Double field theory: a pedagogical review

159

295

We develop doubled-coordinate field theory to determine the α ′ corrections to the massless sector of oriented bosonic closed string theory. Our key tool is a string current algebra of free left-handed bosons that makes O(D,D) T-duality manifest. While T-dualities are unchanged, diffeomorphisms and b-field gauge transformations receive corrections, with a gauge algebra given by an α ′ -deformation of the duality-covariantized Courant bracket. The action is cubic in a double metric field, an unconstrained extension of the generalized metric that encodes the gravitational fields. Our approach provides a consistent truncation of string theory to massless fields with corrections that close at finite order in α ′ .

Section: Jhep02(2014)065mentioning

confidence: 99%

Doubled α ′-geometry

Hohm¹,

Siegel

Zwiebach

2014

159

295

“…[58,[60][61][62][63][64][65][66][67][68][69][70][71][72][73]. We refer the reader to those papers or the reviews [16,17] for an introduction. In what follows we will discern some similarities but also some differences when trying to generalise the finite transformations for O(d, d) to the exceptional groups associated with U-duality.…”

Section: Jhep09(2014)066mentioning

confidence: 99%

Global aspects of double geometry

Berman

Cederwall

Perry³

2014

123

Abstract:We consider the concept of a generalised manifold in the O(d, d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are defined. Triple overlaps are trivial concerning their action on coordinates, but non-trivial on fields, including the generalised metric. A generalised manifold is an ordinary manifold, but the generalised metric on the manifold carries a gerbe structure. We show how the abelian behaviour of the gerbe is embedded in the non-abelian T-duality group. We also comment on possibilities and difficulties in the U-duality setting.

“…This implies that they depend on only ten coordinates and, therefore, locally DFT is equivalent to generalised geometry. The strong constraint can be locally relaxed [12][13][14]. Some works in the direction of understanding, from the world sheet perspective, the origin of the strong constraint and its possible relaxation have appeared in the literature [15][16][17].…”

Section: Jhep09(2015)153mentioning

confidence: 99%

On the exceptional generalised Lie derivative for d ≥ 7

Rosabal

2015

In this work we revisit the E 8 × R + generalised Lie derivative encoding the algebra of diffeomorphisms and gauge transformations of compactifications of M-theory on eight-dimensional manifolds, by extending certain features of the E 7 × R + one. Compared to its E d × R + , d ≤ 7 counterparts, a new term is needed for consistency. However, we find that no compensating parameters need to be introduced, but rather that the new term can be written in terms of the ordinary generalised gauge parameters by means of a connection. This implies that no further degrees of freedom, beyond those of the field content of the E 8 group, are needed to have a well defined theory. We discuss the implications of the structure of the E 8 × R + generalised transformation on the construction of the d = 8 generalised geometry. Finally, we suggest how to lift the generalised Lie derivative to eleven dimensions.