Selected problems in quantum field theory in different dimensions

Abstract

This thesis examines quantum field theories in different dimensions. We investigate three models defined in different dimensions and spacetime backgrounds: the generalized large q Sachdev-Ye-Kitaev (SYK) model in one dimension, the holographic dual theory to the giant Wilson loops in anti-de Sitter space (AdS) of two dimensions, and the field theory in de Sitter space (dS) of general dimensions.

First, we study the generalized large q SYK model. The effective action of the model in the large q limit is derived and a universal expression for the thermodynamic quantities of the model is presented. We also consider the chaos exponent using the retarded kernel method and find an efficient way to compute the Lyapunov exponent numerically for the generalized large q SYK model.

Next, we consider the 1/2-BPS Wilson loops in the large-rank symmetric and antisymmetric representations, which have holographic dual descriptions in terms of D3-branes and D5-branes in AdS5✕S5. We study the spectrums of the fluctuations on the D3-branes and the D5-branes. Using the AdS2/dCFT1 correspondence, we compute the correlation functions of operator insertions on the Wilson loop from perturbation theory on the D-branes. The results in special kinematic configurations agree with the prediction of localization.

Finally, we study the scalar field and the Dirac spinor field in the global dSd space. The effective actions of the scalar field and the spinor field are computed using the in-/out-state formalism. We show that there is particle production in even dimensions for both scalar field and spinor field. The in-out vacuum amplitude Zin/out is divergent at late times. By using dimensional regularization, we extract the finite part of log(Zin/out) in the even d cases and the logarithmically divergent part of log(Zin/out) in the odd d cases. We show that the regularized in-out amplitude equals the ratio of determinants associated with different quantizations in AdSd upon the identification of certain parameters in the two theories.