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Supersymmetry and Positive Energy in Classical and Quantum Two-Dimensional Dilaton Gravity | | Youngchul Park
; Andrew Strominger
; | | Date: |
3 Oct 1992 | | Journal: | Phys.Rev. D47 (1993) 1569-1575 | | Subject: | hep-th | | Abstract: | An $N = 1$ supersymmetric version of two dimensional dilaton gravity coupled to matter is considered. It is shown that the linear dilaton vacuum spontaneously breaks half the supersymmetries, leaving broken a linear combination of left and right supersymmetries which squares to time translations. Supersymmetry suggests a spinorial expression for the ADM energy $M$, as found by Witten in four-dimensional general relativity. Using this expression it is proven that ${M}$ is non-negative for smooth initial data asymptotic (in both directions) to the linear dilaton vacuum, provided that the (not necessarily supersymmetric) matter stress tensor obeys the dominant energy condition. A {it quantum} positive energy theorem is also proven for the semiclassical large-$N$ equations, despite the indefiniteness of the quantum stress tensor. For black hole spacetimes, it is shown that $M$ is bounded from below by $e^{- 2 phi_H}$, where $phi_H$ is the value of the dilaton at the apparent horizon, provided only that the stress tensor is positive outside the apparent horizon. This is the two-dimensional analogue of an unproven conjecture due to Penrose. Finally, supersymmetry is used to prove positive energy theorems for a large class of generalizations of dilaton gravity which arise in consideration of the quantum theory. | | Source: | arXiv, hep-th/9210017 | | Other source: | [GID 391605] pmid10015734 | | Services: | Forum | Review | PDF | Favorites | |
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