4,003 research outputs found
Duality Between String Junctions and D-Branes on Del Pezzo Surfaces
We revisit local mirror symmetry associated with del Pezzo surfaces in
Calabi-Yau threefolds in view of five-dimensional N=1 E_N theories compactified
on a circle. The mirror partner of singular Calabi-Yau with a shrinking del
Pezzo four-cycle is described as the affine 7-brane backgrounds probed by a
D3-brane. Evaluating the mirror map and the BPS central charge we relate
junction charges to RR charges of D-branes wrapped on del Pezzo surfaces. This
enables us to determine how the string junctions are mapped to D-branes on del
Pezzo surfaces.Comment: 35 pages, Latex, 1 figure; typos corrected, references update
Quantization of gauge fields, graph polynomials and graph cohomology
We review quantization of gauge fields using algebraic properties of
3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian
gauge theory quantized in a covariant gauge from scalar integrands for
connected 3-regular graphs, obtained from the two Symanzik polynomials. The
transition to the full gauge theory amplitude is obtained by the use of a
third, new, graph polynomial, the corolla polynomial. This implies effectively
a covariant quantization without ghosts, where all the relevant signs of the
ghost sector are incorporated in a double complex furnished by the corolla
polynomial -we call it cycle homology- and by graph homology.Comment: 44p, many figures, to appea
Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes
Color codes are topological stabilizer codes with unusual transversality
properties. Here I show that their group of transversal gates is optimal and
only depends on the spatial dimension, not the local geometry. I also introduce
a generalized, subsystem version of color codes. In 3D they allow the
transversal implementation of a universal set of gates by gauge fixing, while
error-detecting measurements involve only 4 or 6 qubits.Comment: 10 pages, 6 figures, as accepted in journa
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