Superstring theoryをめぐって(放談室)

String Theory: Preface

A duality invariant first order action is constructed on the loop group of a Drinfeld double. It gives at the same time the description of both of the pair of $\sigma$-models related by Poisson-Lie T-duality. Remarkably, the action contains a WZW-term on the Drinfeld double not only for conformally invariant $\si$-models. The resulting actions of the models from the dual pair differ just by a total derivative corresponding to an ambiguity in specifying a two-form whose exterior derivative is the WZW three-form. This total derivative is nothing but the Semenov-Tian-Shansky symplectic form on the Drinfeld double and it gives directly a generating function of the canonical transformation relating the $\si$-models from the dual pair.

Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles

differential geometry and lie groups for physicists is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the differential geometry and lie groups for physicists is universally compatible with any devices to read.

Differential Geometry And Lie Groups For Physicists

It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d,d) pairing $${\eta}$$ and an O(2d) generalized metric $${\mathcal{H}}$$. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing $${\omega}$$. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure $${(\eta,\omega,\mathcal{H})}$$ and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics.

A Unique Connection for Born Geometry

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.

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Courant Algebroid Connections and String Effective Actions

We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.

On the Generalized Geometry Origin of Noncommutative Gauge Theory

http://inspirehep.net/record/1225322/files/arXiv:1303.6096.pdf

On the Generalized Geometry Origin of Noncommutative Gauge Theory dedicated to Bruno Zumino on the occasion of his 90th birthday

Motivated by the quest to understand the analog of non-geometric flux compactification in the context of M-theory, we study higher dimensional analogs of generalized Poisson sigma models and corresponding dual string and p-brane models. We find that higher generalizations of the algebraic structures due to Dorfman, Roytenberg and Courant play an important role and establish their relation to Nambu-Poisson structures.

p-Brane Actions and Higher Roytenberg Brackets

Starting from the usual bosonic membrane action, we develop the geometry suitable for the description of $p$-brane backgrounds. Using the tools of generalized geometry we derive the generalization of string open-closed relations. Nambu-Poisson structures are used to generalize the concept of semiclassical noncommutativity of $D$-branes governed by Poisson tensor. We naturally describe the correspondence of recently proposed commutative and noncommutative versions of an effective action for $p$-branes ending on a $p'$-brane. We calculate the power series expansion of the action in background independent gauge. Leading terms in the double scaling limit are given by a generalization of a (semi-classical) matrix model.

/pdf/extended-generalized-geometry-and-a-dbi-type-effective-3frzl4drdo.pdf

Jan Vysoky

Papers

Courant Algebroid Connections and String Effective Actions

On the Generalized Geometry Origin of Noncommutative Gauge Theory

On the Generalized Geometry Origin of Noncommutative Gauge Theory dedicated to Bruno Zumino on the occasion of his 90th birthday

p-Brane Actions and Higher Roytenberg Brackets

Extended generalized geometry and a DBI-type effective action for branes ending on branes