2,701 research outputs found
Hybrid Branching-Time Logics
Hybrid branching-time logics are introduced as extensions of CTL-like logics
with state variables and the downarrow-binder. Following recent work in the
linear framework, only logics with a single variable are considered. The
expressive power and the complexity of satisfiability of the resulting logics
is investigated.
As main result, the satisfiability problem for the hybrid versions of several
branching-time logics is proved to be 2EXPTIME-complete. These branching-time
logics range from strict fragments of CTL to extensions of CTL that can talk
about the past and express fairness-properties. The complexity gap relative to
CTL is explained by a corresponding succinctness result.
To prove the upper bound, the automata-theoretic approach to branching-time
logics is extended to hybrid logics, showing that non-emptiness of alternating
one-pebble Buchi tree automata is 2EXPTIME-complete.Comment: An extended abstract of this paper was presented at the International
Workshop on Hybrid Logics (HyLo 2007
M2-brane Probe Dynamics and Toric Duality
We study the dynamics of a single M2-brane probing toric Calabi-Yau four-fold
singularity in the context of the recently proposed M-theory crystal model of
AdS4/CFT3 dual pairs. We obtain an effective abelian gauge theory in which the
charges of the matter fields are given by the intersection numbers between
loops and faces in the crystal. We argue that the probe theory captures certain
aspects of the CFT3 even though the true M2-brane CFT is unlikely to be a usual
gauge theory. In particular, the moduli space of vacua of the gauge theory
coincides precisely with the Calabi-Yau singularity. Toric duality, partial
resolution, and a possibility of new RG flows are also discussed.Comment: 50 pages, 24 figures; v2. title changed, abstract and introduction
clarified. to appear in Nucl.Phys.
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