Warped branches of flux compactifications

TL;DR

This paper analytically explores warped flux compactifications in higher-dimensional Einstein gravity with positive cosmological constant, revealing phase space structures and thermodynamic properties of warped de Sitter solutions.

Contribution

It provides the first analytical solutions for warped branches in flux compactifications using perturbative methods and Green's functions, detailing their phase space and thermodynamics.

Findings

Derived analytical solutions for warped branches.

Mapped the phase space structure of solutions.

Reproduced the first law of thermodynamics for warped de Sitter branches.

Abstract

We consider Freund-Rubin-type compactifications which are described by (p+q)-dimensional Einstein gravity with a positive cosmological constant and a q-form flux. Using perturbative expansions of Kinoshita's ansatz for warped dS_pxS^q and AdS_pxS^q spacetimes, we obtain analytical solutions describing the warped branches and their respective phase spaces. These equations are given by inhomogeneous Gegenbauer differential equations which can be solved by the Green's function method. The requirement that the Green's functions are regular provides constraints which determine the structure of the phase space of the warped branches. We apply the perturbation results to calculate the thermodynamic variables for the warped dS_pxS^q branch. In particular, the first law of thermodynamics can be reproduced using this method.