13,054 research outputs found
Noncommutative/Nonlinear BPS Equations without Zero Slope Limit
It is widely believed that via the Seiberg-Witten map, the linearly realized
BPS equation in the non-commutative space is related to the non-linearly
realized BPS equation in the commutative space in the zero slope limit. We show
that the relation also holds without taking the zero slope limit as is expected
from the arguments of the BPS equation for the non-Abelian Born-Infeld theory.
This is regarded as an evidence for the relation between the two BPS equations.
As a byproduct of our analysis, the non-linear instanton equation is solved
exactly.Comment: 9 pages, LaTeX, no figures, v2: discussion on the string tension
removed, v3: minor modification
ABJ Fractional Brane from ABJM Wilson Loop
We present a new Fermi gas formalism for the ABJ matrix model. This
formulation identifies the effect of the fractional M2-brane in the ABJ matrix
model as that of a composite Wilson loop operator in the corresponding ABJM
matrix model. Using this formalism, we study the phase part of the ABJ
partition function numerically and find a simple expression for it. We further
compute a few exact values of the partition function at some coupling
constants. Fitting these exact values against the expected form of the grand
potential, we can determine the grand potential with exact coefficients. The
results at various coupling constants enable us to conjecture an explicit form
of the grand potential for general coupling constants. The part of the
conjectured grand potential from the perturbative sum, worldsheet instantons
and bound states is regarded as a natural generalization of that in the ABJM
matrix model, though the membrane instanton part contains a new contribution.Comment: 28 pages, 5 eps figures, v3: typos corrected and references added,
version to appear in JHE
Two-Point Functions in ABJM Matrix Model
We introduce non-trivial two-point functions of the super Schur polynomials
in the ABJM matrix model and study their exact values with the Fermi gas
formalism. We find that, although defined non-trivially, these two-point
functions enjoy two simple relations with the one-point functions. One of them
is associated with the Littlewood-Richardson rule, while the other is more
novel. With plenty of data, we also revisit the one-point functions and study
how the diagonal BPS indices are split asymmetrically by the degree difference.Comment: 53 pages, 5 eps figure
Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
It was known that the ABJM matrix model is dual to the topological string
theory on a Calabi-Yau manifold. Using this relation it was possible to write
down the exact instanton expansion of the partition function of the ABJM matrix
model. The expression consists of a universal function constructed from the
free energy of the refined topological string theory with an overall
topological invariant characterizing the Calabi-Yau manifold. In this paper we
explore two other superconformal Chern-Simons theories of the circular quiver
type. We find that the partition function of one theory enjoys the same
expression from the refined topological string theory as the ABJM matrix model
with different topological invariants while that of the other is more general.
We also observe an unexpected relation between these two theories.Comment: 35 pages, 1 figure; v2: section 3.3 added, references adde
- …