Petr Hořava

Eleven-dimensional supergravity on a manifold with boundary

Abstract 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.

Background duality of open-string models

The moduli space of open-string models is studied showing that the duality between large and small compactification radius extends also to open string theories. Using this, the Chan-Paton factors of a circle-compactified model are partly explained as coming from the set of space-time fixed points of a dual orbifold.

M theory as a holographic field theory

We suggest that M theory could be nonperturbatively equivalent to a local quantum field theory. More precisely, we present a “renormalizable” gauge theory in eleven dimensions, and show that it exhibits various properties expected of quantum M theory, most notably the holographic principle of ’t Hooft and Susskind. The theory also satisfies Mach’s principle: A macroscopically large space-time (and the inertia of low-energy excitations) is generated by a large number of “partons” in the microscopic theory. We argue that at low energies in large eleven dimensions, the theory should be effectively described by eleven-dimensional supergravity. This effective description breaks down at much lower energies than naively expected, precisely when the system saturates the Bekenstein bound on energy density. We show that the number of partons scales like the area of the surface surrounding the system, and discuss how this holographic reduction of degrees of freedom affects the cosmological constant problem. We propose the holographic field theory as a candidate for a covariant, nonperturbative formulation of quantum M theory.

Casimir Effect Between World-Branes in Heterotic M-Theory

We study a non-supersymmetric E_8 × E_8 compactification of M-theory on S^1/Z_2, related to the supersymmetric E_8 × E_8 theory by a chirality flip at one of the boundaries. This system represents an M-theory analog of the D-brane anti-D-brane systems of string theory. Alternatively, this compactification can be viewed as a model of supersymmetry breaking in the “brane-world” approach to phenomenology. We calculate the Casimir energy of the system at large separations, and show that there is an attractive Casimir force between the E_8 × E_8 boundary. We predict that a tachyonic instability develops at separations of order the Planck scale, and discuss the possibility that the M-theory fivebrane might appear as a topological defect supported by the E_8 × E_8 system. Finally, we analyze the eventual fate of the configuration, in the semiclassical approximation at large separations: the two ends of the world annihilate by nucleating wormholes between the two boundaries.

Lifshitz Gravity for Lifshitz Holography

We argue that Hořava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and a dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization of HL gravity, and show how it reproduces the full structure of the z=2 anisotropic Weyl anomaly in dual field theories in 2+1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.

Deconstructing de Sitter

Semiclassical gravity predicts that de Sitter space has a finite entropy. We suggest a picture for Euclidean de Sitter space in string theory, and use the AdS/CFT correspondence to argue that de Sitter entropy can be understood as the number of degrees of freedom in a quantum mechanical dual.

Matrix theory and heterotic strings on tori

We consider compactifications of the matrix model of M-theory on S1/Z2 × Td for d > 0, and interpret them as orbifolds of the supersymmetric U(N) Yang-Mills theory on R × Td+1. The orbifold group acts both on the gauge group and on the Td+1, reduces the gauge group to O(N) over 1 + 1-dimensional fixed-point submanifolds, and breaks half of the supersymmetry. We clarify some puzzling aspects of the gauge anomaly cancellation in the presence of spacetime Wilson lines; in general, the Yang-Mills theory requires certain Chern-Simons couplings to supergravity background fields. We discuss the possibility that D8-branes are present as certain matrix configurations in the yang-Mills theory, and the fundamental fermions emerge as zero-modes. Finally, we point out that the correspondence between matrix theory and string theory suggests the existence of a multitude of non-trivial RG fixed points and dualities in orbifold Yang-Mills theories with eight supercharges in various dimensions.

Some exact solutions of string theory in four and five dimensions

Abstract We find several classes of exact classical solutions of critical bosonic string theory, constructed as twisted products of one euclidean and one minkowskian 2D black hole coset. One class of these solutions leads (after tensoring with free scalars and supersymmetrizing) to a rotating version of the recently discovered exact black fivebrane. Another class represents a one-parameter family of axisymmetric stationary four-dimensional targets with horizons. Global properties and target duality f the solutions are briefly analyzed.We find several classes of exact classical solutions of critical bosonic string theory, constructed as twisted products of one Euclidean and one Minkowskian 2D black hole coset. One class of these solutions leads (after tensoring with free scalars and supersymmetrizing) to a rotating version of the recently discovered exact black fivebrane. Another class represents a one-parameter family of axisymmetric stationary four-dimensional targets with horizons. Global properties and target duality of the 4D solutions are briefly analyzed.

Topological rigid string theory and two-dimensional QCD

Abstract We present a string theory that reproduces the large-N expansion of two-dimensional Yang-Mills gauge theory on arbitrary surfaces. First, a new class of topological sigma models is introduced, with path integrals localized to the moduli space of harmonic maps. The Lagrangian of these harmonic topological sigma models is of fourth order in worldsheet derivatives. Then we gauge worldsheet diffeomorphisms by introducing the induced worldsheet metric. This leads to a topological string theory, whose Lagrangian coincides in the bose sector with the rigid string Lagrangian discussed some time ago by Polyakov and others as a candidate for QCD string theory. The path integral of this topological rigid string theory is localized to the moduli spaces of minimal-area maps, and calculates their Euler numbers. The dependence of the large- N QCD partition functions on the target area emerges from measuring the volume of the moduli spaces, and can be reproduced by adding a Nambu-Goto term (improved by fermionic terms) to the Lagrangian of the topological rigid string.

Equivariant topological sigma models

We identify and examine a generalization of topological sigma models suitable for coupling to topological open strings. The targets are Kahler manifolds with a real structure, i.e. with an involution acting as a complex conjugation, compatible with the Kahler metric. These models satisfy axioms of what might be called “equivariant topological quantum field theory”, generalizing the axioms of topological field theory as given by Atiyah. Observables of the equivariant topological sigma models correspond to cohomological classes in an equivariant cohomology theory of the targets. Their correlation functions can be computed, leading to intersection theory on instanton moduli spaces with a natural real structure. An equivariant CP1 × CP1 model is discussed in detail, and solved explicitly. Finally, we discuss the equivariant formulation of topological gravity on surfaces of unoriented open and closed string theory, and find a Z2 anomaly explaining some problems with the formulation of topological open string theory.