Duality of type-II 7-branes and 8-branes

Abstract

We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing 10-form field strength, F 10 , and to those of the 'massive' IIA theory for non-vanishing F 10 . We present a multi 8-brane solution of these equations that generalizes the 8-brane of Polchinski and Witten. We show that this solution is T-dual to a new multi 7-brane solution of S 1 compactified IIB supergravity, and that the latter is T-dual to the IIA 6-brane. When combined with the Sl(2; Z) U-duality of the type IIB superstring, the T-duality between type II 7-branes and 8-branes implies a quantization of the cosmological constant of type IIA superstring theory. These results are made possible by the construction of a new massive N=2 D=9 supergravity theory. We also discuss the 11-dimensional interpretation of these type II p-branes.2

Branes and the gauge hierarchy

“…As a result φ (2) is a constant in transverse space, equal to its classical value, and independent of the positions of the D-branes as well as of the geometric torus moduli. This can be checked alternatively from the explicit form of the seven-brane solution [32] in which e −φ ω 4 can be seen to be constant. The coefficient e −φ of the F 4 term, on the other hand, has a variation which can be read off the F-theory solution.…”

New supersymmetric vacua for D=4, N=4 gauged supergravity

“…For example the generalised Scherk and Schwarz dimensional reduction scheme [15] do give rise to massive supergravities. Under generalised reduction scheme some of the higher dimensional fields are given linear dependences along the directions to be compactified [3,4]. This procedure has been used in [3] to demonstrate the type IIA and IIB duality in D=9 for the massive case.…”

“…Under generalised reduction scheme some of the higher dimensional fields are given linear dependences along the directions to be compactified [3,4]. This procedure has been used in [3] to demonstrate the type IIA and IIB duality in D=9 for the massive case. Other methods require the gauging of internal global symmetries in the supergravity theory [16,17].…”

“…Recent understanding of the nonperturbative aspects in string theories and its duality symmetries [1] has triggered a series of new developments in the study of massive supergravity theories in various dimensions [2,3,4,5,6,7,8,9,10]. It is viewed that the massive supergravities are required for the spacetime interpretations of higher dimensional world volume Dirichlet objects (D-p-branes) of type II superstrings.…”

“…It is viewed that the massive supergravities are required for the spacetime interpretations of higher dimensional world volume Dirichlet objects (D-p-branes) of type II superstrings. For example, massive (gauged) type IIA supergravity [2] is a candidate theory for type IIA D-8-brane [11,3,12] whose field strength is a 10-form. The dual of a 10-form in ten dimensions is a constant which can be identified as a mass term (cosmological constant) of massive type IIA supergravity.…”