Jeong-Hyuck Park

Stringy differential geometry, beyond Riemann

While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry that treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also

Differential geometry with a projection: application to double field theory

\mathbf{O}(D,D)

Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory

T-duality, and enables us to rewrite the known low energy effective action of them as a single term. Further, we develop a corresponding vielbein formalism and gauge the internal symmetry that is given by a direct product of two local Lorentz groups,

Comments on double field theory and diffeomorphisms

\mathbf{S}\mathbf{O}(1,D\ensuremath{-}1)\ifmmode\times\else\texttimes\fi{}\overline{\mathbf{S}\mathbf{O}}(1,D\ensuremath{-}1)

Incorporation of fermions into double field theory

. We comment that the notion of cosmological constant naturally changes.

Taking off the square root of Nambu–Goto action and obtaining Filippov–Lie algebra gauge theory action

In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D, D) rotation. In this paper, we conceive a differential geometry characterized by a O(D, D) symmetric projection, as the underlying mathematical structure of double field theory. We introduce a differential operator compatible with the projection, which, contracted with the projection, can be covariantized and may replace the ordinary derivatives in the generalized Lie derivative that generates the gauge symmetry of double field theory. We construct various gauge covariant tensors which include a scalar and a tensor carrying two O(D, D) vector indices.

Superalgebra for M-theory on a pp-wave

Abstract To the full order in fermions, we construct D = 10 type II supersymmetric double field theory. We spell the precise N = 2 supersymmetry transformation rules as for 32 supercharges. The constructed action unifies type IIA and IIB supergravities in a manifestly covariant manner with respect to O ( 10 , 10 ) T-duality and a pair of local Lorentz groups, or Spin ( 1 , 9 ) × Spin ( 9 , 1 ) , besides the usual general covariance of supergravities or the generalized diffeomorphism. While the theory is unique, the solutions are twofold. Type IIA and IIB supergravities are identified as two different types of solutions rather than two different theories.

U-geometry: SL(5)

A bstractAs the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a ‘gauge orbit’ in the coordinate space. The diffeomorphism symmetry then implies an invariance under arbitrary reparametrizations of the gauge orbits. Within this generalized sense of diffeomorphism, we show that a recently proposed tensorial transformation rule for finite coordinate transformations is actually (i) consistent with the standard exponential map, and further (ii) compatible with the full covariance of the ‘semi-covariant’ derivatives and curvatures after projectors are properly imposed.

Ramond-Ramond cohomology and O(D, D) T-duality

A bstractBased on the stringy differential geometry we proposed earlier, we incorporate fermions such as gravitino and dilatino into double field theory in a manifestly covariant manner with regard to O(D, D) T-duality, diffeomorphism, one-form gauge symmetry for B-field and a pair of local Lorentz symmetries. We note that there are two kinds of fermions in double field theory: O(D, D) singlet and non-singlet which may be identified, respectively as the common and the non-common fermionic sectors in type IIA and IIB suergravities. For each kind, we construct corresponding covariant Dirac operators. Further, we derive a simple criterion for an O(D, D) rotation to flip the chirality of the O(D, D) non-singlet chiral fermions, which implies the exchange of type IIA and IIB supergravities.

Superconformal symmetry and correlation functions

We propose a novel prescription to take off the square root of the Nambu–Goto action for a p-brane, which generalizes the Brink–Di Vecchia–Howe–Tucker, also known as the Polyakov method. With an arbitrary decomposition, d+n=p+1, our resulting action is a modified d-dimensional Polyakov action, which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of d-dimensional diffeomorphism and n-dimensional volume preserving diffeomorphism. We show that the latter naturally leads to a novel Filippov–Lie n-algebra based gauge theory action in d dimensions.