Making Non-Associative Algebra Associative

Based on results about open string correlation functions, a nonassociative algebra was proposed in a recent paper for D-branes in a background with nonvanishing $H$. We show that our associative algebra obtained by quantizing the endpoints of an open string in an earlier work can also be used to reproduce the same correlation functions. The novelty of this algebra is that functions on the D-brane do not form a closed algebra. This poses a problem to define gauge transformations on such noncommutative spaces. We propose a resolution by generalizing the description of gauge transformations which naturally involves global symmetries. This can be understood in the context of matrix theory.Comment: 12 pages, Latex, acknowledgement adde

Nambu Bracket for M Theory

In this article we give a concise review of recent progress in our understanding of the Lie 3-algebra and their application to the Bagger-Lambert-Gustavsson model describing multiple M2-branes in M theory.Comment: 13 pages, prepared for The Fourth International Symposium on Symmetries in Subatomic Physics (SSP 2009), minor modification, references adde

Comment on Self-Consistent Model of Black Hole Formation and Evaporation

In an earlier work, Kawai et al proposed a model of black-hole formation and evaporation, in which the geometry of a collapsing shell of null dust is studied, including consistently the back reaction of its Hawking radiation. In this note, we illuminate the implications of their work, focusing on the resolution of the information loss paradox and the problem of the firewall.Comment: 16 pages, 6 figures, references adde

The Absence of Horizon in Black-Hole Formation

With the back-reaction of Hawking radiation taken into consideration, the work of Kawai, Matsuo and Yokokura has shown that, under a few assumptions, the collapse of matter does not lead to event horizon nor apparent horizon. In this paper, we relax their assumptions and elaborate on the space-time geometry of a generic collapsing body with spherical symmetry. The geometry outside the collapsing sphere is found to be approximated by the geometry outside the white-hole horizon, hence the collapsing matter remains outside the Schwarzschild radius. As particles in Hawking radiation are created in the vicinity of the collapsing matter, the information loss paradox is alleviated. Assuming that the collapsing body evaporates within finite time, there is no event horizon.Comment: 28 pages, minor modificatio

Aspects of Effective Theory for Multiple M5-Branes Compactified On Circle

A supersymmetric non-Abelian self-dual gauge theory with the explicit introduction of Kaluza-Klein modes is proposed to give a classical description of multiple M5-branes on $R^5 \times S^1$. The gauge symmetry is parametrized by Lie-algebra valued 1-forms with the redundancy of a 0-form, and the supersymmetry transformations without gauge-fixing are given. We study BPS configurations involving KK modes, including M-waves and M2-branes with non-trivial distributions around the circle. Finally, this supersymmetric gauge theory of two-forms can be equipped with more general non-Abelian gerbes in five dimensions.Comment: 34 pages, minor modificatio