454 research outputs found
A G_2 Unification of the Deformed and Resolved Conifolds
We find general first-order equations for G_2 metrics of cohomogeneity one
with S^3\times S^3 principal orbits. These reduce in two special cases to
previously-known systems of first-order equations that describe regular
asymptotically locally conical (ALC) metrics \bB_7 and \bD_7, which have
weak-coupling limits that are S^1 times the deformed conifold and the resolved
conifold respectively. Our more general first-order equations provide a
supersymmetric unification of the two Calabi-Yau manifolds, since the metrics
\bB_7 and \bD_7 arise as solutions of the {\it same} system of first-order
equations, with different values of certain integration constants.
Additionally, we find a new class of ALC G_2 solutions to these first-order
equations, which we denote by \wtd\bC_7, whose topology is an \R^2 bundle over
T^{1,1}. There are two non-trivial parameters characterising the homogeneous
squashing of the T^{1,1} bolt. Like the previous examples of the \bB_7 and
\bD_7 ALC metrics, here too there is a U(1) isometry for which the circle has
everywhere finite and non-zero length. The weak-coupling limit of the \wtd\bC_7
metrics gives S^1 times a family of Calabi-Yau metrics on a complex line bundle
over S^2\times S^2, with an adjustable parameter characterising the relative
sizes of the two S^2 factors.Comment: Latex, 14 pages, Major simplification of first-order equations;
references amende
New G_2 metric, D6-branes and Lattice Universe
We construct a new (singular) cohomogeneity-three metric of G_2 holonomy. The
solution can be viewed as a triple intersection of smeared Taub-NUTs. The
metric comprises three non-compact radial-type coordinates, with the principal
orbits being a T^3 bundle over S^1. We consider an M-theory vacuum
(Minkowski)_4\times M_7 where M_7 is the G_2 manifold. Upon reduction on a
circle in the T^3, we obtain the intersection of a D6-brane, a Taub-NUT and a
6-brane with R-R 2-form flux. Reducing the solution instead on the base space
S^1, we obtain three intersecting 6-branes all carrying R-R 2-form flux. These
two configurations can be viewed as a classical flop in the type IIA string
theory. After reducing on the full principal orbits and the spatial
world-volume, we obtain a four-dimensional metric describing a lattice
universe, in which the three non-compact coordinates of the G_2 manifold are
identified with the spatial coordinates of our universe.Comment: Latex, 8 page
Amplitudes in Pure Yang-Mills and MHV Diagrams
We show how to calculate the one-loop scattering amplitude with all gluons of
negative helicity in non-supersymmetric Yang-Mills theory using MHV diagrams.
We argue that the amplitude with all positive helicity gluons arises from a
Jacobian which occurs when one performs a Backlund-type holomorphic change of
variables in the lightcone Yang-Mills Lagrangian. This also results in
contributions to scattering amplitudes from violations of the equivalence
theorem. Furthermore, we discuss how the one-loop amplitudes with a single
positive or negative helicity gluon arise in this formalism. Perturbation
theory in the new variables leads to a hybrid of MHV diagrams and lightcone
Yang-Mills theory.Comment: 31 pages, 4 figures. v2: references added, JHEP versio
Notes on Equivalences and Higgs Branches in N=2 Supersymmetric Yang-Mills Theory
In this paper we investigate how various equivalences between effective field
theories of SUSY Yang-Mills theory with matter can be understood through
Higgs breaking, i.e. by giving expectation values to squarks. We give explicit
expressions for the flat directions for a wide class of examples.Comment: 11 pages, Late
General Metrics of G_2 Holonomy and Contraction Limits
We obtain first-order equations for G_2 holonomy of a wide class of metrics
with S^3\times S^3 principal orbits and SU(2)\times SU(2) isometry, using a
method recently introduced by Hitchin. The new construction extends previous
results, and encompasses all previously-obtained first-order systems for such
metrics. We also study various group contractions of the principal orbits,
focusing on cases where one of the S^3 factors is subjected to an Abelian,
Heisenberg or Euclidean-group contraction. In the Abelian contraction, we
recover some recently-constructed G_2 metrics with S^3\times T^3 principal
orbits. We obtain explicit solutions of these contracted equations in cases
where there is an additional U(1) isometry. We also demonstrate that the only
solutions of the full system with S^3\times T^3 principal orbits that are
complete and non-singular are either flat R^4 times T^3, or else the direct
product of Eguchi-Hanson and T^3, which is asymptotic to R^4/Z_2\times T^3.
