String theory is the most promising candidate for the unification of the Standard Model with General Relativity in a framework consistent with Quantum Theory. The Anti-de Sitter/Conformal Field Theory (AdS/CFT) conjecture has revolutionized the field by providing a quantitative correspondence between Yang-Mills theory in 4 dimensions and string theory in 10 dimensions. The goal of the research proposed here is to improve our understanding of perturbative and non-perturbative string theory, including the dynamics of black holes, the time evolution of gravitational systems, certain aspects of QCD, and non-equilibrium thermodynamics in strongly coupled gauge theories, often through the AdS/CFT correspondence. Developing a precise quantitative prescription for superstring perturbation theory is also a goal of this proposal. The PIs plan to further their study of exact solutions of Supergravity theories with extended supersymmetry, investigate their AdS/CFT duals, and related interface conformal field theories. The broader impacts of this research group are as follows: the PIs run a weekly journal club on string theory and related topics, and help organize a bi-annual seminar series with local institutions. They are actively involved in outreach and participate in the QuarkNet program. One PI developed and teaches yearly a "Scientific Writing Course" for UCLA's Graduate Assistants in Areas of National Need (GAANN) program, and presents "Scientific Writing Workshops" for UCLA's Office of Outreach, Diversity and Fellowship. D'Hoker is involved in the leadership of the Aspen Center for Physics.
The outcomes of the research supported by this grant are in the general area of string theory and gauge/gravity duality. Some of the major achievements of this work include an improved understanding of perturbative supersymmetry breaking in Heterotic superstring theory and the associated generation of a vacuum energy; the discovery of black hole solutions in higher spin theories and the establishment of their role in the dynamics of higher spin theories; the discovery of a holographic meta-magnetic phase transition whose predicted critical exponents are comparable to experimental values; and the construction of exact supergravity solutions which play a key role in the gauge/gravity duality of theories with topological defects and interfaces. Below, two of these outcomes will be highlighted in more detail at a non-technical level. Gauge/gravity duality is a conjectured correspondence between a quantum field theory which does not include gravity and a gravitational theory living in a higher dimensional curved space. This correspondence is holographic in the sense that all the information of the higher dimensional theory is encoded in the lower dimensional theory and vice versa. In the last decade gauge/gravity duality has become an important tool in theoretical physics, both for studying field theories and for gaining understanding on the workings of gravity. The duality was discovered, and originally developed, for systems with relativistic invariance (which is a symmetry of space and time analogous to the rotational symmetry which relates different spatial directions). While relativistic invariance is important for elementary particles, many real world systems do not enjoy this symmetry. It has since become clear that the gauge/gravity duality extends to certain non-relativistic systems, thereby paving the way for applications to condensed matter physics. In particular, the temperature and entropy of a thermal state in quantum field theory correspond to the Bekenstein-Hawking temperature and entropy of an associated black hole on the gravity side. Spin is a fundamental attribute of any particle; for example, the electron has spin 1/2 and the photon, which is the quantum of light, has spin 1. The graviton, which is the quantum of the gravitational force, has spin 2. Research was carried out on the topic of higher spin gravity, which is a theory that generalizes Einstein's theory of general relativity to incorporate massless particles of spin greater than 2. Although such theories do not directly describe our universe, they are of much theoretical interest for a variety reasons, among them that they serve as a toy-model to understand a foundational question in string theory: What are the underlying symmetry principles of string theory ? In addition they provide qualitatively new examples of holographic duality. One of the major achievements of work funded by this grant was the characterization and study of black hole solutions in the three-dimensional version of higher spin gravity. Black hole solutions play a central role in attempts to understand quantum gravity and holographic duality, primarily due to the discovery by Hawking in the 1970s that they are thermodynamic objects carrying a huge amount of entropy, the microscopic basis of which is still not entirely understood. Black holes are usually defined by the causal properties of their spacetime geometry; namely they are associated with event horizons, regions of spacetime from which no particle or signal can escape. However, standard geometrical notions do not apply in a world governed by higher spin gravity, and so one needs new criteria to define black holes in these theories. The PIs made a new proposal for defining higher spin black holes, and went on to make detailed checks by comparing with the properties of a generalized thermal state in the holographically dual description. More specifically, the entropy of these black holes, as well as the propagation of matter fields in their presence, was studied and successfully matched to microscopic computations in conformal field theory. Subsequent work by many other authors has confirmed, extended, and elaborated on this story. Another major outcome of the research supported by this grant is the discovery, via holography, of a quantum phase transition in a system with non-zero charge density and external magnetic field. The system is studied using gauge/gravity duality via an Einstein/Maxwell/Chern-Simons theory in five space-time dimensions, whose black hole solutions correspond to definite quantum states in the gauge theory. The transition is meta-magnetic as it occurs across a point of non-zero magnetic field. One the gravity side, the quantum critical point corresponds to a transition from a charged black hole to a neutral black hole of vanishing size. Holography allows not only to establish the existence of such a quantum phase transition, but also to study the entire critical region and to derive critical exponents. Remarkably, a good match was found, where applicable, with critical exponents obtained experimentally in certain Ruthenates, which are materials studied experimentally in superconductivity.
