29 research outputs found
A tentative theory of large distance physics
A theoretical mechanism is devised to determine the large distance physics of
spacetime. It is a two dimensional nonlinear model, the lambda model, set to
govern the string worldsurface to remedy the failure of string theory. The
lambda model is formulated to cancel the infrared divergent effects of handles
at short distance on the worldsurface. The target manifold is the manifold of
background spacetimes. The coupling strength is the spacetime coupling
constant. The lambda model operates at 2d distance , very much
shorter than the 2d distance where the worldsurface is seen. A large
characteristic spacetime distance is given by .
Spacetime fields of wave number up to 1/L are the local coordinates for the
manifold of spacetimes. The distribution of fluctuations at 2d distances
shorter than gives the {\it a priori} measure on the target
manifold, the manifold of spacetimes. If this measure concentrates at a
macroscopic spacetime, then, nearby, it is a measure on the spacetime fields.
The lambda model thereby constructs a spacetime quantum field theory, cutoff at
ultraviolet distance , describing physics at distances larger than . The
lambda model also constructs an effective string theory with infrared cutoff
, describing physics at distances smaller than . The lambda model evolves
outward from zero 2d distance, , building spacetime physics
starting from and proceeding downward in . can be taken
smaller than any distance practical for experiments, so the lambda model, if
right, gives all actually observable physics. The harmonic surfaces in the
manifold of spacetimes are expected to have novel nonperturbative effects at
large distances.Comment: Latex, 107 page
Some Consequences of Noncommutative Worldsheet of Superstring
In this paper some properties of the superstring with noncommutative
worldsheet are studied. We study the noncommutativity of the spacetime,
generalization of the Poincar\'e symmetry of the superstring, the changes of
the metric, antisymmetric tensor and dilaton.Comment: 11 pages, Latex, no figure, a new action and some references have
been adde
g-function in perturbation theory
We present some explicit computations checking a particular form of gradient
formula for a boundary beta function in two-dimensional quantum field theory on
a disc. The form of the potential function and metric that we consider were
introduced in hep-th/9210065, hep-th/9311177 in the context of background
independent open string field theory. We check the gradient formula to the
third order in perturbation theory around a fixed point. Special consideration
is given to situations when resonant terms are present exhibiting logarithmic
divergences and universal nonlinearities in beta functions. The gradient
formula is found to work to the given order.Comment: 1+14 pages, Latex; v.2: typos corrected; v.3: minor corrections, to
appear in IJM
Elliptic Genera and 3d Gravity
We describe general constraints on the elliptic genus of a 2d supersymmetric
conformal field theory which has a gravity dual with large radius in Planck
units. We give examples of theories which do and do not satisfy the bounds we
derive, by describing the elliptic genera of symmetric product orbifolds of
, product manifolds, certain simple families of Calabi-Yau hypersurfaces,
and symmetric products of the "Monster CFT." We discuss the distinction between
theories with supergravity duals and those whose duals have strings at the
scale set by the AdS curvature. Under natural assumptions we attempt to
quantify the fraction of (2,2) supersymmetric conformal theories which admit a
weakly curved gravity description, at large central charge.Comment: 50 pages, 9 figures, v2: minor corrections to section
The Computability-Theoretic Content of Emergence
In dealing with emergent phenomena, a common task is to identify useful descriptions of them in terms of the underlying atomic processes, and to extract enough computational content from these descriptions to enable predictions to be made. Generally, the underlying atomic processes are quite well understood, and (with important exceptions) captured by mathematics from which it is relatively easy to extract algorithmic con- tent. A widespread view is that the difficulty in describing transitions from algorithmic activity to the emergence associated with chaotic situations is a simple case of complexity outstripping computational resources and human ingenuity. Or, on the other hand, that phenomena transcending the standard Turing model of computation, if they exist, must necessarily lie outside the domain of classical computability theory. In this article we suggest that much of the current confusion arises from conceptual gaps and the lack of a suitably fundamental model within which to situate emergence. We examine the potential for placing emer- gent relations in a familiar context based on Turing's 1939 model for interactive computation over structures described in terms of reals. The explanatory power of this model is explored, formalising informal descrip- tions in terms of mathematical definability and invariance, and relating a range of basic scientific puzzles to results and intractable problems in computability theory