233,331 research outputs found
Subdivision Directional Fields
We present a novel linear subdivision scheme for face-based tangent
directional fields on triangle meshes. Our subdivision scheme is based on a
novel coordinate-free representation of directional fields as halfedge-based
scalar quantities, bridging the finite-element representation with discrete
exterior calculus. By commuting with differential operators, our subdivision is
structure-preserving: it reproduces curl-free fields precisely, and reproduces
divergence-free fields in the weak sense. Moreover, our subdivision scheme
directly extends to directional fields with several vectors per face by working
on the branched covering space. Finally, we demonstrate how our scheme can be
applied to directional-field design, advection, and robust earth mover's
distance computation, for efficient and robust computation
Locality in GNS Representations of Deformation Quantization
In the framework of deformation quantization we apply the formal GNS
construction to find representations of the deformed algebras in pre-Hilbert
spaces over and establish the notion of local operators
in these pre-Hilbert spaces. The commutant within the local operators is used
to distinguish `thermal' from `pure' representations. The computation of the
local commutant is exemplified in various situations leading to the physically
reasonable distinction between thermal representations and pure ones. Moreover,
an analogue of von Neumann's double commutant theorem is proved in the
particular situation of a GNS representation with respect to a KMS functional
and for the Schr\"odinger representation on cotangent bundles. Finally we prove
a formal version of the Tomita-Takesaki theorem.Comment: LaTeX2e, 29 page
Mirror Symmetry And Loop Operators
Wilson loops in gauge theories pose a fundamental challenge for dualities.
Wilson loops are labeled by a representation of the gauge group and should map
under duality to loop operators labeled by the same data, yet generically, dual
theories have completely different gauge groups. In this paper we resolve this
conundrum for three dimensional mirror symmetry. We show that Wilson loops are
exchanged under mirror symmetry with Vortex loop operators, whose microscopic
definition in terms of a supersymmetric quantum mechanics coupled to the theory
encode in a non-trivial way a representation of the original gauge group,
despite that the gauge groups of mirror theories can be radically different.
Our predictions for the mirror map, which we derive guided by branes in string
theory, are confirmed by the computation of the exact expectation value of
Wilson and Vortex loop operators on the three-sphere.Comment: 92 pages, v2: minor clarifications in the introduction, to be
published in JHE
Giant Gravitons in Conformal Field Theory
Giant gravitons in AdS_5 x S^5, and its orbifolds, have a dual field theory
representation as states created by chiral primary operators. We argue that
these operators are not single-trace operators in the conformal field theory,
but rather are determinants and subdeterminants of scalar fields; the stringy
exclusion principle applies to these operators. Evidence for this
identification comes from three sources: (a) topological considerations in
orbifolds, (b) computation of protected correlators using free field theory and
(c) a Matrix model argument. The last argument applies to AdS_7 x S^4 and the
dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to
compute the expectation value of a giant graviton operator along the Coulomb
branch of the theory.Comment: 37 pages, LaTeX, 1 figure. v2: references and acknowledgements added,
small correction
Polynomial approximation of non-Gaussian unitaries by counting one photon at a time
In quantum computation with continous-variable systems, quantum advantage can
only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian
unitary evolutions and measurements suited for computation are challenging to
realize in the lab. We propose and analyze two methods to apply a polynomial
approximation of any unitary operator diagonal in the amplitude quadrature
representation, including non-Gaussian operators, to an unknown input state.
Our protocols use as a primary non-Gaussian resource a single-photon counter.
We use the fidelity of the transformation with the target one on Fock and
coherent states to assess the quality of the approximate gate.Comment: 11 pages, 7 figure
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