A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine

Combining insights from the study of type refinement systems and of monoidal closed chiralities, we show how to reconstruct Lawvere's hyperdoctrine of presheaves using a full and faithful embedding into a monoidal closed bifibration living now over the compact closed category of small categories and distributors. Besides revealing dualities which are not immediately apparent in the traditional presentation of the presheaf hyperdoctrine, this reconstruction leads us to an axiomatic treatment of directed equality predicates (modelled by hom presheaves), realizing a vision initially set out by Lawvere (1970). It also leads to a simple calculus of string diagrams (representing presheaves) that is highly reminiscent of C. S. Peirce's existential graphs for predicate logic, refining an earlier interpretation of existential graphs in terms of Boolean hyperdoctrines by Brady and Trimble. Finally, we illustrate how this work extends to a bifibrational setting a number of fundamental ideas of linear logic.Comment: Identical to the final version of the paper as appears in proceedings of LICS 2016, formatted for on-screen readin

Scalar Dark Matter From Theory Space

The scalar dark matter candidate in a prototypical theory space little Higgs model is investigated. We review all details of the model pertinent to dark matter. We perform a thermal relic density calculation including couplings to the gauge and Higgs sectors of the model. We find two regions of parameter space that give acceptable dark matter abundances. The first region has a dark matter candidate with a mass of order 100 GeV, the second region has a heavy candidate with a mass greater than about 500 GeV$. The dark matter candidate in either region is an admixture of an SU(2) triplet and an SU(2) singlet, thereby constituting a WIMP (weakly interacting massive particle).Comment: 18 pages, 2 figures, version to appear in PR

Spectral cutoffs in indirect dark matter searches

Indirect searches for dark matter annihilation or decay products in the cosmic-ray spectrum are plagued by the question of how to disentangle a dark matter signal from the omnipresent astrophysical background. One of the practically background-free smoking-gun signatures for dark matter would be the observation of a sharp cutoff or a pronounced bump in the gamma-ray energy spectrum. Such features are generically produced in many dark matter models by internal Bremsstrahlung, and they can be treated in a similar manner as the traditionally looked-for gamma-ray lines. Here, we discuss prospects for seeing such features with present and future Atmospheric Cherenkov Telescopes.Comment: 4 pages, 2 figures, 1 table; conference proceedings for TAUP 2011, Munich 5-9 Se

Client-Server Sessions in Linear Logic

We introduce coexponentials, a new set of modalities for Classical Linear Logic. As duals to exponentials, the coexponentials codify a distributed form of the structural rules of weakening and contraction. This makes them a suitable logical device for encapsulating the pattern of a server receiving requests from an arbitrary number of clients on a single channel. Guided by this intuition we formulate a system of session types based on Classical Linear Logic with coexponentials, which is suited to modelling client-server interactions. We also present a session-typed functional programming language for server-client programming, which we translate to our system of coexponentials

Logical Step-Indexed Logical Relations

Appel and McAllester's "step-indexed" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference types. However, proofs using step-indexed models typically involve tedious, error-prone, and proof-obscuring step-index arithmetic, so it is important to develop clean, high-level, equational proof principles that avoid mention of step indices. In this paper, we show how to reason about binary step-indexed logical relations in an abstract and elegant way. Specifically, we define a logic LSLR, which is inspired by Plotkin and Abadi's logic for parametricity, but also supports recursively defined relations by means of the modal "later" operator from Appel, Melli\`es, Richards, and Vouillon's "very modal model" paper. We encode in LSLR a logical relation for reasoning relationally about programs in call-by-value System F extended with general recursive types. Using this logical relation, we derive a set of useful rules with which we can prove contextual equivalence and approximation results without counting steps

Phenomenological Aspects of Heterotic Orbifold Models at One Loop

We provide a detailed study of the phenomenology of orbifold compactifications of the heterotic string within the context of supergravity effective theories. Our investigation focuses on those models where the soft Lagrangian is dominated by loop contributions to the various soft supersymmetry breaking parameters. Such models typically predict non-universal soft masses and are thus significantly different from minimal supergravity and other universal models. We consider the pattern of masses that are governed by these soft terms and investigate the implications of certain indirect constraints on supersymmetric models, such as flavor-changing neutral currents, the anomalous magnetic moment of the muon and the density of thermal relic neutralinos. These string-motivated models show novel behavior that interpolates between the phenomenology of unified supergravity models and models dominated by the superconformal anomaly.Comment: 47 pages, 14 figure