Worldvolume Theories, Holography, Duality and Time

TL;DR

This paper explores duality transformations linking various M-theory and string theories across different signatures, constructs world-volume theories with 16 supersymmetries, and discusses their holographic duals and geometric solutions.

Contribution

It constructs supersymmetric world-volume theories for branes in diverse signatures and links them via dualities to higher-dimensional theories, extending holographic correspondences.

Findings

World-volume theories have 16 supersymmetries across signatures.

All generalized D-branes' theories arise from compactifications of 9+1 or 5+5 dimensional SYM.

Holographic duals include string or M-theories in constant curvature backgrounds.

Abstract

Duality transformations involving compactifications on timelike as well as spacelike circles link M-theory, the 10+1-dimensional strong coupling limit of IIA string theory, to other 11-dimensional theories in signatures 9+2 and 6+5 and to type II string theories in all 10-dimensional signatures. These theories have BPS branes of various world-volume signatures, and here we construct the world-volume theories for these branes, which in each case have 16 supersymmetries. For the generalised D-branes of the various type II string theories, these are always supersymmetric Yang-Mills theories with 16 supersymmetries, and we show that these all arise from compactifications of the supersymmetric Yang-Mills theories in 9+1 or 5+5 dimensions. We discuss the geometry of the brane solutions and, for the cases in which the world-volume theories are superconformally invariant, we propose holographically dual string or M theories in constant curvature backgrounds. For product space solutions $X\times Y$, there is in general a conformal field theory associated with the boundary of $X$ and another with the boundary of $Y$.