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

Journal Article · Mon Feb 15 00:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.1569· OSTI ID:6787185

Park, Y; Strominger, A ^[1]

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1. Department of Physics, University of California, Santa Barbara, California 93106 (United States)

An [ital 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 Arnowitt-Deser-Misner energy [ital M], as found by Witten in four-dimensional general relativity. Using this expression it is proven that [ital 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 [ital quantum] positive-energy theorem is also proven for the semiclassical large-[ital N] equations, despite the indefiniteness of the quantum stress tensor. For black-hole spacetimes, it is shown that [ital M] is bounded from below by [ital e][sup [minus]2[phi]][sub [ital H]], where [phi][sub [ital 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.

• DOE Contract Number: FG03-91ER40618
• OSTI ID: 6787185
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 47:4; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
GENERAL RELATIVITY THEORY
SUPERSYMMETRY
QUANTUM GRAVITY
BLACK HOLES
CLASSICAL MECHANICS
EQUATIONS OF MOTION
FOUR-DIMENSIONAL CALCULATIONS
GRAVITATIONAL FIELDS
RENORMALIZATION
SPACE-TIME
SPINORS
TWO-DIMENSIONAL CALCULATIONS
VACUUM STATES
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
SYMMETRY
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