies that would destroy the structure of the theory. All these spectra are associated with specific string theory vacua, so at the level of the low-energy (massless) spectrum of the theory, all 10-dimensional and 11-dimensional theories of quantum gravity with supersymmetry are realized in string theory, so string theory is essentially the unique theory of quantum gravity in this context. The goal of Taylor's research program is to classify and understand theories in progressively lower dimensions, aiming at understanding four-dimensional theories that may describe observed physics.
In six dimensions, the space of supergravity theories, and the corresponding space of string theory solutions, forms a single continuous connected space. Taylor and collaborators, and other researchers, have developed a fairly complete global picture of the space of 6D supergravity theories that come from string theory using an approach known as "F-theory". Constraints on 6D supergravity theories from the cancellation of anomalies and other quantum consistency conditions provide strong bounds on the set of allowed gauge groups and matter that can arise in six dimensions. In some regimes, these constraints match closely with the constraints of string theory. There are also, however, some low-energy theories with gauge fields and matter that appear consistent but that cannot be realized in any known string theory construction. Part of the goal of Taylor's current work is to understand whether models in this "swampland" actually suffer from as-yet-unknown quantum inconsistencies, or may be realized using as-yet-unknown string theory constructions. In addition to its physical relevance and providing insight that can be applied in four dimensions as well, this work has also given rise to new insights and progress on the long-standing mathematical problem of classifying Calabi-Yau manifolds.
Taylor and collaborators are now applying analogous methods in four dimensions to identify generic features in the large class of string theory vacua described through F-theory.
At a more technical level, primary specific goals of this program currently include:
Taylor's current graduate students are:
Different 4D F-theory vacua are constructed using geometric spaces known as elliptically fibered Calabi-Yau fourfolds. Elliptic Calabi-Yau fourfolds can be classified according to the complex three-dimensional manifold that acts as the base for the fibration. While the work of Taylor, Wang, and others has led to a global picture of the set of 6D F-theory models and the associated elliptic Calabi-Yau threefolds, the number of complex threefold bases that support an elliptically fibered Calabi-Yau fourfold is enormous, and until recently has not been understood in any systematic way. In a pair of recent papers (TW-MC-1, TW-MC-2), Taylor and Wang have developed Monte Carlo methods for systematically studying a connected graph describing toric threefold bases. This gives for the first time a global picture of the structure of an enormous space of connected string theory vacua in four dimensions.
String theory famously has a huge number of vacuum solutions, usually understood in terms of an exponentially large number of distinct "fluxes" that can be placed on compactification geometries, but this work shows that even the number of geometries can be exponentially large, with at least 10^3000 threefold geometries appearing in this analysis.
The most fundamental feature of matter fields is how they transform under the gauge symmetry of a theory, which is described mathematically by a representation of the gauge group. In the standard model, for example, quarks transform in the fundamental representation of the SU(3) strong nuclear force, and electrons and quarks have fixed charges under the electromagnetic U(1) gauge group. While string theory can give rise to matter in a variety of representations, at least in known formulations of string theory not all representations are possible. In F-theory, for example, only a simple set of representations appear generically, and until recently only a few specific examples of more "exotic" representations had been found. In a recent paper, Raghuram and Taylor, with co-authors David Morrison (UCSB) and Denis Klevers (CERN), found a systematic way of understanding exotic matter representations in F-theory, which appear when the elliptic fibration describing the F-theory geometry becomes singular over a seven-brane locus that is itself singular. This analysis gives a systematic way of understanding the representations of matter that are possible in F-theory, and shows that the constraints on the representation/charges of matter from this formulation of string theory are quite strong. This suggests that more generally, string theory may only give rise to a very limited set of possible representations and charges for low-energy theories. This paper focuses on matter representations under nonabelian gauge groups. More recently, in another paper Raghuram has identified some exotic (higher charge) matter constructions under abelian U(1) groups (analogous to electromagnetism) in F-theory.
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