1,795 research outputs found
Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace
We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The
resulting non-abelian tensor hierarchy can be interpreted via an equivariant
chain complex. We lift this structure to N=1 superspace by constructing
superfield analogs for the tensor fields, along with covariant superfield
strengths. Next we construct Chern-Simons actions, for both the bosonic and N=1
cases, and note that the condition of gauge invariance can be presented
cohomologically. Finally, we provide an explicit realization of these
structures by dimensional reduction, for example by reducing the three-form of
eleven-dimensional supergravity into a superspace with manifest 4D, N=1
supersymmetry.Comment: 40pp, v2 added reference
New Bounds for the Garden-Hose Model
We show new results about the garden-hose model. Our main results include
improved lower bounds based on non-deterministic communication complexity
(leading to the previously unknown bounds for Inner Product mod 2
and Disjointness), as well as an upper bound for the
Distributed Majority function (previously conjectured to have quadratic
complexity). We show an efficient simulation of formulae made of AND, OR, XOR
gates in the garden-hose model, which implies that lower bounds on the
garden-hose complexity of the order will be
hard to obtain for explicit functions. Furthermore we study a time-bounded
variant of the model, in which even modest savings in time can lead to
exponential lower bounds on the size of garden-hose protocols.Comment: In FSTTCS 201
On the power of symmetric linear programs
© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We consider families of symmetric linear programs (LPs) that decide a property of graphs (or other relational structures) in the sense that, for each size of graph, there is an LP defining a polyhedral lift that separates the integer points corresponding to graphs with the property from those corresponding to graphs without the property. We show that this is equivalent, with at most polynomial blow-up in size, to families of symmetric Boolean circuits with threshold gates. In particular, when we consider polynomial-size LPs, the model is equivalent to definability in a non-uniform version of fixed-point logic with counting (FPC). Known upper and lower bounds for FPC apply to the non-uniform version. In particular, this implies that the class of graphs with perfect matchings has polynomial-size symmetric LPs while we obtain an exponential lower bound for symmetric LPs for the class of Hamiltonian graphs. We compare and contrast this with previous results (Yannakakis 1991) showing that any symmetric LPs for the matching and TSP polytopes have exponential size. As an application, we establish that for random, uniformly distributed graphs, polynomial-size symmetric LPs are as powerful as general Boolean circuits. We illustrate the effect of this on the well-studied planted-clique problem.Peer ReviewedPostprint (author's final draft
Three-forms in Supergravity and Flux Compactifications
We present a duality procedure that relates conventional four-dimensional
matter-coupled N=1 supergravities to dual formulations in which auxiliary
fields are replaced by field-strengths of gauge three-forms. The duality
promotes specific coupling constants appearing in the superpotential to vacuum
expectation values of the field-strengths. We then apply this general duality
to type IIA string compactifications on Calabi-Yau orientifolds with RR fluxes.
This gives a new supersymmetric formulation of the corresponding effective
four-dimensional theories which includes gauge three-forms.Comment: 37 pages, v3: minor correction
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