37,863 research outputs found
A PBW commutator lemma for U_q[gl(m|n)]
We present and prove in detail a Poincare--Birkhoff--Witt commutator lemma
for the quantum superalgebra U_q[gl(m|n)].Comment: 16 pages, no figure
On Lagrangians and Gaugings of Maximal Supergravities
A consistent gauging of maximal supergravity requires that the T-tensor
transforms according to a specific representation of the duality group. The
analysis of viable gaugings is thus amenable to group-theoretical analysis,
which we explain and exploit for a large variety of gaugings. We discuss the
subtleties in four spacetime dimensions, where the ungauged Lagrangians are not
unique and encoded in an E_7(7)\Sp(56,R)/GL(28) matrix. Here we define the
T-tensor and derive all relevant identities in full generality. We present a
large number of examples in d=4,5 spacetime dimensions which include
non-semisimple gaugings of the type arising in (multiple) Scherk-Schwarz
reductions. We also present some general background material on the latter as
well as some group-theoretical results which are necessary for using computer
algebra.Comment: 39 pages, LaTeX2
Lagrangians with electric and magnetic charges of N=2 supersymmetric gauge theories
General Lagrangians are constructed for N=2 supersymmetric gauge theories in
four space-time dimensions involving gauge groups with (non-abelian) electric
and magnetic charges. The charges induce a scalar potential, which, when the
charges are regarded as spurionic quantities, is invariant under
electric/magnetic duality. The resulting theories are especially relevant for
supergravity, but details of the extension to local supersymmetry will be
discussed elsewhere. The results include the coupling to hypermultiplets.
Without the latter, it is demonstrated how an off-shell representation can be
constructed based on vector and tensor supermultiplets.Comment: 34 pages, LaTe
The Vector-Tensor Supermultiplet with Gauged Central Charge
The vector-tensor multiplet is coupled off-shell to an N=2 vector multiplet
such that its central charge transformations are realized locally. A gauged
central charge is a necessary prerequisite for a coupling to supergravity and
the strategy underlying our construction uses the potential for such a coupling
as a guiding principle. The results for the action and transformation rules
take a nonlinear form and necessarily include a Chern-Simons term. After a
duality transformation the action is encoded in a homogeneous holomorphic
function consistent with special geometry.Comment: 8 pages, LATE
Special geometry in hypermultiplets
We give a detailed analysis of pairs of vector and hypermultiplet theories
with N=2 supersymmetry in four spacetime dimensions that are related by the
(classical) mirror map. The symplectic reparametrizations of the special
K\"ahler space associated with the vector multiplets induce corresponding
transformations on the hypermultiplets. We construct the Sp(1)Sp()
one-forms in terms of which the hypermultiplet couplings are encoded and
exhibit their behaviour under symplectic reparametrizations. Both vector and
hypermultiplet theories allow vectorial central charges in the supersymmetry
algebra associated with integrals over the K\"ahler and hyper-K\"ahler forms,
respectively. We show how these charges and the holomorphic BPS mass are
related by the mirror map.Comment: Latex 36 pp. A few minor correction
Tensor supermultiplets and toric quaternion-Kahler geometry
We review the relation between 4n-dimensional quaternion-Kahler metrics with
n+1 abelian isometries and superconformal theories of n+1 tensor
supermultiplets. As an application we construct the class of eight-dimensional
quaternion-Kahler metrics with three abelian isometries in terms of a single
function obeying a set of linear second-order partial differential equations.Comment: 8 pages, Contribution to the proceedings of the RTN ForcesUniverse
Network Workshop, Napoli, October 9th - 13th, 200
Open and Closed Supermembranes with Winding
Motivated by manifest Lorentz symmetry and a well-defined large-N limit
prescription, we study the supersymmetric quantum mechanics proposed as a model
for the collective dynamics of D0-branes from the point of view of the
11-dimensional supermembrane. We argue that the continuity of the spectrum
persists irrespective of the presence of winding around compact target-space
directions and discuss the central charges in the superalgebra arising from
winding membrane configurations. Along the way we comment on the structure of
open supermembranes.Comment: Contribution to the proc. Strings '97, 10 pages, LaTeX, uses espcrc
When do finite sample effects significantly affect entropy estimates ?
An expression is proposed for determining the error caused on entropy
estimates by finite sample effects. This expression is based on the Ansatz that
the ranked distribution of probabilities tends to follow an empirical Zipf law.Comment: 10 pages, 2 figure
Maximal Supergravity from IIB Flux Compactifications
Using a recently proposed group-theoretical approach, we explore novel
gaugings of maximal supergravity in four dimensions with gauge group embeddings
that can be generated by fluxes of IIB string theory. The corresponding
potentials are positive without stationary points. Some allow domain wall
solutions which can be elevated to ten dimensions. Appropriate truncations
describe type-IIB flux compactifications on T^6 orientifolds leading to
non-maximal, four-dimensional, supergravities.Comment: 13 pages, LaTeX2e, references added, version to appear in PL
Special geometry and symplectic transformations
Special Kahler manifolds are defined by coupling of vector multiplets to
supergravity. The coupling in rigid supersymmetry exhibits similar
features. These models contain vectors in rigid supersymmetry and in
supergravity, and complex scalars. Apart from exceptional cases they are
defined by a holomorphic function of the scalars. For supergravity this
function is homogeneous of second degree in an -dimensional projective
space. Another formulation exists which does not start from this function, but
from a symplectic - or -dimensional complex space. Symplectic
transformations lead either to isometries on the manifold or to symplectic
reparametrizations. Finally we touch on the connection with special
quaternionic and very special real manifolds, and the classification of
homogeneous special manifolds.Comment: 11 pages, latex using espcrc2, no figures. Some factors and minor
corrections. Version to be published in the proceedings of the Spring
workshop on String theory, Trieste, April 199
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