Steven B. Giddings

Axion-induced topology change in quantum gravity and string theory

Abstract We consider a system comprised of an axion (described by a rank-three antisymmetric tensor field strength) coupled to gravity. Instantons are found which describe the nucleation of a Planck-sized baby Robertson-Walker universe. Information loss to the baby universe can lead to an effective loss of quantum coherence. An estimate of the magnitude of this effect on particle propagation is made in the semi-classical approximation. This magnitude depends on the parameters of the theory (which includes a cutoff since the theory is non-renormalizable) and on the quantum state of the many-universe system. In contrast to the naive expectation that Planck-scale dynamics should lead to very small effects at low energies, the effects of these instantons can be large. The case of string theory is considered in some detail, and it is found that a massless dilaton can suppress the tunneling.

Loss of incoherence and determination of coupling constants in quantum gravity

The wave function of an interacting ‘family’ of one large ‘parent’ and many Planck-sized ‘baby’ universes is computed in a semiclassical approximation using an adaptation of Hartle-Hawking initial conditions. A recently discovered gravitational instanton which exists for general relativity coupled to axions is employed. The outcome of a single experiment in the parent universe is in general described by a mixed state, even if the initial state is pure. However, a sequence of measurements rapidly collapses the wave function of the family of universes into one of an infinite number of ‘coherent’ states for which quantum incoherence is not observed in the parent universe. This provides a concrete illustration of an unexpected phenomena whose existence has been argued for on quite general grounds by Coleman: quantum incoherence due to information loss to baby universes is not experimentally observable. We further argue that all coupling constants governing dynamics in the parent universe depend on the parameters describing the particular coherent state into which the family wave function collapses. In particular, generically terms that violate any global symmetries will be induced in the effective action for the parent universe. These last results have much broader applicability that our specific model.

What do CFTs tell us about anti-de Sitter spacetimes?

The AdS/CFT conjecture relates quantum gravity on anti-de Sitter (AdS) space to a conformal field theory (CFT) defined on the spacetime boundary. We interpret the CFT in terms of natural analogues of the bulk S-matrix. Our first approach finds the bulk S-matrix as a limit of scattering from an AdS bubble immersed in a space admitting asymptotic states. Next, we show how the periodicity of geodesics obstructs a standard LSZ prescription for scattering within global AdS. To avoid this subtlety we partition global AdS into patches within which CFT correlators reconstruct transition amplitudes of AdS states. Finally, we use the AdS/CFT duality to propose a large N collective field theory that describes local, perturbative supergravity. Failure of locality in quantum gravity should be related to the difference between the collective 1/N expansion and genuine finite N dynamics.

Baby Universes, Third Quantization and the Cosmological Constant

Abstract A general third-quantized framework for a system of interacting universes is described. The third-quantized fields create and annihilate second-quantized single-universe states, and are equivalent to second-quantized spacetime coupling constants. This implies that the spacetime couplings obey dynamical equations. A direct consequence of this is that the spacetime coupling constants are in general subject to uncertainty relations. A concrete illustration of these facts is given using the semiclassical instanton approximation to a theory of gravity coupled to axions. The field theory action is explicitly constructed and the dynamical equation for the long distance axion potential thereby derived. The equation implies that the potential has a minimum with vanishing effective cosmological constant.

High-temperature strings

Abstract The microcanonical density of states for a weakly interacting gas of strings compactified on a torus is computed in the limit of large energy, taking into account conservation of winding number and momentum. These constraints affect the high-energy form of the density of states. Using these results we discuss physical properties of the string ensemble near the Hagedorn temperature. In the free theory the Hagedorn temperature is interpreted as signaling the transition to long string dominance; in the interacting theory the system gravitationally collapses, possibly to a new phase. Formation of long strings may also be relevant to Hawking radiation and to acceleration radiation.

The geometry of super Riemann surfaces

AbstractWe define super Riemann surfaces as smooth 2|2-dimensional supermanifolds equipped with a reduction of their structure group to the group of invertible upper triangular 2×2 complex matrices. The integrability conditions for such a reduction turn out to be (most of) the torsion constraints of 2d supergravity. We show that they are both necessary and sufficient for a frame to admit local superconformal coordinates. The other torsion constraints are merely conditions to fix some of the gauge freedom in this description, or to specify a particular connection on such a manifold, analogous to the Levi-Civita connection in Riemannian geometry. Unlike ordinary Riemann surfaces, a super Riemann surface cannot be regarded as having only one complex dimension. Nevertheless, in certain important aspects super Riemann surfaces behave as nicely as if they had only one dimension. In particular they posses an analog

Conformal Techniques in String Theory and String Field Theory

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Axionic black holes and an Aharonov-Bohm effect for strings.

of the Cauchy-Riemann operator on ordinary Riemann surfaces, a differential operator taking values in the bundle of half-volume forms. This operator furnishes a short resolution of the structure sheaf, making possible a Quillen theory of determinant line bundles. Finally we show that the moduli space of super Riemann surfaces is embedded in the larger space of complex curves of dimension 1|1.