35 research outputs found
Non-trivial flat connections on the 3-torus II: The exceptional groups F_4 and E_6,7,8
We continue the construction of non-trivial vacua for gauge theories on the
3-torus, started in hep-th/9901154. Application of constructions based on twist
in SU(N) with N > 2 produce more extra vacua in theories with exceptional
groups. We calculate the relevant unbroken subgroups, and their contribution to
the Witten index. We show that the extra vacua we find in the exceptional
groups are sufficient to solve the Witten index problem for these groups.Comment: LaTeX, 25 pages, 1 figur
Classifying orientifolds by flat n-gerbes
The discrete tensorial charges carried by orientifold planes define n-gerbes
in space-time. The simplest way to ensure a consistent string compactification
is to require these gerbes to be flat. This results in expressions for the
local gerbe-holonomies around each orientifold plane, describing its charges.
Inverting the procedure and considering all flat gerbes leads to a
classification of orientifold configurations. Requiring that the tadpole is
cancelled by adding D-branes, we classify all supersymmetric orientifolds on
T^k/Z_2 with 2^k O(9-k) planes at the fixed points, for k less or equal to 6.
For k=6 these theories organize in orbits of the SL(2,Z) S-duality symmetry of
N=4 supersymmetric gauge theories.Comment: LaTeX, no figures, 35 pages; v2, references added, no other changes,
conforms with published versio
Oxidation = group theory
Dimensional reduction of theories involving (super-)gravity gives rise to
sigma models on coset spaces of the form G/H, with G a non-compact group, and H
its maximal compact subgroup. The reverse process, called oxidation, is the
reconstruction of the possible higher dimensional theories, given the lower
dimensional theory. In 3 dimensions, all degrees of freedom can be dualized to
scalars. Given the group G for a 3 dimensional sigma model on the coset G/H, we
demonstrate an efficient method for recovering the higher dimensional theories,
essentially by decomposition into subgroups. The equations of motion, Bianchi
identities, Kaluza-Klein modifications and Chern-Simons terms are easily
extracted from the root lattice of the group G. We briefly discuss some aspects
of oxidation from the E_{8(8)}/SO(16) coset, and demonstrate that our formalism
reproduces the Chern-Simons term of 11-d supergravity, knows about the
T-duality of IIA and IIB theory, and easily deals with self-dual tensors, like
the 5-tensor of IIB supergravity.Comment: LaTeX, 8 pages, uses IOP style files; Talk given at the RTN workshop
``The quantum structure of spacetime and the geometric nature of fundamental
interactions'', Leuven, September 200
Orientifolds and twisted boundary conditions
It is argued that the T-dual of a crosscap is a combination of an O+ and an
O- orientifold plane. Various theories with crosscaps and D-branes are
interpreted as gauge-theories on tori obeying twisted boundary conditions.
Their duals live on orientifolds where the various orientifold planes are of
different types. We derive how to read off the holonomies from the positions of
D-branes in the orientifold background. As an application we reconstruct some
results from a paper by Borel, Friedman and Morgan for gauge theories with
classical groups, compactified on a 2-- or 3--torus with twisted boundary
conditions.Comment: 23 pages, LaTeX, 2 eps figures; minor corrections, references adde
E_11: Sign of the times
We discuss the signature of space-time in the context of the E_11
-conjecture. In this setting, the space-time signature depends on the choice of
basis for the ``gravitational sub-algebra'' A_10, and Weyl transformations
connect interpretations with different signatures of space-time. Also the sign
of the 4-form gauge field term in the Lagrangian enters as an adjustable sign
in a generalized signature. Within E_11, the combination of space-time
signature (1,10) with conventional sign for the 4-form term, appropriate to
M-theory, can be transformed to the signatures (2,9) and (5,6) of Hull's M*-
and M'-theories (as well as (6,5), (9,2) and (10,1)). Theories with other
signatures organize in orbits disconnected from these theories. We argue that
when taking E_11 seriously as a symmetry algebra, one cannot discard theories
with multiple time-directions as unphysical. We also briefly explore links with
the SL(32,R) conjecture.Comment: 20 pages, LaTeX, 1 figure; v2. typo's corrected, references adde