21,640 research outputs found

    Work it, wrap it, fix it, fold it

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    The worker/wrapper transformation is a general-purpose technique for refactoring recursive programs to improve their performance. The two previous approaches to formalising the technique were based upon different recursion operators and different correctness conditions. In this paper we show how these two approaches can be generalised in a uniform manner by combining their correctness conditions, extend the theory with new conditions that are both necessary and sufficient to ensure the correctness of the worker/wrapper technique, and explore the benefits that result. All the proofs have been mechanically verified using the Agda system

    Second-Order Functions and Theorems in ACL2

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    SOFT ('Second-Order Functions and Theorems') is a tool to mimic second-order functions and theorems in the first-order logic of ACL2. Second-order functions are mimicked by first-order functions that reference explicitly designated uninterpreted functions that mimic function variables. First-order theorems over these second-order functions mimic second-order theorems universally quantified over function variables. Instances of second-order functions and theorems are systematically generated by replacing function variables with functions. SOFT can be used to carry out program refinement inside ACL2, by constructing a sequence of increasingly stronger second-order predicates over one or more target functions: the sequence starts with a predicate that specifies requirements for the target functions, and ends with a predicate that provides executable definitions for the target functions.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

    Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes

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    We investigate orientifolds of type II string theory on K3 and Calabi-Yau 3-folds with intersecting D-branes wrapping special Lagrangian cycles. We determine quite generically the chiral massless spectrum in terms of topological invariants and discuss both orbifold examples and algebraic realizations in detail. Intriguingly, the developed techniques provide an elegant way to figure out the chiral sector of orientifold models without computing any explicit string partition function. As a new example we derive a non-supersymmetric Standard-like Model from an orientifold of type IIA on the quintic Calabi-Yau 3-fold with wrapped D6-branes. In the case of supersymmetric intersecting brane models on Calabi-Yau manifolds we discuss the D-term and F-term potentials, the effective gauge couplings and the Green-Schwarz mechanism. The mirror symmetric formulation of this construction is provided within type IIB theory. We finally include a short discussion about the lift of these models from type IIB on K3 to F-theory and from type IIA on Calabi-Yau 3-folds to M-theory on G_2 manifolds.Comment: 82 pages, harvmac, 5 figures. v2: references added. v3: T^6 orientifold corrected, JHEP versio

    Calabi-Yau 3-folds from 2-folds

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    We consider type IIA string theory on a Calabi-Yau 2-fold with D6-branes wrapping 2-cycles in the 2-fold. We find a complete set of conditions on the supergravity solution for any given wrapped brane configuration in terms of SU(2) structures. We reduce the problem of finding a supergravity solution for the wrapped branes to finding a harmonic function on R×\timesCY2_2. We then lift this solution to 11-dimensions as a product of R(4.1)^{(4.1)} and a Calabi-Yau 3-fold. We show how the metric on the 3-fold is determined in terms of the wrapped brane solution. We write down the distinguished (3,0) form and the K{\"a}hler form of the 3-fold in terms of structures defined on the base 2-d complex manifold. We discuss the topology of the 3-fold in terms of the D6-branes and the underlying 2-fold. We show that in addition to the non-trivial cycles inherited from the underlying 2-fold there are N1N-1 new 2-cycles. We construct closed (1,1) forms corresponding to these new cycles. We also display some explicit examples. One of our examples is that of D6-branes wrapping the 2-cycle in an A1_1 ALE space, the resulting 3-fold has h(1,1)=Nh^{(1,1)}=N, where NN is the number of D6-branes.Comment: 30 page

    Moving Five-Branes in Low-Energy Heterotic M-Theory

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    We construct cosmological solutions of four-dimensional effective heterotic M-theory with a moving five-brane and evolving dilaton and T modulus. It is shown that the five-brane generates a transition between two asymptotic rolling-radii solutions. Moreover, the five-brane motion always drives the solutions towards strong coupling asymptotically. We present an explicit example of a negative-time branch solution which ends in a brane collision accompanied by a small-instanton transition. The five-dimensional origin of some of our solutions is also discussed.Comment: 16 pages, Latex, 3 eps figure

    The String Landscape, the Swampland, and the Missing Corner

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    We give a brief overview of the string landscape and techniques used to construct string compactifications. We then explain how this motivates the notion of the swampland and review a number of conjectures that attempt to characterize theories in the swampland. We also compare holography in the context of superstrings with the similar, but much simpler case of topological string theory. For topological strings, there is a direct definition of topological gravity based on a sum over a "quantum gravitational foam." In this context, holography is the statement of an identification between a gravity and gauge theory, both of which are defined independently of one another. This points to a missing corner in string dualities which suggests the search for a direct definition of quantum theory of gravity rather than relying on its strongly coupled holographic dual as an adequate substitute (Based on TASI 2017 lectures given by C. Vafa)

    The HERMIT in the Tree

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    This paper describes our experience using the HERMIT tool- kit to apply well-known transformations to the internal core language of the Glasgow Haskell Compiler. HERMIT provides several mechanisms to support writing general-purpose transformations: a domain-specific language for strategic programming specialized to GHC's core language, a library of primitive rewrites, and a shell-style{based scripting language for interactive and batch usage. There are many program transformation techniques that have been described in the literature but have not been mechanized and made available inside GHC - either because they are too specialized to include in a general-purpose compiler, or because the developers' interest is in theory rather than implementation. The mechanization process can often reveal pragmatic obstacles that are glossed over in pen-and-paper proofs; understanding and removing these obstacles is our concern. Using HERMIT, we implement eleven examples of three program transformations, report on our experience, and describe improvements made in the process
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