The DSSYK Model: Charge and Holography

TL;DR

This thesis explores extending holographic principles beyond AdS spacetime to de Sitter space, focusing on the DSSYK model, its charged variants, and their gravitational duals, with implications for understanding our universe's cosmology.

Contribution

It introduces a charged DSSYK model with Dirac fermions, analyzes its thermodynamics and duality constraints, and advances the holographic understanding of de Sitter-like spacetimes.

Findings

Charged DSSYK model with Dirac fermions characterized

Thermodynamic properties of the dual geometry analyzed

Bounds on dual theories constrained by fermionic and scalar modes

Abstract

The Anti-de Sitter/Conformal Field Theory correspondence (AdS/CFT) is one of the most significant findings in theoretical physics and forms the basis of this thesis. Although highly powerful, the main limitation of AdS/CFT is that AdS does not appear in the real world outside of very specific limits. This limitation justifies the attempt to generalize the holographic principle to other spacetimes. In this thesis, we will pursue this direction and seek spacetimes that have at least some connection to de Sitter (dS), whose cosmological interest is evident. dS is, in fact, not only the geometry that best represents our Universe on large scales in the present, but also during the inflationary epoch that followed the Big Bang, where our current description of Nature fails completely. First, we will present some basic facts about the AdS/CFT correspondence. Then, the gravitational path integral will be introduced. After presenting the Sachdev-Ye-Kitaev (SYK) model and dilaton-gravity models, a holographic link between the two will be established. Next, we will discuss the double-scaled limit of SYK, known as DSSYK. We will then consider a ``charged'' variation of SYK with Dirac fermions, for which we will determine the fermionic two-point function. After studying the thermodynamic properties of the gravitational dual of DSSYK and the quasinormal modes of massive real scalars propagating in this geometry, we will conjecture how to modify the duality when considering the Dirac version of the model, showing that several bounds constrain the space of possible dual theories. Finally, we will summarize our findings and present an outlook on possible future developments based on the results described here.