20 research outputs found
A new maximally supersymmetric background of IIB superstring theory
We present a maximally supersymmetric IIB string background. The geometry is
that of a conformally flat lorentzian symmetric space G/K with solvable G, with
a homogeneous five-form flux. We give the explicit supergravity solution,
compute the isometries, the 32 Killing spinors, and the symmetry superalgebra,
and then discuss T-duality and the relation to M-theory.Comment: 17 page
The universal Vassiliev invariant for the Lie superalgebra gl(1|1)
We compute the universal weight system for Vassiliev invariants coming from
the Lie superalgebra gl(1|1) applying the construction of \cite{YB}. This
weight system is a function from the space of chord diagrams to the center
of the universal enveloping algebra of gl(1|1), and we find a combinatorial
expression for it in terms of the standard generators of . The resulting
knot invariants generalize the Alexander-Conway polynomial.Comment: 44 pages with figures, wrapped with uufiles, requires epsf.sty --
Added a short section about deframin
Gauging the Wess-Zumino term of a sigma model with boundary
We investigate the gauging of the Wess-Zumino term of a sigma model with
boundary. We derive a set of obstructions to gauging and we interpret them as
the conditions for the Wess-Zumino term to extend to a closed form in a
suitable equivariant relative de Rham complex. We illustrate this with the
two-dimensional sigma model and we show that the new obstructions due to the
boundary can be interpreted in terms of Courant algebroids. We specialise to
the case of the Wess-Zumino-Witten model, where it is proved that there always
exist suitable boundary conditions which allow gauging any subgroup which can
be gauged in the absence of a boundary. We illustrate this with two natural
classes of gaugings: (twisted) diagonal subgroups with boundary conditions
given by (twisted) conjugacy classes, and chiral isotropic subgroups with
boundary conditions given by cosets.Comment: 18 pages (minor changes in response to referee report
Half-BPS quotients in M-theory: ADE with a twist
We classify Freund-Rubin backgrounds of eleven-dimensional supergravity of
the form AdS_4 x X^7 which are at least half BPS; equivalently, smooth
quotients of the round 7-sphere by finite subgroups of SO(8) which admit an
(N>3)-dimensional subspace of Killing spinors. The classification is given in
terms of pairs consisting of an ADE subgroup of SU(2) and an automorphism
defining its embedding in SO(8). In particular we find novel half-BPS quotients
associated with the subgroups of type D_n (for n>5), E_7 and E_8 and their
outer automorphisms.Comment: 16 pages; V2: notational inconsistencies addressed, final version to
be published in JHE
The return of the four- and five-dimensional preons
We prove the existence of 3/4-BPS preons in four- and five-dimensional gauged
supergravities by explicitly constructing them as smooth quotients of the AdS_4
and AdS_5 maximally supersymmetric backgrounds, respectively. This result
illustrates how the spacetime topology resurrects a fraction of supersymmetry
previously ruled out by the local analysis of the Killing spinor equations.Comment: 10 pages (a minor imprecision has been corrected
Penrose limits of Lie Branes and a Nappi--Witten braneworld
Departing from the observation that the Penrose limit of AdS_3 x S^3 is a
group contraction in the sense of Inonu and Wigner, we explore the relation
between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a
six-dimensional symmetric plane wave analogous to the four-dimensional
Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant
lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy
classes. We determine the (twisted and untwisted) symmetric D-branes in the
plane wave background and we prove the existence of a space-filling D5-brane
and, separately, of a foliation by D3-branes with the geometry of the
Nappi--Witten spacetime which can be understood as the Penrose limit of the
AdS_2 x S^2 D3-brane in AdS_3 x S^3. Parenthetically we also derive a simple
criterion for a symmetric plane wave to be isometric to a lorentzian Lie group.
In particular we observe that the maximally supersymmetric plane wave in IIB
string theory is isometric to a lorentzian Lie group, whereas the one in
M-theory is not.Comment: 21 pages (v2: references added
Supersymmetry and homogeneity of M-theory backgrounds
We describe the construction of a Lie superalgebra associated to an arbitrary
supersymmetric M-theory background, and discuss some examples. We prove that
for backgrounds with more than 24 supercharges, the bosonic subalgebra acts
locally transitively. In particular, we prove that backgrounds with more than
24 supersymmetries are necessarily (locally) homogeneous.Comment: 19 pages (Erroneous Section 6.3 removed from the paper.
On the maximal superalgebras of supersymmetric backgrounds
In this note we give a precise definition of the notion of a maximal
superalgebra of certain types of supersymmetric supergravity backgrounds,
including the Freund-Rubin backgrounds, and propose a geometric construction
extending the well-known construction of its Killing superalgebra. We determine
the structure of maximal Lie superalgebras and show that there is a finite
number of isomorphism classes, all related via contractions from an
orthosymplectic Lie superalgebra. We use the structure theory to show that
maximally supersymmetric waves do not possess such a maximal superalgebra, but
that the maximally supersymmetric Freund-Rubin backgrounds do. We perform the
explicit geometric construction of the maximal superalgebra of AdS_4 x S^7 and
find that is isomorphic to osp(1|32). We propose an algebraic construction of
the maximal superalgebra of any background asymptotic to AdS_4 x S^7 and we
test this proposal by computing the maximal superalgebra of the M2-brane in its
two maximally supersymmetric limits, finding agreement.Comment: 17 page
A One-Parameter Family of Hamiltonian Structures for the KP Hierarchy and a Continuous Deformation of the Nonlinear \W_{\rm KP} Algebra
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson
structures obtained from a generalized Adler map in the space of formal
pseudodifferential symbols with noninteger powers. The resulting \W-algebra
is a one-parameter deformation of \W_{\rm KP} admitting a central extension
for generic values of the parameter, reducing naturally to \W_n for special
values of the parameter, and contracting to the centrally extended
\W_{1+\infty}, \W_\infty and further truncations. In the classical limit,
all algebras in the one-parameter family are equivalent and isomorphic to
\w_{\rm KP}. The reduction induced by setting the spin-one field to zero
yields a one-parameter deformation of \widehat{\W}_\infty which contracts to
a new nonlinear algebra of the \W_\infty-type.Comment: 31 pages, compressed uuencoded .dvi file, BONN-HE-92/20, US-FT-7/92,
KUL-TF-92/20. [version just replaced was truncated by some mailer
Parallelisable Heterotic Backgrounds
We classify the simply-connected supersymmetric parallelisable backgrounds of
heterotic supergravity. They are all given by parallelised Lie groups admitting
a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14
and 16 of the 16 supersymmetries.Comment: 17 pages, AMSLaTe