## Alexander Maloney on Solving Technical Puzzles Regarding Chiral Gravity

#### Fast Moving Front Commentary, May 2011

Article: Chiral gravity, log gravity, and extremal CFT
Authors: |

Alexander Maloney talks with ScienceWatch.com and answers a few questions about this month's Fast Moving Fronts paper in the field of Physics.

**Why do you think your paper is highly
cited?**

This work addresses a fundamental problem in theoretical physics, that of the construction of consistent, quantum mechanical theory of gravity. This is a notoriously difficult problem, and we were able to make a great deal of progress by focusing on a simple model which nevertheless maintains many of the important physical features that make quantum gravity interesting. We were able to study the exact quantum mechanical description of a theory—known as "chiral gravity"—which is a simple version of Einstein's theory of general relativity.

There are very few examples of theories of gravity which can be studied at the quantum mechanical level. To my knowledge this is the only theory of quantum gravity which is simple enough to be exactly solvable, yet is complex enough to exhibit the rich phenomena, such as black holes and cosmologies, which we would like to try to understand. This paper therefore represents an important advance in our understanding of the subject.

**Does it describe a new discovery, methodology, or
synthesis of knowledge?**

In our paper we were able to resolve several outstanding technical puzzles regarding chiral gravity, and to make contact with various related proposals by other authors. The details are too technical to go into here, but we did manage to resolve several apparent contradictions in the literature.

**Would you summarize the significance of your paper
in layman's terms?**

"My current research focuses on studying simple models of quantum cosmology -- based on those of this paper -- where these questions can be addressed directly."

Quantum mechanics and general relativity are two of the most successful theories of physics, yet they appear to be fundamentally incompatible with one another. An outstanding problem in theoretical physics is the development of a theory of quantum gravity, which would simultaneously describe physics of the very small (quantum mechanics) as well as the physics of the very large (general relativity). Such a theory would resolve several important problems, such as those involving the nature of black holes and the basic structure of quantum space-time.

While there are several important and interesting proposals for theories of quantum gravity, most proposals are difficult to study and test, either theoretically or experimentally. Our goal in this paper was to discuss a simple version of quantum gravity which can be understood with a much greater degree of precision than these other more complicated theories, such as those based on string theory. We studied a theory describing quantum gravity in a universe with two spatial dimensions, rather than the traditional three spatial dimensions.

We were able to show that this theory is completely consistent with the rules of quantum mechanics, providing a simple setting in which we can resolve many of these basic conceptual puzzles. While we of course live in a universe with three rather than two spatial dimensions, this represents an important step in our understanding of more complicated and more realistic theories of gravity.

**How did you become involved in this research, and
how would you describe the particular challenges, setbacks, and
successes that you've encountered along the way?**

I have worked on the subject of black holes and quantum gravity for several years, and more recently my work has focused on theories of quantum gravity in one less dimension which can be studied quite explicitly. The primary challenge of the present work was a mathematical one; my collaborators and I had to master several technical tools from number theory and differential geometry and apply them to the present problem.

**Where do you see your research leading in the
future?**

I would like to apply these ideas to understand the quantum theory of cosmology. The best models of cosmology indicate that the size of the universe is expanding rapidly, and indeed may be currently undergoing expansion at an accelerated rate. This seems to contradict basic notions of quantum mechanics, which state that the number of degrees of freedom of a physical system do not change in time. A theory of quantum gravity should resolve this puzzle, and in doing so will surely challenge our essential notions of space and time.

My current research focuses on studying simple models of quantum cosmology—based on those of this paper—where these questions can be addressed directly. The resolution of this puzzle has observational as well as theoretical implications, as current astronomical observations indicate that quantum mechanics played a very important role in the dynamics of the early universe.

**Do you foresee any social or political
implications for your research?**

This is research in fundamental physics for which I do not see any direct social or political implications. But I believe that whenever we expand our knowledge by better understanding the world around us this represents a benefit for society.

**Alexander Maloney
Assistant Professor of Physics
McGill University
Montreal, Quebec, Canada**

KEYWORDS: CHIRAL GRAVITY, LOG GRAVITY, EXTERNAL CFT, TOPOLOGICALLY MASSIVE GRAVITY, CONFORMAL FIELD THEORY, LOCAL BRST COHOMOLOGY, GAUGE THEORIES, CONSERVATION LAWS, BLACK HOLE, ASYMPTOTIC SYMMETRIES, LOGARITHMIC OPERATORS, CENTRAL CHARGES, STABILITY.