4,681 research outputs found
Exceptionally simple PDE
We give local descriptions of parabolic contact structures and show how their
flat models yield explicit PDE having symmetry algebras isomorphic to all
complex simple Lie algebras except . This yields a remarkably
uniform generalization of the Cartan-Engel models from 1893 in the case.
We give a formula for the harmonic curvature of a -contact structure and
describe submaximally symmetric models for general -contact structures.Comment: Abstract and introduction revised; exposition improved and text
reorganized; Section 4.1 on G2-contact structures is ne
4d =2 theories with disconnected gauge groups
In this paper we present a beautifully consistent web of evidence for the
existence of interacting 4d rank-1 SCFTs obtained from gauging
discrete subgroups of global symmetries of other existing 4d rank-1
SCFTs. The global symmetries that can be gauged involve a
non-trivial combination of discrete subgroups of the , low-energy EM
duality group , and the outer automorphism group of the
flavor symmetry algebra, Out().
The theories that we construct are remarkable in many ways: (i) two of them
have exceptional and flavor groups; (ii) they substantially
complete the picture of the landscape of rank-1 SCFTs as they
realize all but one of the remaining consistent rank-1 Seiberg-Witten
geometries that we previously constructed but were not associated to known
SCFTs; and (iii) some of them have enlarged SUSY, and have not
been previously constructed. They are also examples of SCFTs which violate the
Shapere-Tachikawa relation between the conformal central charges and the
scaling dimension of the Coulomb branch vev. We propose a modification of the
formulas computing these central charges from the topologically twisted Coulomb
branch partition function which correctly compute them for discretely gauged
theories.Comment: 45 pages, 3 figure
On Type IIB Vacua With Varying Coupling Constant
We describe type IIB compactifications with varying coupling constant in
d=6,7,8,9 dimensions, where part of the ten-dimensional SL(2,Z) symmetry is
broken by a background with Gamma_0(n) or Gamma(n) monodromy for n=2,3,4. This
extends the known class of F-theory vacua to theories which are dual to
heterotic compactifications with reduced rank. On compactifying on a further
torus, we obtain a description of the heterotic moduli space of G bundles over
elliptically fibered manifolds without vector structure in terms of complex
geometries.Comment: 32 pages, 5 eps figure
Classification of invariant AHS--structures on semisimple locally symmetric spaces
In this article, we discuss which semisimple locally symmetric spaces admit
an AHS--structure invariant to local symmetries. We classify them for all types
of AHS--structures and determine possible equivalence classes of such
AHS--structures.Comment: submited to CEJ
Geometries, the principle of duality, and algebraic groups
Jacques Tits gave a general recipe for producing an abstract geometry from a
semisimple algebraic group. This expository paper describes a uniform method
for giving a concrete realization of Tits's geometry and works through several
examples. We also give a criterion for recognizing the automorphism of the
geometry induced by an automorphism of the group. The E6 geometry is studied in
depth.Comment: The writing has been cleaned up since v
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