Year: 2005
Type: article
Abstract: We have studied volumes of the 3-cycle and the compact 5-volumes for the $\ensuremath{\beta}$ transformed geometry and it comes out to be decreasing except one choice for which the torus does not stay inside the 3-cycle and ``5-cycle.'' There are 3 possible ways to construct these cycles. One is as mentioned above and the other two are when the torus stays inside the cycle and when both the torus and the cycle share a common direction. Also, we have argued that under $\ensuremath{\beta}$-deformation there arises a nontrivial ``potential'' as the $SL(3,R)$ transformation mixes up the fields. If we start with a flat space after the $SL(3,R)$ transformation the Ricci scalar of the transformed geometry does not vanish but the transformed solution is reminiscent of the NS5-brane. We have explicitly checked that $\ensuremath{\beta}$-transformation indeed is a marginal deformation on the gravity side.
Author: Shesansu Sekhar Pal
Institution: Weizmann Institute of Science
Language: Latvian
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W191038285