Rapid Tunneling and Percolation in the Landscape

Motivated by the possibility of a string landscape, we reexamine tunneling of a scalar field across single/multiple barriers. Recent investigations have suggested modifications to the usual picture of false vacuum decay that lead to efficient and rapid tunneling in the landscape when certain conditions are met. This can be due to stringy effects (e.g. tunneling via the DBI action), or by effects arising due to the presence of multiple vacua (e.g. resonance tunneling). In this paper we discuss both DBI tunneling and resonance tunneling. We provide a QFT treatment of resonance tunneling using the Schr\"odinger functional approach. We also show how DBI tunneling for supercritical barriers can naturally lead to conditions suitable for resonance tunneling. We argue using basic ideas from percolation theory that tunneling can be rapid in a landscape where a typical vacuum has multiple decay channels and discuss various cosmological implications. This rapidity vacuum decay can happen even if there are no resonance/DBI tunneling enhancements, solely due to the presence of a large number of decay channels. Finally, we consider various ways of circumventing a recent no-go theorem for resonance tunneling in quantum field theory.Comment: 47 pages, 16 figures. Acknowledgements adde

Inter-Brane Potential and the Decay of a non-BPS-D-brane to Closed Strings

We calculate the potential for Dp-\Dbar p pair and show that the coincident Dp-\Dbar p system has $(11-p)$ tachyonic modes, with $(9-p)$ of them due to radiative corrections. We propose that the decay width of an unstable non-BPS-$Dp$-brane to closed strings is given by the imaginary part of the one-loop contribution to the effective potential of the open string tachyon mode.Comment: 16 Pages, 3 Figure

Spontaneous Creation of Inflationary Universes and the Cosmic Landscape

We study some gravitational instanton solutions that offer a natural realization of the spontaneous creation of inflationary universes in the brane world context in string theory. Decoherence due to couplings of higher (perturbative) modes of the metric as well as matter fields modifies the Hartle-Hawking wavefunction for de Sitter space. Generalizing this new wavefunction to be used in string theory, we propose a principle in string theory that hopefully will lead us to the particular vacuum we live in, thus avoiding the anthropic principle. As an illustration of this idea, we give a phenomenological analysis of the probability of quantum tunneling to various stringy vacua. We find that the preferred tunneling is to an inflationary universe (like our early universe), not to a universe with a very small cosmological constant (i.e., like today's universe) and not to a 10-dimensional uncompactified de Sitter universe. Such preferred solutions are interesting as they offer a cosmological mechanism for the stabilization of extra dimensions during the inflationary epoch.Comment: 52 pages, 7 figures, 1 table. Added discussion on supercritical string vacua, added reference

Topological phases in self-similar systems

The study of topological phases in condensed matter physics has seen remarkable advancements, primarily focusing on systems with a well-defined bulk and boundary. However, the emergence of topological phenomena on self-similar systems, characterized by the absence of a clear distinction between bulk and boundary, presents a fascinating challenge. This thesis focuses on the topological phases on self-similar systems, shedding light on their unique properties through the lens of adiabatic charge pumping. We observe that the spectral flow in these systems exhibits striking qualitative distinctions from that of translationally invariant non-interacting systems subjected to a perpendicular magnetic field. We show that the instantaneous eigenspectra can be used to understand the quantization of the charge pumped over a cycle, and hence to understand the topological character of the system. Furthermore, we establish a correspondence between the local contributions to the Hall conductivity and the spectral flow of edge-like states. We also find that the edge-like states can be approximated as eigenstates of the discrete angular-momentum operator, with their chiral characteristics stemming from this unique perspective. We also investigate the effect of local structure on the topological phases on self-similar structures embedded in two dimensions. We study a geometry dependent model on two self-similar structures having different coordination numbers, constructed from the Sierpinski gasket. For different non-spatial symmetries present in the system, we numerically study and compare the phases on both structures. We characterize these phases by the localization properties of the single-particle states, their robustness to disorder, and by using a real-space topological index. We find that both structures host topologically nontrivial phases and the phase diagrams are different on the two structures, emphasizing the interplay between non-spatial symmetries and the local structure of the self-similar unit in determining topological phases. Furthermore, we demonstrate the presence of topologically ordered chiral spin liquid on fractals by extending the Kitaev model to the Sierpinski Gasket. We show a way to perform the Jordan-Wigner transformation to make this model exactly solvable on the Sierpinski Gasket. This system exhibits a fractal density of states for Majorana modes and showcases a transition from a gapped to a gapless phase. Notably, the gapped phase features symmetry-protected Majorana corner modes, while the gapless phase harbors robust zero-energy and low-energy self-similar Majorana edge-like modes. We also study the vortex excitations, characterized by remarkable localization properties even in small fractal generations. These localized excitations exhibit anyonic behavior, with preliminary calculations hinting at their fundamental differences from Ising anyons observed in the Kitaev model on a honeycomb lattice