3,662 research outputs found
Branes And Supergroups
Extending previous work that involved D3-branes ending on a fivebrane with
, we consider a similar two-sided problem. This
construction, in case the fivebrane is of NS type, is associated to the
three-dimensional Chern-Simons theory of a supergroup U or OSp
rather than an ordinary Lie group as in the one-sided case. By -duality, we
deduce a dual magnetic description of the supergroup Chern-Simons theory; a
slightly different duality, in the orthosymplectic case, leads to a strong-weak
coupling duality between certain supergroup Chern-Simons theories on
; and a further -duality leads to a version of Khovanov
homology for supergroups. Some cases of these statements are known in the
literature. We analyze how these dualities act on line and surface operators.Comment: 143 page
Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory
We construct an approximation to field theories on the noncommutative torus
based on soliton projections and partial isometries which together form a
matrix algebra of functions on the sum of two circles. The matrix quantum
mechanics is applied to the perturbative dynamics of scalar field theory, to
tachyon dynamics in string field theory, and to the Hamiltonian dynamics of
noncommutative gauge theory in two dimensions. We also describe the adiabatic
dynamics of solitons on the noncommutative torus and compare various classes of
noncommutative solitons on the torus and the plane.Comment: 70 pages, 4 figures; v2: References added and update
Aggregated fuzzy answer set programming
Fuzzy Answer Set programming (FASP) is an extension of answer set programming (ASP), based on fuzzy logic. It allows to encode continuous optimization problems in the same concise manner as ASP allows to model combinatorial problems. As a result of its inherent continuity, rules in FASP may be satisfied or violated to certain degrees. Rather than insisting that all rules are fully satisfied, we may only require that they are satisfied partially, to the best extent possible. However, most approaches that feature partial rule satisfaction limit themselves to attaching predefined weights to rules, which is not sufficiently flexible for most real-life applications. In this paper, we develop an alternative, based on aggregator functions that specify which (combination of) rules are most important to satisfy. We extend upon previous work by allowing aggregator expressions to define partially ordered preferences, and by the use of a fixpoint semantics
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