We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z = 3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is power-counting renormalizable in 3 + 1 dimensions. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory flows naturally to the relativistic value z = 1, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. The effective speed of light, the Newton constant and the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic z = 3 theory at short distances.

We propose that the ten-dimensional E 8 × E 8 heterotic string is related to an elevendimensional theory on the orbifold R 10 × S 1 /Z 2 in the same way that the Type IIA string in ten dimensions is related to R 10 × S 1 . This in particular determines the strong coupling behavior of the ten-dimensional E 8 × E 8 theory. It also leads to a plausible scenario whereby duality between SO(32) heterotic and Type I superstrings follows from the classical symmetries of the eleven-dimensional world, just as the SL(2, Z) duality of the ten-dimensional Type IIB theory follows from eleven-dimensional diffeomorphism invariance.October, 1995 * horava@puhep1.princeton.edu.

In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with boundary, which is believed to be relevant to the strong coupling limit of the E 8 ×E 8 heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of E 8 for each boundary component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum M -theory with eleven-dimensional supergravity as its low energy limit.March, 1996 * horava@puhep1.princeton.edu.

We propose a quantum theory of membranes designed such that the ground-state wavefunction of the membrane with compact spatial topology Σ h reproduces the partition function of the bosonic string on worldsheet Σ h . The construction involves worldvolume matter at quantum criticality, described in the simplest case by Lifshitz scalars with dynamical critical exponent z = 2. This matter system must be coupled to a novel theory of worldvolume gravity, also exhibiting quantum criticality with z = 2. We first construct such a nonrelativistic "gravity at a Lifshitz point" with z = 2 in D + 1 spacetime dimensions, and then specialize to the critical case of D = 2 suitable for the membrane worldvolume. We also show that in the second-quantized framework, the string partition function is reproduced if the spacetime ground state takes the form of a Bose-Einstein condensate of membranes in their first-quantized ground states, correlated across all genera.