Data di Pubblicazione:
2013
Citazione:
Multi-Centered Invariants, Plethysm and Grassmannians / S.L. Cacciatori, A. Marrani, B. van Geemen. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2013:2(2013 Feb), pp. 049.1-049.35. [10.1007/JHEP02(2013)049]
Abstract:
Motivated by multi-centered black hole solutions of Maxwel
l-Einstein theo-
ries of (super)gravity in
D
= 4 space-time dimensions, we develop some general meth-
ods, that can be used to determine all homogeneous invariant
polynomials on the irre-
ducible (
SL
h
(
p,
R
)
⊗
G
4
)-representation (
p
, R
), where
p
denotes the number of centers,
and
SL
h
(
p,
R
) is the
“horizontal”
symmetry of the system, acting upon the indices la-
belling the centers. The black hole electric and magnetic ch
arges sit in the symplectic
representation
R
of the generalized electric-magnetic (
U
-)duality group
G
4
.
We start with an algebraic approach based on
classical invariant theory
, using Schur
polynomials and the Cauchy formula. Then, we perform a geome
tric analysis, involving
Grassmannians, Pl ̈ucker coordinates, and exploiting Bott
’s Theorem.
We focus on
non-degenerate
groups
G
4
“of type
E
7
”
relevant for (super)gravities whose
(vector multiplets’) scalar manifold is a
symmetric
space. In the
triality-symmetric
stu
model of
N
= 2 supergravity, we explicitly construct a basis for the 10 l
inearly independent
degree-12 invariant polynomials of 3-centered black holes
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Black Holes; Black Holes in String Theory; Global Symmetries; Supergravity Models
Elenco autori:
S.L. Cacciatori, A. Marrani, B. van Geemen
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