These examples are in accord with a general discussion of isometric fibrations
by tori which, as we show, in general split off as direct products. We also
give some (incomplete) examples of fibrations of G_2 manifolds by associative
3-tori with either T^4 or K3 as base.Comment: Latex, 27 page
Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
Comments on gluon 6-point scattering amplitudes in N=4 SYM at strong coupling
We use the AdS/CFT prescription of Alday and Maldacena \cite{am} to analyze
gluon 6-point scattering amplitudes at strong coupling in SYM. By
cutting and gluing we obtain AdS 6-point amplitudes that contain extra boundary
conditions and come close to matching the field theory results. We interpret
them as parts of the field theory amplitudes, containing only certain diagrams.
We also analyze the collinear limits of 6- and 5-point amplitudes and discuss
the results.Comment: 35 pages, 7 figures, latex, references adde
BPS Geometries and AdS Bubbles
Recently, 1/2-BPS AdS bubble solutions have been obtained by Lin, Lunin and
Maldacena, which correspond to Fermi droplets in phase space in the dual CFT
picture. They can be thought of as generalisations of 1/2-BPS AdS black hole
solutions in five or seven dimensional gauged supergravity. In this paper, we
extend these solutions by invoking additional gauge fields and scalar fields in
the supergravity Lagrangians, thereby obtaining AdS bubble generalisations of
the previously-known multi-charge AdS black solutions of gauged supergravity.
We also obtain analogous AdS bubble solutions in four-dimensional gauged
supergravity. Our solutions generically preserve supersymmetry fractions 1/4,
1/8 and 1/8 in seven, five and four dimensions respectively. They can be lifted
to M-theory or type IIB string theory, using previously known formulae for the
consistent Pauli sphere reductions that yield the gauged supergravities. We
also find similar solutions in six-dimensional gauged supergravity, and discuss
their lift to the massive type IIA theory.Comment: Latex, 11 page
Generating MHV super-vertices in light-cone gauge
We constructe the SYM lagrangian in light-cone gauge using
chiral superfields instead of the standard vector superfield approach and
derive the MHV lagrangian. The canonical transformations of the gauge field and
gaugino fields are summarised by the transformation condition of chiral
superfields. We show that MHV super-vertices can be described
by a formula similar to that of the MHV super-amplitude. In the
discussions we briefly remark on how to derive Nair's formula for
SYM theory directly from light-cone lagrangian.Comment: 25 pages, 7 figures, JHEP3 style; v2: references added, some typos
corrected; Clarification on the condition used to remove one Grassmann
variabl
Consistent Sphere Reductions and Universality of the Coulomb Branch in the Domain-Wall/QFT Correspondence
We prove that any D-dimensional theory comprising gravity, an antisymmetric
n-index field strength and a dilaton can be consistently reduced on S^n in a
truncation in which just scalar fields and the metric are retained in
(D-n)-dimensions, provided only that the strength of the couping of the dilaton
to the field strength is appropriately chosen. A consistent reduction can then
be performed for n\le 5; with D being arbitrary when n\le 3, whilst D\le 11 for
n=4 and D\le 10 for n=5. (Or, by Hodge dualisation, can be replaced by
(D-n) in these conditions.) We obtain the lower dimensional scalar potentials
and construct associated domain wall solutions. We use the consistent reduction
Ansatz to lift domain-wall solutions in the (D-n)-dimensional theory back to D
dimensions, where we show that they become certain continuous distributions of
(D-n-2)-branes. We also examine the spectrum for a minimally-coupled scalar
field in the domain-wall background, showing that it has a universal structure
characterised completely by the dimension n of the compactifying sphere.Comment: latex file, 21 pages, 1 figure, minor typo correction
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