Theoretical Research

STRING THEORY

Professor Brian Greene


String theory has emerged as the most promising mathematical framework for a unified description of nature. A fascinating aspect of string theory is that extended objects (strings) perceive spacetime geometry very differently from point particles. Processes which rip or tear the fabric of spacetime are physically allowed in string theory; the strings simply don't realize that a singularity is present. This makes it possible to have physical processes which change the topology of spacetime.

String theory is automatically a theory of quantum gravity. As such, it should be possible to understand the process of black hole formation and evaporation within string theory. This is made difficult by the fact that black holes are intrinsically non-perturbative. The discovery of AdS/CFT duality and its generalizations has given a whole new perspective on this problem. These dualities provide a non-perturbative definition of string theory, in terms of a dual non-gravitational quantum field theory. The challenge then becomes understanding the way in which gravitational physics, and in particular the physics of black holes, emerges from the dual field theory.

QUANTUM FIELD THEORY

Professor Al Mueller, Professor Erick Weinberg

Quantum field theory provides the underlying framework for almost every area of theoretical physics, from inflationary cosmology to condensed matter physics. Extracting physical predictions from quantum field theory is a real challenge, in some cases requiring numerical simulations (for example lattice gauge theory). However in some cases analytical tools are available.

An important analytical approach to understanding quantum field theory is through the study of classical field configurations. Many quantum field theories have soliton solutions which carry magnetic charge. By studying the dynamics of these magnetic monopoles, one can obtain non-perturbative information about the behavior of the quantum field theory. In particular, in certain supersymmetric field theories, magnetic monopoles have provided crucial evidence for S-duality -- a symmetry which maps strong coupling to weak coupling, and exchanges electric and magnetic charge.

PARTICLE & NUCLEAR THEORY

Professor Norman Christ, Professor Robert Mawhinney, Professor Al Mueller & Professor Erick Weinberg

A major goal of current work on strong interactions is to understand QCD under extreme conditions. In large part this is due to the exciting prospect of creating a deconfined quark-gluon plasma at RHIC, a heavy ion collider now running at Brookhaven. Given the complicated multi-particle dynamics of a heavy ion collision, clear signatures of a quark-gluon plasma are difficult to come by. Reliable predictions require a good understanding of nuclear and nucleon structure, thermalization processes in a heavy-ion collision, the nature of the QCD phase transition, and the hydrodynamics of a quark-gluon plasma.

QCD also exhibits interesting behavior at high baryon density. When the baryon density is sufficiently large, it becomes energetically favorable for quarks to bind together in pairs. This pairing is the analog of Cooper pairing in ordinary superconductivity. The pairing turns the QCD ground state into a color superconductor -- a novel phenomenon which could be important for understanding core-collapse supernovae.

LATTICE GAUGE THEORY

Professor Norman Christ, Professor Robert Mawhinney

Columbia has a large group working on lattice gauge theory. The group has pioneered the practical applications of domain wall fermions to lattice QCD. This technique allows one to realize chiral symmetry on a lattice, at the price of introducing an extra spatial dimension. Good control over chiral symmetry makes it possible to study many previously intractable problems. For example, using domain wall fermions, the lattice group recently carried out a benchmark theoretical calculation of the CP-violating parameter epsilon'/epsilon, recently measured in kaon decays at CERN and Fermilab.

The necessary large-scale lattice calculations have been made possible through the in-house development of some impressive computer resources. A custom-built massively parallel supercomputer (20000 processors, teraflop performance) has been running lattice simulations for the past 3 years. A next-generation, 10 teraflop machine is currently under development. See the lattice page for more information.

CONDENSED MATTER THEORY

Professor Igor Aleiner, Professor Allan Blaer, Assoc. Professor Timothy Halpin-Healy, Professor Andrew Millis

The Columbia condensed matter theory group investigates many aspects of the physics of matter, from the possibility of novel electronic states in new materials or near quantum critical points to the applied physics of spins in semiconductors and heterostructures. The group has strong connections to faculty in chemistry and chemical engineering working on biophysics and other topics. A. J. Millis has recently joined the group, which is expected to grow further in the coming years.

ASTROPHYSICS & COSMOLOGY

Assoc. Professor Andrei Belobodorov, Professor Brian Greene, Professor Lam Hui, Professor Mal Ruderman, Professor Erick Weinberg

According to the inflationary paradigm, the early universe underwent a period of exponential expansion. This exponential expansion was originally proposed as a way of solving many of the problems of conventional cosmology. Inflation could make cosmology very sensitive to Planck-scale physics, since the enormous expansion can easily stretch sub-Planckian distances to have the size of today's observable universe. Thus cosmology may turn out to be the best arena for testing string theory, a possibility which is being vigorously explored at the ISCAP center.