4 research outputs found
Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra Models
We study the BPS spectrum and vacuum moduli spaces in dimensional reductions
of Chern-Simons-matter theories with N>=2 supersymmetry to zero dimensions. Our
main example is a matrix model version of the ABJM theory which we relate
explicitly to certain reduced 3-algebra models. We find the explicit maps from
Chern-Simons quiver matrix models to dual IKKT matrix models. We address the
problem of topologically twisting the ABJM matrix model, and along the way
construct a new twist of the IKKT model. We construct a cohomological matrix
model whose partition function localizes onto a moduli space specified by
3-algebra relations which live in the double of the conifold quiver. It
computes an equivariant index enumerating framed BPS states with specified
R-charges which can be expressed as a combinatorial sum over certain filtered
pyramid partitions.Comment: 47 page
Membrane matrix models and 3-algebras
In this thesis we study the BPS spectrum and vacuum moduli spaces of membrane
matrix models derived from dimensional reduction of the BLG and ABJM M2-
brane theories. We explain how these reduced models may be mapped into each
other, and describe their relationship with the IKKT matrix model. We construct
BPS solutions to the reduced BLG model, and interpret them as quantized Nambu-
Poisson manifolds. We study the problem of topologically twisting the reduced
ABJM model, and along the way construct a new twist of the IKKT matrix model.
We construct a cohomological matrix model whose partition function localizes onto
the BPS moduli space of the ABJM matrix model. This partition function computes
an equivariant index enumerating framed BPS states with specified R-charges
Quantized Nambu-Poisson Manifolds and n-Lie Algebras
We investigate the geometric interpretation of quantized Nambu-Poisson
structures in terms of noncommutative geometries. We describe an extension of
the usual axioms of quantization in which classical Nambu-Poisson structures
are translated to n-Lie algebras at quantum level. We demonstrate that this
generalized procedure matches an extension of Berezin-Toeplitz quantization
yielding quantized spheres, hyperboloids, and superspheres. The extended
Berezin quantization of spheres is closely related to a deformation
quantization of n-Lie algebras, as well as the approach based on harmonic
analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms
of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative
hyperplanes. Some applications to the quantum geometry of branes in M-theory
are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde
Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model
We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to
a zero-dimensional 3-Lie algebra model and construct various stable solutions
corresponding to quantized Nambu-Poisson manifolds. A recently proposed Higgs
mechanism reduces this model to the IKKT matrix model. We find that in the
strong coupling limit, our solutions correspond to ordinary noncommutative
spaces arising as stable solutions in the IKKT model with D-brane backgrounds.
In particular, this happens for S^3, R^3 and five-dimensional Neveu-Schwarz
Hpp-waves. We expand our model around these backgrounds and find effective
noncommutative field theories with complicated interactions involving
higher-derivative terms. We also describe the relation of our reduced model to
a cubic supermatrix model based on an osp(1|32) supersymmetry algebra.Comment: 22 page