Albion Lawrence

Open string instantons and superpotentials

The authors study the F-terms in N = 1 supersymmetric, d = 4 gauge theories arising from D(p + 3)-branes wrapping supersymmetric p-cycles in a Calabi-Yau threefold. If p is even the spectrum and superpotential for a single brane are determined by purely classical ({alpha}{prime} {r{underscore}arrow} 0) considerations. If p = 3, superpotentials for massless modes are forbidden to all orders in {alpha}{prime} and may only be generated by open string instantons. For this latter case the authors find that such instanton effects are generically present. Mirror symmetry relates even and odd p and thus perturbative and nonperturbative superpotentials; the authors provide a preliminary discussion of a class of examples of such mirror pairs.

An ignoble approach to large field inflation

We study an inflationary model developed by Kaloper and Sorbo, in which the inflaton is an axion with a sub-Planckian decay constant, whose potential is generated by mixing with a topological 4-form field strength. This gives a 4d construction of ``axion monodromy inflation: the axion winds many times over the course of inflation and draws energy from the 4-form. The classical theory is equivalent to chaotic inflation with a quadratic inflaton potential. Such models can produce ``high scale inflation driven by energy densities of the order of (1016GeV)4, which produces primordial gravitational waves potentially accessible to CMB polarization experiments. We analyze the possible corrections to this scenario from the standpoint of 4d effective field theory, identifying the physics which potentially suppresses dangerous corrections to the slow-roll potential. This yields a constraint relation between the axion decay constant, the inflaton mass, and the 4-form charge. We show how these models can evade the fundamental constraints which typically make high-scale inflation difficult to realize. Specifically, the moduli coupling to the axion-four-form sector must have masses higher than the inflationary Hubble scale (1014GeV). There are also constraints from states that become light due to multiple windings of the axion, as happens in explicit string theory constructions of this scenario. Further, such models generally have a quantum-mechanical ``tunneling mode in which the axion jumps between windings, which must be suppressed. Finally, we outline possible observational signatures.

Signatures of short distance physics in the cosmic microwave background

We systematically investigate the effect of short distance physics on the spectrum of temperature anistropies in the Cosmic Microwave Background produced during inflation. We present a general argument-assuming only low energy locality-that the size of such effects are of order H^2/M^2, where H is the Hubble parameter during inflation, and M is the scale of the high energy physics. We evaluate the strength of such effects in a number of specific string and M theory models. In weakly coupled field theory and string theory models, the effects are far too small to be observed. In phenomenologically attractive Horava-Witten compactifications, the effects are much larger but still unobservable. In certain M theory models, for which the fundamental Planck scale is several orders of magnitude below the conventional scale of grand unification, the effects may be on the threshold of detectability. However, observations of both the scalar and tensor fluctuation contributions to the Cosmic Microwave Background power spectrum-with a precision near the cosmic variance limit-are necessary in order to unambiguously demonstrate the existence of these signatures of high energy physics. This is a formidable experimental challenge.

Causality & holographic entanglement entropy

A bstractWe identify conditions for the entanglement entropy as a function of spatial region to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove that the covariant holographic entanglement entropy prescription (which relates entanglement entropy of a given spatial region on the boundary to the area of a certain extremal surface in the bulk) obeys these conditions, as long as the bulk obeys the null energy condition. While necessary for the validity of the prescription, this consistency requirement is quite nontrivial from the bulk standpoint, and therefore provides important additional evidence for the prescription. In the process, we introduce a codimension-zero bulk region, named the entanglement wedge, naturally associated with the given boundary spatial region. We propose that the entanglement wedge is the most natural bulk region corresponding to the boundary reduced density matrix.

Mirror symmetry for open strings

The authors discuss the generation of superpotentials in d = 4, N = 1 supersymmetric field theories arising from type IIA D6-branes wrapped on supersymmetric three-cycles of a Calabi-Yau threefold. In general, nontrivial superpotentials arise from sums over disc instantons. They then find several examples of special Lagrangian three-cycles with nontrivial topology which are mirror to obstructed rational curves, conclusively demonstrating the existence of such instanton effects. In addition, they present explicit examples of disc instantons ending on the relevant three-cycles. Finally, they give a preliminary construction of a mirror map for the open string moduli, in a large-radius limit of the type IIA compactification.

Initial Conditions for Inflation

Free scalar fields in de Sitter space have a one-parameter family of states invariant under the de Sitter group, including the standard thermal vacuum. We show that, except for the thermal vacuum, these states are unphysical when gravitational interactions are included. We apply these observations to the quantum state of the inflaton, and find that at best, dramatic fine tuning is required for states other than the thermal vacuum to lead to observable features in the CMBR anisotropy.

Derived Categories and Zero-Brane Stability

We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This derivation is a variant of some ideas proposed recently by Douglas. We then argue that any 0-brane on any Calabi-Yau threefold must become unstable along some path in the Kahler moduli space. As a byproduct of this analysis we see how the derived category can be invariant under a birational transformation between Calabi-Yaus.

On the instability of 3d null singularities

Apparatus for supporting a body on a carrier in a desired angular position while the carrier is mounted on a moving base, such as a ship, includes an electrically operated drive for angularly moving the carrier relative to the base about a normally horizontally extending axis. The control device for controlling the drive includes a first signal generator which senses the rate of angular movement of the carrier in a plane perpendicular to the afore-mentioned axis and generates a first signal indicative of the sensed rate. A second signal generator includes a mercury switch and generates a second, constant, D.C. signal indicative of the absence or presence of a predetermined angular position of the mercury switch in plane perpendicular to the axis. A circuit connected to the signal generators and the drive transmits to the drive an electrical operating signal in response to the first and second signals and thereby causes the mercury switch to be moved by the drive into its predetermined angular position.

Insightful D-branes

We study a simple model of a black hole in AdS and obtain a holographic description of the region inside the horizon. A key role is played by the dynamics of the scalar fields in the dual gauge theory. This leads to a proposal for a dual description of D-branes falling through the horizon of any AdS black hole. The proposal uses a field-dependent time reparameterization in the field theory. We relate this reparametrization to various gauge invariances of the theory. Finally, we speculate on information loss and the black hole singularity in this context.

Black hole evaporation along macroscopic strings.

We develop the quantization of a macroscopic string which extends radially from a Schwarzschild black hole. The Hawking process excites a thermal bath of string modes that causes the black hole to lose mass. The resulting typical string configuration is a random walk in the angular coordinates. We show that the energy flux in string excitations is approximately that of spacetime field modes.