Supersymmetry and positive energy in classical and quantum two-dimensional dilaton gravity
Oct 12, 199221 pages
Published in:
- Phys.Rev.D 47 (1993) 1569-1575
e-Print:
- hep-th/9210017 [hep-th]
Report number:
- UCSBTH-92-39
Citations per year
Abstract:
An 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 , as found by Witten in four-dimensional general relativity. Using this expression it is proven that 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- equations, despite the indefiniteness of the quantum stress tensor. For black hole spacetimes, it is shown that is bounded from below by , where 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.- supersymmetry
- gravitation
- quantum gravity
- field theory: dilaton
- dimension: 2
- invariance: conformal
- energy: >0
- black hole
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