AdS/CFT Correspondence

Motivation:

Answering some of the most fascinating questions in fundamental physics, such as those concerning the origin of the Universe or the structure of spacetime, requires a better understanding of quantum gravity than we presently possess. Motivated by this, my research has focused on gravitational aspects of string theory, especially within the framework of AdS/CFT correspondence. My aim is to use this holographic relation between string theory and quantum field theory to recast profound quantum gravitational questions into a more tractable field theoretic language. However, in order to use the AdS/CFT correspondence to probe quantum gravity, we must understand the explicit dictionary between the two sides. My past work has in large part focused on extending this dictionary. In particular, much of my previous research was aimed at elucidating the nature of spacetime in quantum gravity.

This page gives a short background and motivation for using the AdS/CFT framework to explore quantum gravity. (For a more extensive review I’ve written for the GR audience, see the chapter “The AdS/CFT Correspondence” published in ‘Milestones of General Relativity’ focus issue of CQG for the Centenary Year of GR.)

Background:

General Relativity and Quantum Mechanics, the two pillars of theoretical physics developed in the early part of the 20th century, comprise the framework to formulate the Standard Model of Particle Physics and of Cosmology. General Relativity is a theory of gravity; in particular, it identifies gravity with curvature of spacetime. Its effects are therefore most pronounced in strongly gravitational settings, such as in the context of black holes and cosmology. On the other hand, Quantum Mechanics, which involves an intrinsically probabilistic description, exhibits its most striking effects on small scales. Within their respective regimes of applicability, these theories have been substantially tested and found to describe the observed universe with remarkable accuracy.

However, as they stand, the two theories are mutually incompatible. General relativity is a classical (i.e. non-quantum) theory; spacetime is dynamical, but not subject to quantum fluctuations and uncertainties. This gives rise to profound paradoxes and poses fundamental obstacles in applying ideas of quantum mechanics to strongly gravitational systems. More importantly, many intriguing questions in fundamental physics, such as those pertaining to the origin of the Universe or the structure of spacetime, require deeper understanding of quantum gravity.

Happily, string theory offers a framework wherein one can explore the basic ideas of quantum gravity, since it manifestly obeys the axioms of quantum mechanics while incorporating gravitational interactions. Indeed, the main appeal of string theory stems from its elegant unification of gravity with the other interactions. An especially useful paradigm to investigate the properties of quantum gravity within string theory is provided by the AdS/CFT correspondence.

Statement of the AdS/CFT correspondence:

This conjectured duality, formulated by Maldacena in 1997, states that the same physical system is described by two seemingly disparate theories. Specifically, string theory on asymptotically Anti-de Sitter (AdS) spacetime is dual, i.e. physically equivalent, to a 4-dimensional supersymmetric Yang-Mills conformal field theory (CFT). The CFT can be pictured as living on the boundary of AdS; hence this is an example of a holographic duality: the two theories, describing the same physics, are formulated in different number of spacetime dimensions. As quantum field theories have been well-studied, this correspondence provides a new perspective to address long standing quantum gravitational questions.

The AdS/CFT duality has been immensely useful in clarifying many qualitative aspects of gravitational dynamics. For instance, unitarity of the gauge theory indicates that the process of black hole formation and evaporation in the full quantum gravity should likewise be unitary (though precisely how the CFT descpribes this process is presently a subject of lively debate generally referred to as “firewalls” discussion). However, quantitative checks have proved difficult to carry out, largely because spacetime is “emergent” in the field theoretic description. In other words, the intrinsic variables describing the gauge dynamics have to rearrange themselves to act according to the laws of gravitation; the precise manner in which they do so remains a deep open question, but one ripe for exploration. Indeed, this has formed the underlying motivation for much of my past work.