Skip to content Skip to navigation

Formal Quantum Field and String Theory

The study of the formal and mathematical structure of quantum field theory and string theory has undergone a renaissance in recent decades.  These subjects underlie our descriptions of phenomena across a range of energy scales, from condensed matter physics and particle physics at accessible energies, to more speculative thoughts about early-universe cosmology and physics of the Big Bang and Black Holes.  Development of understanding of the mathematical structures underlying quantum field theories and string theories in their own right has thus often had fruitful applications.   Theorists at Stanford have contributed to some fascinating developments in this area.

One direction has involved the exploration of exactly soluble models.  Theorists presently at Stanford (Kachru, Shenker) were involved with the discovery of exactly solvable models of conformal field theory in two dimensions; soluble models of string theory in d<2 dimensions; and the first techniques to find exact solutions of 4d N=2 supersymmetric field theories using string dualities and the geometry of Calabi-Yau singularities.

Stanford theorists (Kachru, Silverstein) led the development of techniques to find concrete candidate "flux vacua" in the landscape of string theory, and explore their mathematical structure. These include foundational studies of the structure of Calabi-Yau flux vacua, as well solutions involving strings on spaces of negative curvature.

A major direction in recent years is the exploration of finiteness properties of supergravity.   Kallosh was involved with this subject since its inception and has contributed many conjectures and results.

Mysterious dualities lie at the foundation of many new discoveries in string theory and its interaction with mathematical physics.  The "D-duality" relating strings on negatively curved spaces to supercritical string theory was first described at Stanford.  Explorations of new avatars of the mysterious "moonshine" relating (mock) modular forms, sporadic simple groups, algebraic geometry, and string vacua has been a subject of significant recent interest at Stanford.

 

Video Brief

Quantum Mathematics and the Fate of Space, Time, and Matter

Many mathematical concepts trace their origins to everyday experience, from astronomy to mechanics. Remarkably, ideas from quantum theory turn out to carry tremendous mathematical power too, even though we have little intuition dealing with elementary particles. The bizarre quantum world not only represents a more fundamental description of nature, it also inspires a new realm of mathematics that might be called “quantum mathematics” that turns out to be a powerful tool to solve deep outstanding mathematical problems.

Person

Liam McAllister

Liam McAllister is a professor at Cornell University.  He received his Ph.D from Stanford University in 2005.  He is interested in using string theory to understand the early universe, and in developing compactifications of string theory that lead to realistic four-dimensional physics.  Examples of his work include explicit models of D-brane inflation; applications of the AdS/CFT correspondence to determining the structure of D-brane inflation models; a model of large-field inflation based on axion shift symmetries and axion monodromy; signatures of axion monodromy inflation in the CM

Raphael Flauger

Raphael Flauger is a professor at the University of California, San Diego.  He received his Ph.D from the University of Texas at Austin in 2009.  His research interests range from phenomenological questions in cosmology and particle physics to formal questions in quantum field theory and string theory. Currently, he is interested in extracting clues about fundamental physics from cosmological observations.

News Item

Two dimensional conformal field theories (CFTs) have a very powerful property called modular invariance, which relates the high and low temperature limits of the theory.  This can give nontrivial relations between the low-energy spectrum of the theory and the high-energy spectrum.

Quantum gravity in anti de Sitter space in three spacetime dimensions is conjectured to be dual to two dimensional conformal field theories (CFTs) with sparse spectra.

One of the most powerful mathematical principles guiding our current understanding of quantum physics is symmetry.

Since 1997 physicists have understood that anti-de Sitter quantum gravity in d+1 dimensions can emerge from suitable d dimensional conformally invariant quantum field theories. This is a primary example of holography.

A talk describing a new candidate dual to pure 3d supergravity, as well as the relationship between enumerative geometry of K3 and moonshine.

Pages

Subscribe to Formal Quantum Field and String Theory