Dimensional QFT Research Articles

The entanglement entropy of typical pure states and replica wormholes

In a 1+1 dimensional QFT on a circle, we consider the von Neumann entanglement entropy of an interval for typical pure states. As a function of the interval size, we expect a Page curve in the entropy. We employ a specific ensemble average of pure states, and show how to write the ensemble-averaged Rényi entropy as a path integral on a singular replicated geometry. Assuming that the QFT is a conformal field theory with a gravitational dual, we then use the holographic dictionary to obtain the Page curve. For short intervals the thermal saddle is dominant. For large intervals (larger than half of the circle size), the dominant saddle connects the replicas in a non-trivial way using the singular boundary geometry. The result extends the ‘island conjecture’ to a non-evaporating setting.

Holography for the very early universe and the classic puzzles of hot big bang cosmology

We show that standard puzzles of hot Big Bang cosmology that motivated the introduction of cosmological inflation, such as the smoothness and horizon problem, the flatness problem and the relic problem are also solved by holographic models for very early universe based on perturbative three dimensional QFT. In the holographic setup, cosmic evolution is mapped to inverse renormalization group (RG) flow of the dual QFT, and the resolution of the puzzles relies on properties of the RG flow.

False vacuum decay in quantum mechanics and four dimensional scalar field theory

When the Higgs boson was discovered in 2012 it was realized that electroweak vacuum may suffer a possible metastability on the Planck scale and can eventually decay. To understand this problem it is important to have reliable predictions for the vacuum decay rate within the framework of quantum field theory. For now, it can only be done at one loop level, which is apparently is not enough. The aim of this work is to develop a technique for the calculation of two and higher order radiative corrections to the false vacuum decay rate in the framework of four dimensional scalar quantum field theory and then apply it to the case of the Standard Model. To achieve this goal, we first start from the case of d=1 dimensional QFT i.e. quantum mechanics. We show that for some potentials two and three loop corrections can be very important and must be taken into account. Next, we use quantum mechanical example as a template for the general d=4 dimensional theory. In it we are concentrating on the calculations of bounce solution and corresponding Green function in so called thin wall approximation. The obtained Green function is then used as a main ingredient for the calculation of two loop radiative corrections to the false vacuum decay rate.

Cosmic energy disorder in terms of four dimensional QFT and anti de sitter space conformal theory

Cosmic energy disorder in terms of four dimensional QFT and anti de sitter space conformal theory

Self-duality from new massive gravity holography

The holographic renormalization group (RG) flows in certain self-dual two dimensional QFT’s models are studied. They are constructed as holographic duals to specific New Massive 3d Gravity (NMG) models coupled to scalar matter with “partially self-dual” superpotentials. The standard holographic RG constructions allow us to derive the exact form of their β-functions in terms of the corresponding NMG’s domain walls solutions. By imposing invariance of the free energy, the central function and of the anomalous dimensions under specific matter field’s duality transformation, we have found the conditions on the superpotentials of two different NMG’s models, such that their dual 2d QFT’s are related by a simple strong-weak coupling transformation.

Wilson loops in 3d QFT from D-branes in AdS4×CP3

We study the Wilson loops and defects in the three dimensional QFT from the D-branes in the AdS(4) x CP**3 geometry. We find out explicit D-brane configurations in the bulk which correspond to both straight and circular Wilson lines extended to the boundary of AdS(4). We analyze critically the role of boundary contributions to the D2-branes with various topology and to the fundamental string actions.

Boundary one-point function, Casimir energy and boundary state formalism in [formula omitted] dimensional QFT

We consider quantum field theories with boundary on a codimension one hyperplane. Using 1 + 1 dimensional examples, we clarify the relation between three parameters characterizing one-point functions, finite size corrections to the ground state energy and the singularity structure of scattering amplitudes, respectively. We then develop the formalism of boundary states in general D + 1 spacetime dimensions and relate the cluster expansion of the boundary state to the correlation functions using reduction formulae. This allows us to derive the cluster expansion in terms of the boundary scattering amplitudes, and to give a derivation of the conjectured relations between the parameters in 1 + 1 dimensions, and their generalization to D + 1 dimensions. We use these results to express the large volume asymptotics of the Casimir effect in terms of the one-point functions or alternatively the singularity structure of the one-particle reflection factor, and for the case of vanishing one-particle couplings we give a complete proof of our previous result for the leading behaviour.