Shaun D. Hampton

A bstract: An interesting class of time dependent backgrounds in 1 + 1 dimensional string theory involves worldsheet Liouville walls which move in (target space) time. When a parameter in such a background exceeds a certain critical value, the speed of the Liouville wall exceeds the speed of light, and there is no usual S-Matrix. We examine such backgrounds in the dual c = 1 matrix model from the point of view of fluctuations of the collective field, and determine the nature of the emergent space-time perceived by these fluctuations. We show that so long as the corresponding Liouville wall remains time-like, the emergent space time is conformal to full Minkowski space with a time-like wall. However, for the cases where the Liouville wall is superluminal, the emergent space-time has a space-like boundary where the collective field couplings diverge. This appears as a space-like singularity in perturbative collective field theory. We comment on the necessity of incorporating finite N , as well as finite (double-scaled) coupling, effects to understand the behavior of the exact theory near this boundary.

A bstract: Orbifold CFTs contain twist operators that can join and split copies of the CFT. In this paper, we study the effects of four twist-2 operators on two copies of a single free boson. A recent study analyzed their effects on the vacuum, finding a nontrivial left-right mixing that arises from the fact that the covering surface is a torus, while the effects of one or two twist-2 operators do not produce such mixing. Here, we extend this analysis to excited states and find a similar left-right mixing. Furthermore, we explore the continuum, or high-energy, limit and show that the left-right mixing becomes negligible in this limit.

Using the D1D5 CFT we investigate transitions involving a member of a certain class of states called superstrata states, which are holographically dual to certain smooth, horizonless, 1/8-BPS, three-charge black hole microstates known as superstrata. We study these transitions by deforming the CFT away from the free orbifold point using a marginal deformation which contains a twist operator and a supercharge operator. We apply two marginal deformations to an initial state containing a graviton acting on a superstratum state. We compute amplitudes capturing transitions from this state to a graviton acting on a microstratum state, a member of a class of states which are holographically dual to certain smooth, horizonless, non-BPS, three-charge black hole microstates known as microstrata, non-BPS analogues of superstrata. We compare the resulting amplitude for various initial and final state energies to determine the preferred transition process. This may give hints as to how the dual superstratum geometry may preferentially back-react in this setting.

Symmetric orbifold CFTs contain twist operators that can join and split copies of the CFT, leading to the creation of pairs from the vacuum. In this paper, we study the pair creation processes involving four twist-2 operators. In addition to the pair creation previously observed purely in the left or right moving sectors, we find a novel mixing between left and right movers during pair creation. This phenomenon arises from nontrivial monodromy conditions that originate from a genus-one covering surface, where left and right movers become coupled through the torus.

Using the D1D5 CFT we investigate transitions involving a member of a certain class of states called superstrata states, which are holographically dual to certain smooth, horizonless, $1/8$-BPS, three-charge black hole microstates known as superstrata. We study these transitions by deforming the CFT away from the free orbifold point using a marginal deformation which contains a twist operator and a supercharge operator. We apply two marginal deformations to an initial state containing a graviton acting on a superstratum state. We compute amplitudes capturing transitions from this state to a graviton acting on a microstratum state, a member of a class of states which are holographically dual to certain smooth, horizonless, non-BPS, three-charge black hole microstates known as microstrata, non-BPS analogues of superstrata. We compare the resulting amplitude for various initial and final state energies to determine the preferred transition process. This may give hints as to how the dual superstratum geometry may preferentially back-react in this setting.

Symmetric orbifold CFTs contain twist operators that can join and split copies of the CFT, leading to the creation of pairs from the vacuum. In this paper, we study the pair creation processes involving four twist-2 operators. In addition to the pair creation previously observed purely in the left or right moving sectors, we find a novel mixing between left and right movers during pair creation. This phenomenon arises from nontrivial monodromy conditions that originate from a genus-one covering surface, where left and right movers become coupled through the torus.

We investigate the effects of the twist-2 operator in 2D symmetric orbifold CFTs. The twist operator can join together a twist-M state and a twist-N state, creating a twist-(M + N) state. This process involves three effects: pair creation, propagation, and contraction. We study these effects by using a Bogoliubov ansatz and conformal symmetry. In this multi-wound scenario, pair creation no longer decouples from propagation, in contrast to the previous study where M = N = 1. We derive equations for these effects, which organize themselves into recursion relations and constraints. Using the recursion relations, we can determine the infinite number of coefficients in the effects through a finite number of inputs. Moreover, the number of required inputs can be further reduced by applying constraints.

Microstate geometries are proposed microstates of black holes which can be described within supergravity. Even though their number may not reproduce the full entropy of black holes with finite-sized horizons, they still offer a glimpse into the microscopic structure of black holes. In this paper we construct a new set of microstate geometries of the supersymmetric D1-D5-P black hole, where the momentum charge is carried by a vector field, as seen from the perspective of six-dimensional supergravity. To aid our construction, we develop an algorithm which solves a complicated partial differential equation using the regularity of the geometries. The new solutions are asymptotically AdS₃ × S ³, and have a long, but finite AdS₂ throat that caps off without ever developing a horizon. These microstate geometries have a holographic interpretation as coherent superpositions of heavy states in the boundary D1-D5 CFT. We identify the states which are dual to our newly constructed solutions and carry out some basic consistency checks to support our identification.

We use families of circular null geodesics as probes of a family of microstate geometries, known as (1, 0, n) superstrata. These geometries carry a left-moving momentum wave and the behavior of some of the geodesic probes is very sensitive to this background wave. The left-moving geodesics behave like BPS particles and so can be placed in circular orbits anywhere in the geometry and actually “float” at fixed radius and angle in the three-dimensional “capped BTZ” geometry. The right-moving geodesics behave like non-BPS particles. We show that they provide a simple geometric characterization of the black-hole bound: when the momentum charge of the geometry is below this bound, such geodesics can be placed anywhere, but exceeding the bound, even by a small amount, means these geodesics are restricted to the deep interior of the geometry. We also show that for left-moving string probes, the tidal forces remain comparable with those of global AdS₃. Nevertheless, for some of these probes, the “bumps” in the geometry induce an oscillatory mass term and we discuss how this can lead to chaotic scrambling of the state of the string.