4,949 research outputs found
Tensor models and hierarchy of n-ary algebras
Tensor models are generalization of matrix models, and are studied as models
of quantum gravity. It is shown that the symmetry of the rank-three tensor
models is generated by a hierarchy of n-ary algebras starting from the usual
commutator, and the 3-ary algebra symmetry reported in the previous paper is
just a single sector of the whole structure. The condition for the Leibnitz
rules of the n-ary algebras is discussed from the perspective of the invariance
of the underlying algebra under the n-ary transformations. It is shown that the
n-ary transformations which keep the underlying algebraic structure invariant
form closed finite n-ary Lie subalgebras. It is also shown that, in physical
settings, the 3-ary transformation practically generates only local
infinitesimal symmetry transformations, and the other more non-local
infinitesimal symmetry transformations of the tensor models are generated by
higher n-ary transformations.Comment: 13 pages, some references updated and correcte
Exact Results in Quiver Quantum Mechanics and BPS Bound State Counting
We exactly evaluate the partition function (index) of N=4 supersymmetric
quiver quantum mechanics in the Higgs phase by using the localization
techniques. We show that the path integral is localized at the fixed points,
which are obtained by solving the BRST equations, and D-term and F-term
conditions. We turn on background gauge fields of R-symmetries for the chiral
multiplets corresponding to the arrows between quiver nodes, but the partition
function does not depend on these R-charges. We give explicit examples of the
quiver theory including a non-coprime dimension vector. The partition functions
completely agree with the mathematical formulae of the Poincare polynomials
(chi_y-genus) and the wall crossing for the quiver moduli spaces . We also
discuss exact computation of the expectation values of supersymmetric
(Q-closed) Wilson loops in the quiver theory.Comment: 40 pages, 7 figures; v2: minor corrections and references are added;
v3: references added, typos corrected, discrepancy in the non-coprime case
resolve
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