281 research outputs found
NC Wilson lines and the inverse Seiberg-Witten map for nondegenerate star products
Open Wilson lines are known to be the observables of noncommutative gauge
theory with Moyal-Weyl star product. We generalize these objects to more
general star products. As an application we derive a formula for the inverse
Seiberg-Witten map for star products with invertible Poisson structures.Comment: 8 page
Type II Superstring Field Theory: Geometric Approach and Operadic Description
We outline the construction of type II superstring field theory leading to a
geometric and algebraic BV master equation, analogous to Zwiebach's
construction for the bosonic string. The construction uses the small Hilbert
space. Elementary vertices of the non-polynomial action are described with the
help of a properly formulated minimal area problem. They give rise to an
infinite tower of superstring field products defining a
generalization of a loop homotopy Lie algebra, the genus zero part generalizing
a homotopy Lie algebra. Finally, we give an operadic interpretation of the
construction.Comment: 37 pages, 1 figure, corrected typos and added reference
Construction of Gauge Theories on Curved Noncommutative Spacetime
We present a method where derivations of star-product algebras are used to
build covariant derivatives for noncommutative gauge theory. We write down a
noncommutative action by linking these derivations to a frame field induced by
a nonconstant metric. An example is given where the action reduces in the
classical limit to scalar electrodynamics on a curved background. We further
use the Seiberg-Witten map to extend the formalism to arbitrary gauge groups. A
proof of the existence of the Seiberg-Witten-map for an abelian gauge potential
is given for the formality star-product. We also give explicit formulas for the
Weyl ordered star-product and its Seiberg-Witten-maps up to second order.Comment: 35 pages, v2: references added, v3: PACS added, v4: final version,
changes in the order of presentatio
Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
We discuss Levi-Civita connections on Courant algebroids. We define an
appropriate generalization of the curvature tensor and compute the
corresponding scalar curvatures in the exact and heterotic case, leading to
generalized (bosonic) Einstein-Hilbert type of actions known from supergravity.
In particular, we carefully analyze the process of the reduction for the
generalized metric, connection, curvature tensor and the scalar curvature.Comment: New section and several references added based on the journal revie
Courant algebroid connections and string effective actions
Courant algebroids are a natural generalization of quadratic Lie algebras,
appearing in various contexts in mathematical physics. A connection on a
Courant algebroid gives an analogue of a covariant derivative compatible with a
given fiber-wise metric. Imposing further conditions resembling standard
Levi-Civita connections, one obtains a class of connections whose curvature
tensor in certain cases gives a new geometrical description of equations of
motion of low energy effective action of string theory. Two examples are given.
One is the so called symplectic gravity, the second one is an application to
the the so called heterotic reduction. All necessary definitions, propositions
and theorems are given in a detailed and self-contained way.Comment: Proceedings of Tohoku Forum for Creativity, Special volume:
Noncommutative Geometry and Physics I
Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle
For a particular class of backgrounds, equations of motion for string sigma
models targeted in mutually dual Poisson-Lie groups are equivalent. This
phenomenon is called the Poisson-Lie T-duality. On the level of the
corresponding string effective actions, the situation becomes more complicated
due to the presence of the dilaton field.
A novel approach to this problem using Levi-Civita connections on Courant
algebroids is presented. After the introduction of necessary geometrical tools,
formulas for the Poisson-Lie T-dual dilaton fields are derived. This provides a
version of Poisson-Lie T-duality for string effective actions.Comment: One subsection added, several typos and minor mistakes correcte
- …