• Corpus ID: 9068879

Turing's Landscape: decidability, computability and complexity in string theory

@article{Rej2009TuringsLD,
  title={Turing's Landscape: decidability, computability and complexity in string theory},
  author={Abhijnan Rej},
  journal={arXiv: High Energy Physics - Theory},
  year={2009}
}
  • A. Rej
  • Published 10 September 2009
  • Mathematics
  • arXiv: High Energy Physics - Theory
I argue that questions of algorithmic decidability, computability and complexity should play a larger role in deciding the "ultimate" theoretical description of the Landscape of string vacua. More specifically, I examine the notion of the average rank of the (unification) gauge group in the Landscape, the explicit construction of Ricci-flat metrics on Calabi-Yau manifolds as well as the computability of fundamental periods to show that undecidability questions are far more pervasive than that… 
View PDF on arXiv
1 Citations
Background Citations
1

One Citation

Ranks of gauge groups and an NP-complete problem on the Landscape
We prove that the problem of determination of factor gauge groups given the rank of the gauge group at any given vacuum in the Landscape is in the computational complexity class NPC. This extends a…

References

SHOWING 1-10 OF 46 REFERENCES
Computational complexity of the landscape I
Computers and Intractability: A Guide to the Theory of NP-Completeness
Horn formulae play a prominent role in artificial intelligence and logic programming. In this paper we investigate the problem of optimal compression of propositional Horn production rule knowledge…
Periods for Calabi-Yau and Landau-Ginzburg vacua☆
String Theory on Calabi-Yau Manifolds
These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments…
A Finite Landscape
We present evidence that the number of string/$M$ theory vacua consistent with experiments is a finite number. We do this both by explicit analysis of infinite sequences of vacua and by applying…
The Fractal Nature of Riem/Diff I
This paper is devoted to large scale aspects of the geometry of the space of isometry classes of Riemannian metrics, with a 2-sided curvature bound, on a fixed compact smooth manifold of dimension at…
Landscape cartography: A coarse survey of gauge group rank and stabilization of the proton
The landscape of string/M theory is surveyed over a large class of type IIB flux compactification vacua. We derive a simple formula for the average size of the gauge group rank on the landscape under…
The trouble with Physics: The rise of string theory, the fall of a Science, and what comes next
The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next is a book about the history of physics from Copernicus forward. It is also a book that discusses the…
Multiple Mellin-Barnes integrals as periods of Calabi-Yau manifolds with several moduli
We give a representation, in terms of iterated Mellin-Barnes integrals, of periods on multi-moduli Calabi-Yau manifolds arising in superstring theory. Using this representation and the theory of…
The statistics of supersymmetric D-brane models
...
...