63 research outputs found
Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher Dimensions
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations
on the noncommutative space R^{2n}_\theta x S^2 which have manifest spherical
symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show
that the solutions imply an equivalence between instantons on R^{2n}_\theta x
S^2 and nonabelian vortices on R^{2n}_\theta, which can be interpreted as a
blowing-up of a chain of D0-branes on R^{2n}_\theta into a chain of spherical
D2-branes on R^{2n} x S^2. The low-energy dynamics of these configurations is
described by a quiver gauge theory which can be formulated in terms of new
geometrical objects generalizing superconnections. This formalism enables the
explicit assignment of D0-brane charges in equivariant K-theory to the
instanton solutions.Comment: 45 pages, 4 figures; v2: minor correction
String states, loops and effective actions in noncommutative field theory and matrix models
Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string
states as a tool for loop computations in noncommutative field theory and
matrix models. Defined in terms of coherent states, they exhibit the stringy
features of noncommutative field theory. This leads to a closed form for the
1-loop effective action in position space, capturing the long-range non-local
UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces.
The non-locality is tamed in the maximally supersymmetric IKKT or IIB model,
where it gives rise to supergravity. The linearized supergravity interactions
are obtained directly in position space at one loop using string states on
generic noncommutative branes.Comment: 31 pages, 2 figure
Fuzzy hyperspheres via confining potentials and energy cutoffs
We simplify and complete the construction of fully -equivariant fuzzy
spheres , for all dimensions , initiated in [G.
Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451]. This is based on
imposing a suitable energy cutoff on a quantum particle in
subject to a confining potential well with a very sharp minimum on the
sphere of radius ; the cutoff and the depth of the well diverge with
. We show that the irreducible representation
of on the space of harmonic homogeneous
polynomials of degree in the Cartesian coordinates of
(which we express via trace-free completely symmetric
projections) is isomorphic to the Hilbert space of the
particle, as a reducible representation of . Moreover,
we show that the algebra of observables is isomorphic to
. As diverges
(commutative limit) so does the dimension of , and we
recover ordinary quantum mechanics on the sphere ; more formally, we have
a fuzzy quantization of a coadjoint orbit of that goes to the
classical phase space .Comment: Latex file, 40 pages, 3 figure
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
Boundary State from Ellwood Invariants
Boundary states are given by appropriate linear combinations of Ishibashi
states. Starting from any OSFT solution and assuming Ellwood conjecture we show
that every coefficient of such a linear combination is given by an Ellwood
invariant, computed in a slightly modified theory where it does not trivially
vanish by the on-shell condition. Unlike the previous construction of
Kiermaier, Okawa and Zwiebach, ours is linear in the string field, it is
manifestly gauge invariant and it is also suitable for solutions known only
numerically. The correct boundary state is readily reproduced in the case of
known analytic solutions and, as an example, we compute the energy momentum
tensor of the rolling tachyon from the generalized invariants of the
corresponding solution. We also compute the energy density profile of
Siegel-gauge multiple lump solutions and show that, as the level increases, it
correctly approaches a sum of delta functions. This provides a gauge invariant
way of computing the separations between the lower dimensional D-branes.Comment: v2: 63 pages, 14 figures. Major improvements in section 2. Version
published in JHE
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