2005_06_01_archive

Playing Catch-Up

(Or some E11 related papers on hep-th)

Summer is high, well it's not raining every day at least, and seminars

are rare. I have just got back from Riga, in Latvia, where I went for

a stag-do, and I hope this explains the recent lack of posting, not

even a postcard I'm afraid. Riga is very pretty by the way.

In the past two weeks there have been no less than three papers with

some relevance to E11 and my line of research, and I really ought to

try and understand them all. In the meantime let me simply list them

and make some comments:

1. Dualities and signatures of G++ invariant theories by Sophie de

Buyl, Laurent Houart and Nassiba Tabti

The first paper makes use of Keurentjes' observation that Weyl

reflections do not commute with the involution used to choose the

local subalgebra. In an earlier paper one of the authors, Laurent

Houart, together with Francois Englert and Marc Henneaux had applied

the observation that a reduction from a very-extended theory, E11, to

an over-extended theory, E10, by the deletion of an "end node" on the

Dynkin diagram gives rise to two distinct theories. The two theories

are arrived at by, in one case, applying a Weyl reflection in the

deleted node's associated root before deleting the node, and in the

other case by direct deletion of the node. The two resulting E10

theories have different signatures. This paper extends considerations

of this idea to all the other G++ theories.

2. Hidden Symmetries and Dirac Fermions by Sophie de Buyl, Marc

Henneaux and Louis Paulot

The second paper introduces spin one-half fermions into the G++

theories, but as I haven't read this thoroughly yet I will not say

much. According to the introduction this results in the chaotic motion

reported in the cosmological billiards picture being lost. Furthermore

the null geodesic in E10/K(10), which encodes dynamics, becomes

timelike once the spin one half fermions are present. I will add any

further comments here later, if they come to me :)

3. IIB Supergravity Revisited by Eric A. Bergshoeff, Mees de Roo, Sven

F. Kerstan and Fabio Riccioni

The third paper is also very interesting, and the idea is

straightforward to describe. Back in 1983 when the IIB supersymmetry

algebra was first written down, branes were not an important concept,

so the only gauge fields that were considered were the two scalars,

the two-form and the four-form. These couple to a string and a

three-brane. Since then more emphasis has been placed on the

five-brane, the seven-brane and the space-filling nine brane, which

couple to a six-form, an eight-form and a ten-form respectively. The

authors of this paper introduce these extra gauge fields to the IIB

multiplet of fields without introducing any degrees of freedom, by

asserting that a duality relation between the extra fields to the 1983

multiplet of fields. The supersymmetric variations of the new fields

are given, and it is noted that the duality condition that was

asserted is really a necessary condition for the algebra to close.

They find that the ten-form can transform as a doublet and a

quadruplet of SU(1,1) and the authors argue that no other independent

ten-forms can be added. The findings for the ten-form multiplets match

the previous deductions from E11 given in Very-extended Kac-Moody