Daniel Grumiller

Instability in cosmological topologically massive gravity at the chiral point

This thesis explores three different aspects of quantum gravity. First we study D3-brane black holes in Calabi-Yau compactifications of type IIB string theory. Using the OSV conjecture and a relation between topological strings and matrix models we show that some black holes have a matrix model description. This is the case if the attractor mechanism fixes the internal geometry to a conifold at the black hole horizon. We also consider black holes in a flux compactification and compare the effects of the black holes and fluxes on the internal geometry. We find that the fluxes dominate. Second, we study the scalar potential of type IIB flux compactifications. We demonstrate that monodromies of the internal geometry imply as a general feature the existence of long series of continuously connected minima. This allows for the embedding of scenarios such as chain inflation and resonance tunneling into string theory. The concept of monodromies is also extended to include geometric transitions: passing to a different Calabi-Yau topology, performing its monodromies and then returning to the original space allows for novel transformations. All constructions are performed explicitly, using both analytical and numerical techniques, in the mirror quintic Calabi-Yau. Third, we study cosmological topologically massive gravity at the chiral point, a prime candidate for quantization of gravity in three dimensions. The prospects of this scenario depend crucially of the stability of the theory. We demonstrate the presence of a negative energy bulk mode that grows logarithmically toward the AdS boundary. The AdS isometry generators have non-unitary matrix representations like in logarithmic CFT, and we propose that the CFT dual for this theory is logarithmic. In a complementing canonical analysis we also demonstrate the existence of this bulk degree of freedom, and we present consistent boundary conditions encompassing the new mode.

Non-existence of a dilaton gravity action for the exact string black hole

We prove that no local diffeomorphism invariant two-dimensional theory of the metric and the dilaton without higher derivatives can describe the exact string black hole solution found a decade ago by Dijkgraaf, Verlinde and Verlinde. One of the key points in this proof is the concept of dilaton-shift invariance. We present and solve (classically) all dilaton-shift invariant theories of two-dimensional dilaton gravity. Two such models, resembling the exact string black hole and generalizing the CGHS model, are discussed explicitly.

On the collision of two shock waves in AdS5

We consider two ultrarelativistic shock waves propagating and colliding in five-dimensional Anti-de-Sitter spacetime. By transforming to Rosen coordinates, we are able to find the form of the metric shortly after the collision. Using holographic renormalization, we calculate the energy-momentum tensor on the boundary of AdS space for early times after the collision. Via the gauge-gravity duality, this gives some insights on bulk dynamics of systems created by high energy scattering in strongly coupled gauge theories. We find that Bjorken boost-invariance is explicitely violated at early times and we obtain an estimate for the thermalization time in this simple system.

Dark matter: A Spin one half fermion field with mass dimension one?

We report an unexpected theoretical discovery of a spin one-half matter field with mass dimension one. It is based on a complete set of eigenspinors of the charge conjugation operator. Because of its unusual properties with respect to charge conjugation and parity, it belongs to a nonstandard Wigner class. Consequently, the theory exhibits nonlocality with (CPT){sup 2}=-I. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate it as a first-principle candidate for dark matter.

Holographic applications of logarithmic conformal field theories

We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in anti-de Sitter space and logarithmic conformal field theories in various dimensions. We summarize the developments in the past five years, include some novel generalizations and provide an outlook on possible future developments.

AdS3/LCFT2 – Correlators in new massive gravity

We calculate 2-point correlators for New Massive Gravity at the chiral point and find that they behave precisely as those of a logarithmic conformal field theory, which is characterized in addition to the central charges cL=cR=0 by ‘new anomalies’ bL=bR=−σ12lGN, where σ is the sign of the Einstein–Hilbert term, l the AdS radius and GN Newtons constant.

CONSISTENT BOUNDARY CONDITIONS FOR COSMOLOGICAL TOPOLOGICALLY MASSIVE GRAVITY AT THE CHIRAL POINT

We show that cosmological topologically massive gravity at the chiral point allows not only Brown–Henneaux boundary conditions as consistent boundary conditions, but also slightly more general ones which encompass the logarithmic primary found in J. High Energy Phys.07 (2008) 134 as well as all its descendants.

Spin-3 gravity in three-dimensional flat space.

Hamid Afshar, ∗ Arjun Bagchi, 3, † Reza Fareghbal, 4, ‡ Daniel Grumiller, § and Jan Rosseel ¶ Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8–10/136, A-1040 Vienna, Austria School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom Indian Institute of Science Education and Research (IISER), Pune, Maharashtra 411008, India School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran (Dated: May 11, 2014)

Flat-Space Chiral Gravity

We provide the first evidence for a holographic correspondence between a gravitational theory in flat space and a specific unitary field theory in one dimension lower. The gravitational theory is a flat-space limit of topologically massive gravity in three dimensions at a Chern-Simons level of k=1. The field theory is a chiral two-dimensional conformal field theory with a central charge of c=24.

AdS3/LCFT2 — correlators in cosmological topologically massive gravity

For cosmological topologically massive gravity at the chiral point we calculate momentum space 2- and 3-point correlators of operators in the postulated dual CFT on the cylinder. These operators are sourced by the bulk and boundary gravitons. Our correlators are fully consistent with the proposal that cosmological topologically massive gravity at the chiral point is dual to a logarithmic CFT. In the process we give a complete classification of normalizable and non-normalizeable left, right and logarithmic solutions to the linearized equations of motion in global AdS3.