Double field theory for double D-branes

Abstract

We consider Hull's doubled formalism for open strings on D-branes in flat space and construct the corresponding effective double field theory. We show that the worldsheet boundary conditions of the doubled formalism describe in a unified way a T-dual pair of D-branes, which we call double D-branes. We evaluate the one-loop beta function for the boundary gauge coupling and then obtain the effective field theory for the double D-branes. The effective field theory is described by a DBI action of double fields. The T-duality covariant form of this DBI action is thus a kind of "master" action, which describes all the double D-brane configurations related by T-duality transformations. We discuss a number of aspects of this effective theory.

Towards an invariant geometry of double field theory

“…As this has to agree with (7.25) for arbitrary ξ we conclude 27) which is the differential Bianchi identity we wanted to prove.…”

“…There we introduced 'generalized coordinate' transformations X Ñ X 1 and defined a generalized vector A M as transforming according to 27) where the matrix F is defined by 28) and the indices on coordinates are raised and lowered with η M N . We take this to be the definition of a generalized vector since, as mentioned above, currently we do not know of an invariant 'intrinsic' definition.…”

Incorporation of fermions into double field theory

“…It will be of interest to identify the pair of local Lorentz symmetries directly from the string worldsheet or M-theory points of view [19][20][21][40][41][42][43][44][45][46][47].…”

“…Recent developments initiated by Hull and Zwiebach developed this idea further, in the name of Double Field Theory (DFT), by writing the D-dimensional effective action entirely in terms of the 2D-dimensional language, i.e. 2D tensors [9][10][11][12] (see also [13][14][15][16][17][18][19][20][21][22][23][24]). Yet, as a field theory counterpart to the level matching condition in closed string theories, it is required that all the fields as well as all of their possible products should be annihilated by the O(D, D) d'Alembert operator, ∂ 2 = ∂ A ∂ A ,…”

Gauged double field theory

“…The original formulation was done in [1][2][3][4], following previous ideas by Siegel [5,6] and Tseytlin [7,8] (see also [9,10]). Since then, DFT has been extended in many different ways [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]- [32]. Some very recent related works on duality based constructions are [33][34][35][36][37][38][39][40].…”