187,277 research outputs found
String Theory and Unification
The use of the AdS/CFT correspondence to arrive at quiver gauge field
theories is discussed. An abelian orbifold with the finite group can
give rise to a nonsupersymmetric gauge theory with chiral fermions
and complex scalars in different bi-fundamental representations of . The
precision measurements at the resonance suggest the values and , and a unifications scale TeV. Dedicated to the 65th birthday
of Pran Nath.Comment: 11 pages, 2 figures, talk at PASCOS 2004 / Nath Fes
The Algebraic Intersection Type Unification Problem
The algebraic intersection type unification problem is an important component
in proof search related to several natural decision problems in intersection
type systems. It is unknown and remains open whether the algebraic intersection
type unification problem is decidable. We give the first nontrivial lower bound
for the problem by showing (our main result) that it is exponential time hard.
Furthermore, we show that this holds even under rank 1 solutions (substitutions
whose codomains are restricted to contain rank 1 types). In addition, we
provide a fixed-parameter intractability result for intersection type matching
(one-sided unification), which is known to be NP-complete.
We place the algebraic intersection type unification problem in the context
of unification theory. The equational theory of intersection types can be
presented as an algebraic theory with an ACI (associative, commutative, and
idempotent) operator (intersection type) combined with distributivity
properties with respect to a second operator (function type). Although the
problem is algebraically natural and interesting, it appears to occupy a
hitherto unstudied place in the theory of unification, and our investigation of
the problem suggests that new methods are required to understand the problem.
Thus, for the lower bound proof, we were not able to reduce from known results
in ACI-unification theory and use game-theoretic methods for two-player tiling
games
Unification Scale in String Theory
We study the unification scale and gauge coupling constant in 4D string
theory. We show that the fine structure constant is determined by the dimension
of the hidden gauge group and only and are consistent with
minimal string unification while the unification scale can be of order of
.Comment: 12 pages (LaTeX
Set Unification
The unification problem in algebras capable of describing sets has been
tackled, directly or indirectly, by many researchers and it finds important
applications in various research areas--e.g., deductive databases, theorem
proving, static analysis, rapid software prototyping. The various solutions
proposed are spread across a large literature. In this paper we provide a
uniform presentation of unification of sets, formalizing it at the level of set
theory. We address the problem of deciding existence of solutions at an
abstract level. This provides also the ability to classify different types of
set unification problems. Unification algorithms are uniformly proposed to
solve the unification problem in each of such classes.
The algorithms presented are partly drawn from the literature--and properly
revisited and analyzed--and partly novel proposals. In particular, we present a
new goal-driven algorithm for general ACI1 unification and a new simpler
algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of
Logic Programming (TPLP
Gravitational Correction to Running of Gauge Couplings
We calculate the contribution of graviton exchange to the running of gauge
couplings at lowest non-trivial order in perturbation theory. Including this
contribution in a theory that features coupling constant unification does not
upset this unification, but rather shifts the unification scale. When
extrapolated formally, the gravitational correction renders all gauge couplings
asymptotically free.Comment: 4 pages, 2 figures; v2: Clarified awkward sentences and notations.
Corrected typos. Added references and discussion thereof in introduction.
Minor copy editting changes to agree with version to be published in Physical
Review Letter
Optimality in Goal-Dependent Analysis of Sharing
We face the problems of correctness, optimality and precision for the static
analysis of logic programs, using the theory of abstract interpretation. We
propose a framework with a denotational, goal-dependent semantics equipped with
two unification operators for forward unification (calling a procedure) and
backward unification (returning from a procedure). The latter is implemented
through a matching operation. Our proposal clarifies and unifies many different
frameworks and ideas on static analysis of logic programming in a single,
formal setting. On the abstract side, we focus on the domain Sharing by Jacobs
and Langen and provide the best correct approximation of all the primitive
semantic operators, namely, projection, renaming, forward and backward
unification. We show that the abstract unification operators are strictly more
precise than those in the literature defined over the same abstract domain. In
some cases, our operators are more precise than those developed for more
complex domains involving linearity and freeness.
To appear in Theory and Practice of Logic Programming (TPLP
Gauge Coupling Unification via A Novel Technicolor Model
We show that the recently proposed minimal walking technicolor theory
together with a small modification of the Standard Model fermionic matter
content leads to an excellent degree of unification of the gauge couplings. We
compare the degree of unification with various time-honored technicolor models
and the minimal supersymmetric extension of the Standard Model. We find that,
at the one-loop level, the new theory provides a degree of unification higher
than any of the other extensions above. The phenomenology of the present model
is very rich with various potential dark matter candidates.Comment: Final version to match the published on
Standard Model and Graviweak Unification with (Super)Renormalizable Gravity. Part I: Visible and Invisible Sectors of the Universe
We develop a self-consistent -invariant model of the unification
of gravity with weak gauge and Higgs fields in the visible and
invisible sectors of our Universe. We consider a general case of the graviweak
unification, including the higher-derivative super-renormalizable theory of
gravity, which is a unitary, asymptotically-free and perturbatively consistent
theory of the quantum gravity.Comment: 27 page
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