96,056 research outputs found
On the strength of proof-irrelevant type theories
We present a type theory with some proof-irrelevance built into the
conversion rule. We argue that this feature is useful when type theory is used
as the logical formalism underlying a theorem prover. We also show a close
relation with the subset types of the theory of PVS. We show that in these
theories, because of the additional extentionality, the axiom of choice implies
the decidability of equality, that is, almost classical logic. Finally we
describe a simple set-theoretic semantics.Comment: 20 pages, Logical Methods in Computer Science, Long version of IJCAR
2006 pape
Deconstruction and other approaches to supersymmetric lattice field theories
This report contains both a review of recent approaches to supersymmetric
lattice field theories and some new results on the deconstruction approach. The
essential reason for the complex phase problem of the fermion determinant is
shown to be derivative interactions that are not present in the continuum.
These irrelevant operators violate the self-conjugacy of the fermion action
that is present in the continuum. It is explained why this complex phase
problem does not disappear in the continuum limit. The fermion determinant
suppression of various branches of the classical moduli space is explored, and
found to be supportive of previous claims regarding the continuum limit.Comment: 70 page
Proof-irrelevant model of CC with predicative induction and judgmental equality
We present a set-theoretic, proof-irrelevant model for Calculus of
Constructions (CC) with predicative induction and judgmental equality in
Zermelo-Fraenkel set theory with an axiom for countably many inaccessible
cardinals. We use Aczel's trace encoding which is universally defined for any
function type, regardless of being impredicative. Direct and concrete
interpretations of simultaneous induction and mutually recursive functions are
also provided by extending Dybjer's interpretations on the basis of Aczel's
rule sets. Our model can be regarded as a higher-order generalization of the
truth-table methods. We provide a relatively simple consistency proof of type
theory, which can be used as the basis for a theorem prover
Perturbative search for dead-end CFTs
To explore the possibility of self-organized criticality, we look for CFTs
without any relevant scalar deformations (a.k.a dead-end CFTs) within
power-counting renormalizable quantum field theories with a weakly coupled
Lagrangian description. In three dimensions, the only candidates are pure
(Abelian) gauge theories, which may be further deformed by Chern-Simons terms.
In four dimensions, we show that there are infinitely many non-trivial
candidates based on chiral gauge theories. Using the three-loop beta functions,
we compute the gap of scaling dimensions above the marginal value, and it can
be as small as and robust against the perturbative
corrections. These classes of candidates are very weakly coupled and our
perturbative conclusion seems difficult to refute. Thus, the hypothesis that
non-trivial dead-end CFTs do not exist is likely to be false in four
dimensions.Comment: 23 pages, v2: published version with improvement
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