1,843,139 research outputs found
Internal Parametricity for Cubical Type Theory
We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives. The combined theory supports both univalence and its relational equivalent, which we call relativity. We demonstrate the use of the theory by analyzing polymorphic functions between higher inductive types, and we give an account of the identity extension lemma for internal parametricity
A General Framework for the Semantics of Type Theory
We propose an abstract notion of a type theory to unify the semantics of
various type theories including Martin-L\"{o}f type theory, two-level type
theory and cubical type theory. We establish basic results in the semantics of
type theory: every type theory has a bi-initial model; every model of a type
theory has its internal language; the category of theories over a type theory
is bi-equivalent to a full sub-2-category of the 2-category of models of the
type theory
Modalities in homotopy type theory
Univalent homotopy type theory (HoTT) may be seen as a language for the
category of -groupoids. It is being developed as a new foundation for
mathematics and as an internal language for (elementary) higher toposes. We
develop the theory of factorization systems, reflective subuniverses, and
modalities in homotopy type theory, including their construction using a
"localization" higher inductive type. This produces in particular the
(-connected, -truncated) factorization system as well as internal
presentations of subtoposes, through lex modalities. We also develop the
semantics of these constructions
T Duality Between Perturbative Characters of and SO(32) Heterotic Strings Compactified On A Circle
Characters of and SO(32) heterotic strings involving the
full internal symmetry Cartan subalgebra generators are defined after circle
compactification so that they are T dual. The novel point, as compared with an
earlier study of the type II case (hep-th/9707107), is the appearence of Wilson
lines. Using SO(17,1) transformations between the weight lattices reveals the
existence of an intermediate theory where T duality transformations are
disentangled from the internal symmetry. This intermediate theory corresponds
to a sort of twisted compactification of a novel type. Its modular invariance
follows from an interesting interplay between three representations of the
modular group.Comment: 17 pages LateX 2E, 2 figures (eps
A Supersymmetric and Smooth Compactification of M-theory to AdS(5)
We obtain smooth M-theory solutions whose geometry is a warped product of
AdS_5 and a compact internal space that can be viewed as an S^4 bundle over
S^2. The bundle can be trivial or twisted, depending on the even or odd values
of the two diagonal monopole charges. The solution preserves N=2 supersymmetry
and is dual to an N=1 D=4 superconformal field theory, providing a concrete
framework to study the AdS_5/CFT_4 correspondence in M-theory. We construct
analogous embeddings of AdS_4, AdS_3 and AdS_2 in massive type IIA, type IIB
and M-theory, respectively. The internal spaces have generalized holonomy and
can be viewed as S^n bundles over S^2 for n=4, 5 and 7. Surprisingly, the
dimensions of spaces with generalized holonomy includes D=9. We also obtain a
large class of solutions of AdS\times H^2.Comment: Latex, 12 pages, references added, incorrect statement remove
Relativistic theory of tidal Love numbers
In Newtonian gravitational theory, a tidal Love number relates the mass
multipole moment created by tidal forces on a spherical body to the applied
tidal field. The Love number is dimensionless, and it encodes information about
the body's internal structure. We present a relativistic theory of Love
numbers, which applies to compact bodies with strong internal gravities; the
theory extends and completes a recent work by Flanagan and Hinderer, which
revealed that the tidal Love number of a neutron star can be measured by
Earth-based gravitational-wave detectors. We consider a spherical body deformed
by an external tidal field, and provide precise and meaningful definitions for
electric-type and magnetic-type Love numbers; and these are computed for
polytropic equations of state. The theory applies to black holes as well, and
we find that the relativistic Love numbers of a nonrotating black hole are all
zero.Comment: 25 pages, 8 figures, many tables; final version to be published in
Physical Review
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