Non-susy D3 brane and an interpolating solution between AdS$_5$ black hole, AdS$_5$ soliton and a `soft-wall' gravity solution

TL;DR

This paper constructs a family of solutions in AdS$_5$ that interpolate between black holes, solitons, and a soft-wall gravity model, revealing new connections in non-supersymmetric D3-brane configurations.

Contribution

It introduces a four-parameter interpolating solution connecting various AdS$_5$ geometries without double Wick rotation, extending previous non-supersymmetric D3-brane solutions.

Findings

Interpolates between AdS$_5$ black hole and soliton solutions.

Includes a soft-wall gravity solution relevant to AdS/QCD.

Generalizes previous solutions to broader D$p$ brane contexts.

Abstract

It is known from the work in \cite{Lu:2007bu} of Lu et. al. that the non-supersymmetric charged D3-brane (with anisotropies in time as well as one of the spatial directions of D3-brane) of type IIB string theory is characterized by five independent parameters. By fixing one of the parameters and zooming into a particular region of space-time we construct a four parameter family of solution in AdS$_5$, which interpolates between AdS$_5$ black hole and AdS$_5$ soliton (when one of spatial directions in the Poincare coordinates is compact) by continuously changing the parameters (there is no need to take a double Wick rotation as is usual to go from one solution to the other) from one set of values to another. We consider two cases. In the first case the dilaton is constant for this transition and there are only three independent parameters, whereas in the second case the dilaton varies and there are four independent parameters. In the latter case, the solution interpolates between AdS$_5$ black hole, AdS$_5$ soliton as well as the so-called `soft-wall' gravity solution of AdS/QCD model. We also compare our solution to the previously obtained Constable-Myers solution which is helpful in generalizing the solution for other D$p$ (for $p\neq 3$) branes.