D-branes and non-Abelian T-duality

Abstract

We study the effect of non-Abelian T-duality (NATD) on D-brane solutions of type II supergravity. Knowledge of the full brane solution allows us to track the brane charges and the corresponding brane configurations, thus providing justification for brane setups previously proposed in the literature and for the common lore that Dp brane solutions give rise to D(p+1)-D(p+3)-NS5 backgrounds under SU(2) NATD transverse to the brane. In brane solutions where spacetime is empty and flat at spatial infinity before NATD, the spatial infinity of the NATD is universal, i.e. independent of the initial brane configuration. Furthermore, it gives enough information to determine the ranges of all coordinates after NATD. In the more complicated examples of the D2 branes considered here, where spacetime is not asymptotically flat before NATD, the interpretation of the dual solutions remains unclear. In the case of supersymmetric D2 branes arising from M2 reductions to IIA on Sasaki-Einstein seven-manifolds, we explicitly verify that the solution obeys the appropriate generalized spinor equations for a supersymmetric domain wall in four dimensions. We also investigate the existence of supersymmetric mass-deformed D2 brane solutions. 1 rterrisse@ipnl.in2p3.fr, 2 tsimpis@ipnl.in2p3.fr, 3 cwhiting@bates.edu arXiv:1811.05800v3 [hep-th] 2 Sep 2019Furthermore, all examples considered here will be seen to be consistent with the common lore that Dp brane solutions give rise to D(p+1)-D(p+3)-NS5 backgrounds under SU(2) NATD transverse to the brane [14] 2 .More generally, for nonstandard brane solutions, such as the D2 branes considered here in sections 4, 5, 6, the geometry may not asymptote to flat space even before NATD. In that case the original solution and its dual will in general contain non-vanishing fluxes even at spatial infinity. Nevertheless, by zooming in near the locus of the NS5, one can still see the presence of a continuous distribution of NS5 branes in accordance with the harmonic superposition prescription for intersecting branes.

The Tension between 10D Supergravity and dS Uplifts

“…This resonates well with suggestions that fermion condensate naturally lead to dS vacua. See [] for recent papers on the matter.…”

Wrapped brane solutions in romans F(4) gauged supergravity

“…[65][66][67][68][69][70][71]. It is also established that IIA and IIB descriptions are related through a non-Abelian T-duality [72][73][74][75][76]. and all other bosonic (and also fermionic) fields are trivial.…”

Generalised U-dual solutions via ISO(7) gauged supergravity

“…where from above C 6 = ρ 7 /(r 2 + ρ 2 )Vol S 6 . We could try to specify a seven-cycle to evaluate this charge (generalising the argument of [26] for non-abelian T-dual solutions) by integrating from ρ = ρ 0 to some value ρ = ρ 1 at a fixed value of r = r 0 , and then integrate from r = r 0 to r = r 1 at fixed ρ = ρ 1 , such that the six-sphere part of the solution vanishes at ρ = ρ 0 and r = r 1 . The result is independent of r 0 , and gives 16π 3 ρ 7 1 /15(r 2 1 + ρ 2 1 ).…”