Supersymmetry and positive energy in classical and quantum two-dimensional dilaton gravity

Oct 12, 1992
21 pages
Published in:
  • Phys.Rev.D 47 (1993) 1569-1575
e-Print:
Report number:
  • UCSBTH-92-39

Citations per year

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Abstract:
An N=1N = 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 MM, as found by Witten in four-dimensional general relativity. Using this expression it is proven that M{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-NN equations, despite the indefiniteness of the quantum stress tensor. For black hole spacetimes, it is shown that MM is bounded from below by e 2ϕHe~{- 2 \phi_H}, where ϕH\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.
  • supersymmetry
  • gravitation
  • quantum gravity
  • field theory: dilaton
  • dimension: 2
  • invariance: conformal
  • energy: >0
  • black hole