Strong correlations in gravity and biophysics

Abstract

The unifying theme of this dissertation is the use of correlations. In the first part (chapter 2), we investigate correlations in quantum field theories in de Sitter space. In the second part (chapters 3,4,5), we use correlations to investigate a theoretical proposal that real (observed in nature) transcriptional networks of biological organisms are operating at a critical point in their phase diagram.

In chapter 2 we study the infrared dependence of correlators in various external backgrounds. Using the Schwinger-Keldysh formalism we calculate loop corrections to the correlators in the case of the Poincare patch and the complete de Sitter space. In the case of the Poincare patch, the loop correction modifies the behavior of the correlator at large distances. In the case of the complete de Sitter space, the loop correction has a strong dependence on the infrared cutoff in the past. It grows linearly with time, suggesting that at some point the correlations become strong and break the symmetry of the classical background.

In chapter 3 we derive the signatures of critical behavior in a model organism, the embryo of Drosophila melanogaster. They are: strong correlations in the fluctuations of different genes, a slowing of dynamics, long range correlations in space, and departures from a Gaussian distribution of these fluctuations. We argue that these signatures are observed experimentally.

In chapter 4 we construct an effective theory for the zero mode in this system. This theory is different from the standard Landau-Ginsburg description. It contains gauge fields (the result of the broken translational symmetry inside the cell), which produce observable contributions to the two-point function of the order parameter. We show that the behavior of the two-point function for the network of N genes is described by the action of a relativistic particle moving on the surface of the N-1 dimensional sphere. We derive a theoretical bound on the decay of the correlations and compare it with experimental data.

How difficult is it to tune a network to criticality? In chapter 5 we construct the space of all possible networks within a simple thermodynamic model of biological enhancers. We demonstrate that there is a reasonable number of models within this framework that accurately capture the mean expression profiles of the gap genes that are observed experimentally.