9,381 research outputs found
Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions
We show that noncommutative gauge theory in two dimensions is an exactly
solvable model. A cohomological formulation of gauge theory defined on the
noncommutative torus is used to show that its quantum partition function can be
written as a sum over contributions from classical solutions. We derive an
explicit formula for the partition function of Yang-Mills theory defined on a
projective module for arbitrary noncommutativity parameter \theta which is
manifestly invariant under gauge Morita equivalence. The energy observables are
shown to be smooth functions of \theta. The construction of noncommutative
instanton contributions to the path integral is described in some detail. In
general, there are infinitely many gauge inequivalent contributions of fixed
topological charge, along with a finite number of quantum fluctuations about
each instanton. The associated moduli spaces are combinations of symmetric
products of an ordinary two-torus whose orbifold singularities are not resolved
by noncommutativity. In particular, the weak coupling limit of the gauge theory
is independent of \theta and computes the symplectic volume of the moduli space
of constant curvature connections on the noncommutative torus.Comment: 52 pages LaTeX, 1 eps figure, uses espf. V2: References added and
repaired; V3: Typos corrected, some clarifying explanations added; version to
be published in Communications in Mathematical Physic
Black String Entropy from Anomalous D-brane Couplings
The quantum corrections to the counting of statistical entropy for the
5+1-dimensional extremal black string in type-IIB supergravity with two
observers are studied using anomalous Wess-Zumino actions for the corresponding
intersecting D-brane description. The electric-magnetic duality symmetry of the
anomalous theory implies a new symmetry between D-string and D-fivebrane
sources and renders opposite sign for the RR charge of one of the intersecting
D-branes relative to that of the black string. The electric-magnetic symmetric
Hilbert space decomposes into subspaces associated with interior and exterior
regions and it is shown that, for an outside observer, the expectation value of
a horizon area operator agrees with the deviation of the classical horizon area
in going from extremal to near-extremal black strings.Comment: 12 pages, LaTeX; Corrections and clarifying comments adde
Double quiver gauge theory and nearly Kahler flux compactifications
We consider G-equivariant dimensional reduction of Yang-Mills theory with
torsion on manifolds of the form MxG/H where M is a smooth manifold, and G/H is
a compact six-dimensional homogeneous space provided with a never integrable
almost complex structure and a family of SU(3)-structures which includes a
nearly Kahler structure. We establish an equivalence between G-equivariant
pseudo-holomorphic vector bundles on MxG/H and new quiver bundles on M
associated to the double of a quiver Q, determined by the SU(3)-structure, with
relations ensuring the absence of oriented cycles in Q. When M=R^2, we describe
an equivalence between G-invariant solutions of Spin(7)-instanton equations on
MxG/H and solutions of new quiver vortex equations on M. It is shown that
generic invariant Spin(7)-instanton configurations correspond to quivers Q that
contain non-trivial oriented cycles.Comment: 42 pages; v2: minor corrections; Final version to be published in
JHE
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
Quiver Gauge Theory and Noncommutative Vortices
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations
on noncommutative spaces R^{2n}_theta x G/H which are manifestly G-symmetric.
Given a G-representation, by twisting with a particular bundle over G/H, we
obtain a G-equivariant U(k) bundle with a G-equivariant connection over
R^{2n}_theta x G/H. The U(k) Donaldson-Uhlenbeck-Yau equations on these spaces
reduce to vortex-type equations in a particular quiver gauge theory on
R^{2n}_theta. Seiberg-Witten monopole equations are particular examples. The
noncommutative BPS configurations are formulated with partial isometries, which
are obtained from an equivariant Atiyah-Bott-Shapiro construction. They can be
interpreted as D0-branes inside a space-filling brane-antibrane system.Comment: talk by O.L. at the 21st Nishinomiya-Yukawa Memorial Symposium,
Kyoto, 15 Nov. 200
SU(3)-Equivariant Quiver Gauge Theories and Nonabelian Vortices
We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on
Kaehler manifolds of the form M x SU(3)/H, with H = SU(2) x U(1) or H = U(1) x
U(1). The induced rank two quiver gauge theories on M are worked out in detail
for representations of H which descend from a generic irreducible
SU(3)-representation. The reduction of the Donaldson-Uhlenbeck-Yau equations on
these spaces induces nonabelian quiver vortex equations on M, which we write
down explicitly. When M is a noncommutative deformation of the space C^d, we
construct explicit BPS and non-BPS solutions of finite energy for all cases. We
compute their topological charges in three different ways and propose a novel
interpretation of the configurations as states of D-branes. Our methods and
results generalize from SU(3) to any compact Lie group.Comment: 1+56 pages, 9 figures; v2: clarifying comments added, final version
to appear in JHE
Noncommutative theories and general coordinate transformations
We study the class of noncommutative theories in dimensions whose spatial
coordinates can be obtained by performing a smooth change of
variables on , the coordinates of a standard noncommutative
theory, which satisfy the relation , with a
constant tensor. The variables verify a commutation
relation which is, in general, space-dependent. We study the main properties of
this special kind of noncommutative theory and show explicitly that, in two
dimensions, any theory with a space-dependent commutation relation can be
mapped to another where that is constant.Comment: 21 pages, no figures, LaTeX. v2: section 5 added, typos corrected.
Version to appear in Physical Review
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