Free Lunch from T-Duality

TL;DR

The paper introduces a method combining coordinate transformations and T-duality to generate new Einstein gravity solutions with dilaton and gauge fields, leading to novel black string and finite action configurations.

Contribution

It presents a new solution-generating technique using T-duality and coordinate transformations, extending to include S-duality for richer solution sets in higher dimensions.

Findings

Generated charged black strings in five dimensions.

Constructed finite action solutions from flat space in three dimensions.

Amended the effective action with boundary terms for positive action solutions.

Abstract

We consider a simple method of generating solutions to Einstein gravity coupled to a dilaton and a 2-form gauge potential in n dimensions, starting from an arbitrary (n-m)-dimensional Ricci-flat metric with m commuting Killing vectors. It essentially consists of a particular combination of coordinate transformations and T-duality and is related to the so-called null Melvin twists and TsT transformations. Examples obtained in this way include two charged black strings in five dimensions and a finite action configuration in three dimensions derived from empty flat space. The latter leads us to amend the effective action by a specific boundary term required for it to admit solutions with positive action. An extension of our method involving an S-duality transformation that is applicable to four-dimensional seed metrics produces further nontrivial solutions in five dimensions.