54 research outputs found
Wilson Loops on Riemann Surfaces, Liouville Theory and Covariantization of the Conformal Group
The covariantization procedure is usually referred to the translation
operator, that is the derivative. Here we introduce a general method to
covariantize arbitrary differential operators, such as the ones defining the
fundamental group of a given manifold. We focus on the differential operators
representing the sl(2,R) generators, which in turn, generate, by
exponentiation, the two-dimensional conformal transformations. A key point of
our construction is the recent result on the closed forms of the
Baker-Campbell-Hausdorff formula. In particular, our covariantization receipt
is quite general. This has a deep consequence since it means that the
covariantization of the conformal group is {\it always definite}. Our
covariantization receipt is quite general and apply in general situations,
including AdS/CFT. Here we focus on the projective unitary representations of
the fundamental group of a Riemann surface, which may include elliptic points
and punctures, introduced in the framework of noncommutative Riemann surfaces.
It turns out that the covariantized conformal operators are built in terms of
Wilson loops around Poincar\'e geodesics, implying a deep relationship between
gauge theories on Riemann surfaces and Liouville theory.Comment: 39 pages. References added. Version to appear in JHE
Duality Symmetric Actions with Manifest Space-Time Symmetries
We consider a space-time invariant duality symmetric action for a free
Maxwell field and an invariant effective action
describing a low-energy bosonic sector of the heterotic string compactified on
a six-dimensional torus. The manifest Lorentz and general coordinate invariant
formulation of the models is achieved by coupling dual gauge fields to an
auxiliary vector field from an axionic sector of the theory.Comment: 9 pages, LaTeX, no figures, references added, misprints eliminate
Covariant actions for models with non-linear twisted self-duality
We describe a systematic way of the generalization, to models with non-linear
duality, of the space-time covariant and duality-invariant formulation of
duality-symmetric theories in which the covariance of the action is ensured by
the presence of a single auxiliary scalar field. It is shown that the
duality-symmetric action should be invariant under the two local symmetries
characteristic of this approach, which impose constraints on the form of the
action similar to those of Gaillard and Zumino and in the non-covariant
formalism. We show that the (twisted) self-duality condition obtained from this
action upon integrating its equations of motion can always be recast in a
manifestly covariant form which is independent of the auxiliary scalar and thus
corresponds to the conventional on-shell duality-symmetric covariant
description of the same model. Supersymmetrization of this construction is
briefly discussed.Comment: 1+21 pages, v2: typos corrected, references adde
BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D=6 and M5-branes
We reveal non-manifest gauge and SO(1,5) Lorentz symmetries in the Lagrangian
description of a six-dimensional free chiral field derived from the
Bagger-Lambert-Gustavsson model in arXiv:0804.3629 and make this formulation
covariant with the use of a triplet of auxiliary scalar fields. We consider the
coupling of this self-dual construction to gravity and its supersymmetrization.
In the case of the non-linear model of arXiv:0805.2898 we solve the equations
of motion of the gauge field, prove that its non-linear field strength is
self-dual and find a gauge-covariant form of the non-linear action. Issues of
the relation of this model to the known formulations of the M5-brane
worldvolume theory are discussed.Comment: 1+30 pages, v2: added subsection on comparison of different
chiral-field actions, clarifications and reference
On the equivalence of different formulations of the M Theory five--brane
We show that the field equations for the supercoordinates and the self--dual
antisymmetric tensor field derived from the recently constructed
kappa-invariant action for the M theory five-brane are equivalent to the
equations of motion obtained in the doubly supersymmetric geometrical approach
at the worldvolume component level.Comment: TeX file, 12 page
Covariant Action for a D=11 Five-Brane with the Chiral Field
We propose a complete Born-Infeld-like action for a bosonic 5-brane with the
worldvolume chiral field in a background of gravitational and antisymmetric
gauge fields of D=11 supergravity. When the five-brane couples to a three-rank
antisymmetric gauge field local worldvolume symmetries of the five-brane
require the addition to the action of an appropriate Wess-Zumino term. To
preserve general coordinate and Lorentz invariance of the model we introduce a
single auxiliary scalar field. The auxiliary field can be eliminated by gauge
fixing a corresponding local symmetry at the price of the loss of manifest d=6
worldvolume covariance. The double dimensional reduction of the five-brane
model results in the Born-Infeld action with the Wess-Zumino term for a D=10
four-D-brane.Comment: LaTeX file, 10 pages, the form of eq. (8) corrected, a Comment added,
version to appear in Phys. Lett.
- …