The Path Integral for Gravity

Over the past three decades, the idea of a path integral over geometries, describing gravity in various dimensions, has become increasingly central to many areas of theoretical physics, including string and M-theory, holography and quantum aspects of black holes and cosmology.

In each of these areas, the path integral is frequently invoked as a formal device although, as practitioners will admit, except in very special cases the basic formula remains undefined. Typically, classical saddle points are discussed, whether real or complex, but the required integrals are left unperformed.

This state of affairs is untenable because it leaves the theory on a shaky footing and hence does not permit a sound comparison of theoretical predictions with observations. The time has come to critically reassess the foundational ideas of the path integral for gravity, including its definition, evaluation and interpretation; to identify problems with
existing uses and claims based on it, and to seek improvements. The workshop will focus on the continuum theory and its semiclassical limit, with applications to cosmology, black holes and holography. In particular, the notion of a “Euclidean path integral” for a “wavefunction of the universe” will be addressed.

To this effect we intend to revisit discussion of “quantum geometrodynamics” from the path integral viewpoint and to pursue various applications. The developments in this direction that took place in the late 1970's and early 1980's were not incorporated in subsequent efforts, where the emphasis shifted to using a classical background with quantum fluctuations superimposed on it, a split which although useful in particular approximations can hardly be imagined to lie at the  foundation of the theory. The revival of the discussion of the foundation of the path integral for gravity is made timely, we believe, by the introduction of new global methods such as Picard-Lefschetz theory.

The format of the workshop will be unusual. For the first three days, the mornings will begin with a longer, introductory lecture by each of the three organisers, setting out some of the foundational issues. This will be followed by shorter lectures by the participants, tackling the same foundational questions. The morning lectures, held in the Bob room, will be open to all Perimeter residents and visitors. They will be recorded and made available for viewing on PIRSA. Afternoons will be devoted to friendly and informal discussions, with participants invited to offer short contributions which follow up or develop points raised in the mornings, within a relaxed and highly conducive environment. Participation in these afternoon discussion sessions, as well as social events associated with the workshop, will be limited to registered workshop participants. The last two days of the workshop will be an opportunity for participants to continue discussions on topics which emerge as of greatest general interest, as well as to follow up in smaller groups on technical points or new ideas.