A Quantum Correction To Chaos

We use results on Virasoro conformal blocks to study chaotic dynamics in CFT$_2$ at large central charge c. The Lyapunov exponent $\lambda_L$, which is a diagnostic for the early onset of chaos, receives $1/c$ corrections that may be interpreted as $\lambda_L = \frac{2 \pi}{\beta} \left( 1 + \frac{12}{c} \right)$. However, out of time order correlators receive other equally important $1/c$ suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on $\lambda_L$ that emerges at large $c$, focusing on CFT$_2$ and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.Comment: 22+6 pages, 6 figure

Dispersion Relations in String Theory

We analyze the analytic continuation of the formally divergent one-loop amplitude for scattering of the graviton multiplet in the Type II Superstring. In particular we obtain explicit double and single dispersion relations, formulas for all the successive branch cuts extending out to plus infinity, as well as for the decay rate of a massive string state of arbitrary mass 2N into two string states of lower mass. We compare our results with the box diagram in a superposition of $\phi^3$-like field theories. The stringy effects are traced to a convergence problem in this superposition.Comment: 17 pages, COLUMBIA-YITP-UCLA/93/TEP/45 (figures fixed up

Unitarity Meets Channel-Duality for Rolling / Decaying D-Branes

Investigations for decay of unstable D-brane and rolling of accelerated D-brane dynamics have revealed that various proposed prescriptions give different result for spectral amplitudes and observables. Here, we study them with particular attention to unitarity and open-closed channel duality. From "ab initio" derivation in the open string channel, both in Euclidean and Lorentzian worldsheet approaches, we find heretofore overlooked contribution to the spectral amplitudes and obervables. The contribution is fortuitously absent for decay of unstable D-brane, but is present for rolling of accelerated D-brane. We finally show that the contribution is imperative for ensuring unitarity and optical theorem at each order in string loop expansion.Comment: Latex, 28 pages, 2 figures (colored

The Box Graph In Superstring Theory

In theories of closed oriented superstrings, the one loop amplitude is given by a single diagram, with the topology of a torus. Its interpretation had remained obscure, because it was formally real, converged only for purely imaginary values of the Mandelstam variables, and had to account for the singularities of both the box graph and the one particle reducible graphs in field theories. We present in detail an analytic continuation method which resolves all these difficulties. It is based on a reduction to certain minimal amplitudes which can themselves be expressed in terms of double and single dispersion relations, with explicit spectral densities. The minimal amplitudes correspond formally to an infinite superposition of box graphs on $\phi ^3$ like field theories, whose divergence is responsible for the poles in the string amplitudes. This paper is a considerable simplification and generalization of our earlier proposal published in Phys. Rev. Lett. 70 (1993) p 3692.Comment: Plain TeX, 67 pp. and 9 figures, Columbia/UCLA/94/TEP/3

Noncommutativity and theta-locality

In this paper, we introduce the condition of theta-locality which can be used as a substitute for microcausality in quantum field theory on noncommutative spacetime. This condition is closely related to the asymptotic commutativity which was previously used in nonlocal QFT. Heuristically, it means that the commutator of observables behaves at large spacelike separation like $\exp(-|x-y|^2/\theta)$, where $\theta$ is the noncommutativity parameter. The rigorous formulation given in the paper implies averaging fields with suitable test functions. We define a test function space which most closely corresponds to the Moyal star product and prove that this space is a topological algebra under the star product. As an example, we consider the simplest normal ordered monomial $:\phi\star\phi:$ and show that it obeys the theta-locality condition.Comment: LaTeX, 17 pages, no figures; minor changes to agree with published versio

Braided Structure in 4-dimensional conformal Quantum Field Theory

Higher dimensional conformal QFT possesses an interesting braided structure which, different from the d=1+1 models, is restricted to the timelike region and therefore easily escapes euclidean action methods. It lies behind the spectrum of anomalous dimensions which may be viewed as a kind of substitute for a missing particle interpretation in the presence of interactions.Comment: Dedicated to Gerhard Mack and Robert Schrader on the occasion of their 60th birthday, submitted to Phys. Lett. B, 10 pages, improvements of the formulation, shortening of the text, addition of a formula, removal of typo

Does boundary quantum mechanics imply quantum mechanics in the bulk?

Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field $\phi^{(0)}$ as a smeared operator in the CFT. A series of $1/N$ corrections must be added to $\phi^{(0)}$ to represent an interacting bulk field $\phi$. These corrections have been determined in the literature from several points of view. Here we develop a new perspective. We show that correlation functions involving $\phi^{(0)}$ suffer from ambiguities due to analytic continuation. As a result $\phi^{(0)}$ fails to be a well-defined linear operator in the CFT. This means bulk reconstruction can be understood as a procedure for building up well-defined operators in the CFT which thereby singles out the interacting field $\phi$. We further propose that the difficulty with defining $\phi^{(0)}$ as a linear operator can be re-interpreted as a breakdown of associativity. Presumably $\phi^{(0)}$ can only be corrected to become an associative operator in perturbation theory. This suggests that quantum mechanics in the bulk is only valid in perturbation theory around a semiclassical bulk geometry.Comment: 22 pages. v2: references adde

Remarks on Time-Space Noncommutative Field Theories

We propose a physical interpretation of the perturbative breakdown of unitarity in time-like noncommutative field theories in terms of production of tachyonic particles. These particles may be viewed as a remnant of a continuous spectrum of undecoupled closed-string modes. In this way, we give a unified view of the string-theoretical and the field-theoretical no-go arguments against time-like noncommutative theories. We also perform a quantitative study of various locality and causality properties of noncommutative field theories at the quantum level.Comment: 19 pages, LaTe