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Dynamical Transitions in String Landscape
- a project supervised by Prof. Dieter L?st and Dr. Robert Helling -

Von Andrei Constantin (13.10.2008)

This project is part of my research activity at the Max Planck Institute for Physics in Munich. I joined the string theory group of Prof. Dieter L?st towards the end of 2007, a few months after I had started the Elite Master Program 'Theoretical and Mathematical Physics' at the Munich university LMU. Since then, I've been mostly collaborating with Dr. Robert Helling, my supervisor.

The 'philosophical' background of my project is closely linked to the so-called landscape problem in the string theory. In order to understand this issue, we need a short digression into the main ideas and results of string theory.

It is a well known fact that string theory provides a framework for the unification of all fundamental forces (gravitational, weak, strong and electromagnetic). As such, string theory is able to accomplish a consistent description of quantum gravity and gauge interactions. However, the unification takes place at very high, experimentally inaccessible energies. In this situation, the problem of relating the theory to low energy observables is highly non-trivial.

Another complication arises from the fact that string theory requires more than three space dimensions for consistency, namely string theory lives in nine space dimensions. In order to be able to describe everyday physics, one has to explain the fate of the unwanted dimension. This can be done in many ways:  Although in nine space dimensions there exist only five different formulations of the theory, the number of lower-dimensional solutions of the string equations of motion is enormous. This number is commonly quoted as 10 to the power 500. For sure, this rises a big problem concerning the prediction power of the theory since each solution corresponds to a different universe, with a different set of particle physics and cosmological parameters. In the literature, this issue is known as the ?landscape problem?, the landscape being the space of all possible string solutions with three spacial dimensions. For a recent review on the string theory landscape and further references, see [1].

A first step in tackling the problem is to restrict the study to those solutions (string ground-states) which have realistic phenomenological properties, e. g. give the correct number of generations for quarks and leptons. On the other hand, one can think of the possibility that different ground-states exist in different regions of the space-time. The study of dynamics and evolution of such regions forms the main content of our research project.

Tracing back this line of thought, in the hot early universe, the energy fluctuations were high enough to access any of these ground states. As the universe expanded and cooled down, different regions of the space were mapped to different ground-states, forming bubbles. One can think about the nucleation of such bubbles in analogy with the formation of domains in ferromagnetic substances below Curie temperature (see movie).

the nucleation of bubbles in the early universe, in analogy with the formation of domains in ferromagnetic substances[Bildunterschrift / Subline]: The movie shows the nucleation of bubbles in the early universe, in analogy with the formation of domains in ferromagnetic substances. The process is concomitant with the expansion and cooling down of the universe. On the left the temperature parameter is shown in arbitrary units. Source: [2].

Until now, the studies have been concerned with the possibility of creating bubbles with high energy ground-states inside regions of much lower energy, which correspond to the creation of a different universe inside ours. It has been found that, classically, such bubbles cannot avoid collapse. Taking into account the possibility of quantum tunneling, the bubble could tunnel to a different solution in which from the interior perspective it expands forever, while from the outside it is a black hole.

However, these studies have focused on the so called thin wall approximation, which assumes the boundary separating the bubble universe form the surrounding universe infinitesimally thin compared to the size the bubble. Although very useful, this approximation imposes severe restrictions on the geometries describing the two regions. A review of these results can be found in [3]. 

In our study, we investigate a more general situation with finite size and dynamical boundaries. We are looking at two regions in which the space-time geometry asymptotically takes one or another form. As a model, we use a low energy limit of string theory, the so-called scalar-tensor gravity, in which a scalar field is coupled to gravity. The system is non-integrable, hence the need for numerical analysis. 

The scalar field is characterized by the potential V(ϕ) shown in Figure 1. The minima of the potential correspond to stable configurations (ground-states) of the scalar field. On the other hand, each bubble is characterized by such, but not necessarily the same, stable configuration for the scalar field.

General form of the scalar field potential[Bildunterschrift / Subline]: Figure 1. General form of the scalar field potential.

The evolution of the boundary separating different regions is described by rather involved equations. The scalar field dynamics is 'entangled' with that of gravity, described in terms of a metric tensor. Until now, the numerical analysis of these equations has been only partly successful. In most common scenarios, after the fields evolved for a period of time, a singularity in the metric tensor was encountered. This might be just the sign that a black hole is being created. Further investigation should clarify this issue, as well as the general dynamics of the boundaries.



1. D. L?st, ?String Theory Landscape and the Standard Model of Particle Physics?, arXiv:0707.2305v2  [hep-th].
2. 2-D Ising Model Simulation. http://www.pha.jhu.edu/~javalab/ising/ising.html
3. A. Aguirre, M.C. Johnson, ?Dynamics and instability of false vacuum bubbles?, arXiv:0508093v2 [gr-qc].

Andrei Constantin

  • 09/2001 - 06/2005
  • National High School “I.C. Bratianu”, Pitesti, Romania Graduated with highest academic achievements. The program focused on mathematics, physics and computer science
  • 09/2005 - 06/2007
  • Jacobs University, Bremen, Germany Bachelor’s degree in physics with specialization in Mathematical Physics. Bachelor’s thesis: ‘Path Integral Approach to Quantum Geodesics in Noncommutative Spacetimes’
  • from 10/2007
  • Ludwig-Maximilians Universität / Technische Universität München, Germany Enrolled in the Elite Master’s Programme Theoretical and Mathematical Physics

Research Experience
  • 09/2005 – 12/2005
  • Jacobs University, Bremen, Germany Student Assistant in the Molecular and Nanoelectronics Laboratory. Work experience in preparation and analysis of organic field effect transistors
  • 06/2006 – 08/2006
  • Institute for Nuclear Research Pitesti, Romania Involved in a project of designing algorithms for numerical solutions of the integral equation of transport in the formalism of first collision probabilities, computing cross sections and probabilities of col
  • 06/2007 - 07/2007
  • Jacobs University, Bremen, Germany Designed an image processing software for the analysis of Raman resonance structures
  • from 11/2007
  • Max Planck Institute for Physics Munich, Germany Employed as research student in the Department of Theoretical Physics - Mathematical Physics, String Theory conducted by Prof. Dieter Lüst

Awards and Prizes
  • 2003, 2004
  • International Rudolf Ortvay Physics Contest Awarded second and third prizes
  • 2003, 2004, 2005
  • International Physics Olympiad (IPhO) Awarded one gold medal and two silver medals
  • 06/2005
  • National High School “I.C. Bratianu”, Pitesti, Romania Best Graduate Student Award
  • 09/2006
  • Jacobs University, Bremen, Germany Member of the President’s List: awarded for excellent academic achievements in the previous academic year
  • 09/2005 – 06/2007
  • Jacobs University, Bremen, Germany Merit based scholarship
  • 07/2008
  • Lindau Nobel Laureate Meetings, Lindau, Germany Selected to participate in the Meetings as a member of the Elitenetwork of Bavaria