17,840 research outputs found
Closed N=2 Strings: Picture-Changing, Hidden Symmetries and SDG Hierarchy
We study the action of picture-changing and spectral flow operators on a
ground ring of ghost number zero operators in the chiral BRST cohomology of the
closed N=2 string and describe an infinite set of symmetry charges acting on
physical states. The transformations of physical string states are compared
with symmetries of self-dual gravity which is the effective field theory of the
closed N=2 string. We derive all infinitesimal symmetries of the self-dual
gravity equations in 2+2 dimensional spacetime and introduce an infinite
hierarchy of commuting flows on the moduli space of self-dual metrics. The
dependence on moduli parameters can be recovered by solving the equations of
the SDG hierarchy associated with an infinite set of abelian symmetries
generated recursively from translations. These non-local abelian symmetries are
shown to coincide with the hidden abelian string symmetries responsible for the
vanishing of most scattering amplitudes. Therefore, N=2 string theory
"predicts" not only self-dual gravity but also the SDG hierarchy.Comment: 41 pages, no figure
Loop groups in Yang-Mills theory
We consider the Yang-Mills equations with a matrix gauge group on the de
Sitter dS, anti-de Sitter AdS and Minkowski spaces. On all
these spaces one can introduce a doubly warped metric in the form , where and are the functions of
and is the metric on the two-dimensional hyperbolic space .
We show that in the adiabatic limit, when the metric on is scaled down,
the Yang-Mills equations become the sigma-model equations describing harmonic
maps from a two-dimensional manifold (dS, AdS or ,
respectively) into the based loop group of
smooth maps from the boundary circle of into the gauge
group . From this correspondence and the implicit function theorem it
follows that the moduli space of Yang-Mills theory with a gauge group in
four dimensions is bijective to the moduli space of two-dimensional sigma model
with as the target space. The sigma-model field equations can be
reduced to equations of geodesics on , solutions of which yield
magnetic-type configurations of Yang-Mills fields. The group
naturally acts on their moduli space.Comment: 8 pages; v3: clarifying remarks and references adde
Holomorphic Analogs of Topological Gauge Theories
We introduce a new class of gauge field theories in any complex dimension,
based on algebra-valued (p,q)-forms on complex n-manifolds. These theories are
holomorphic analogs of the well-known Chern-Simons and BF topological theories
defined on real manifolds. We introduce actions for different special
holomorphic BF theories on complex, Kahler and Calabi-Yau manifolds and
describe their gauge symmetries. Candidate observables, topological invariants
and relations to integrable models are briefly discussed.Comment: 12 pages, LaTeX2e, shortened PLB versio
Instantons on the six-sphere and twistors
We consider the six-sphere S^6=G_2/SU(3) and its twistor space Z=G_2/U(2)
associated with the SU(3)-structure on S^6. It is shown that a Hermitian
Yang-Mills connection (instanton) on a smooth vector bundle over S^6 is
equivalent to a flat partial connection on a vector bundle over the twistor
space Z. The relation with Tian's tangent instantons on R^7 and their twistor
description are briefly discussed.Comment: 12 pages; v2: clarifying comments added, published versio
On Supertwistors, the Penrose-Ward Transform and N=4 super Yang-Mills Theory
It was recently shown by Witten that B-type open topological string theory
with the supertwistor space CP^{3|4} as a target space is equivalent to
holomorphic Chern-Simons (hCS) theory on the same space. This hCS theory in
turn is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four
dimensions. We review the supertwistor description of self-dual and
anti-self-dual N-extended SYM theory as the integrability of super Yang-Mills
fields on complex (2|N)-dimensional superplanes and demonstrate the equivalence
of this description to Witten's formulation. The equivalence of the field
equations of hCS theory on an open subset of CP^{3|N} to the field equations of
self-dual N-extended SYM theory in four dimensions is made explicit.
Furthermore, we extend the picture to the full N=4 SYM theory and, by using the
known supertwistor description of this case, we show that the corresponding
constraint equations are (gauge) equivalent to the field equations of hCS
theory on a quadric in CP^{3|3}xCP^{3|3}.Comment: 48 pages; version to appear in ATM
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