Lagrangians with electric and magnetic charges of N=2 supersymmetric gauge theories

General Lagrangians are constructed for N=2 supersymmetric gauge theories in four space-time dimensions involving gauge groups with (non-abelian) electric and magnetic charges. The charges induce a scalar potential, which, when the charges are regarded as spurionic quantities, is invariant under electric/magnetic duality. The resulting theories are especially relevant for supergravity, but details of the extension to local supersymmetry will be discussed elsewhere. The results include the coupling to hypermultiplets. Without the latter, it is demonstrated how an off-shell representation can be constructed based on vector and tensor supermultiplets.Comment: 34 pages, LaTe

Generalized gaugings and the field-antifield formalism

We discuss the algebra of general gauge theories that are described by the embedding tensor formalism. We compare the gauge transformations dependent and independent of an invariant action, and argue that the generic transformations lead to an infinitely reducible algebra. We connect the embedding tensor formalism to the field-antifield (or Batalin-Vilkovisky) formalism, which is the most general formulation known for general gauge theories and their quantization. The structure equations of the embedding tensor formalism are included in the master equation of the field-antifield formalism.Comment: 42 pages; v2: some clarifications and 1 reference added; version to be published in JHE

Superconformal hypermultiplets

We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special} hyper-K\"ahler manifolds. Such manifolds can be described as cones over tri-Sasakian metrics and are locally the product of a flat four-dimensional space and a quaternionic manifold. The latter manifolds appear in the coupling of hypermultiplets to N=2 supergravity. We employ local sections of an Sp$(n)\times{\rm Sp}(1)$ bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-K\"ahler and quaternionic manifolds

One-count memory circuit prevents machine mode interaction

One-count memory logic circuit used with electromechanical counter-printer machines operates in either count or print mode. The circuit advances the counter when the machine is in the count mode and provides storage for the count pulse when the machine is in the print mode

Critical Ising model and spanning trees partition functions

We prove that the squared partition function of the two-dimensional critical Ising model defined on a finite, isoradial graph $G=(V,E)$, is equal to $2^{|V|}$ times the partition function of spanning trees of the graph $\bar{G}$, where $\bar{G}$ is the graph $G$ extended along the boundary; edges of $G$ are assigned Kenyon's [Ken02] critical weights, and boundary edges of $\bar{G}$ have specific weights. The proof is an explicit construction, providing a new relation on the level of configurations between two classical, critical models of statistical mechanics.Comment: 38 pages, 26 figure