Wrapping rules (in) string theory

Abstract

In this paper we show that the number of all 1/2-BPS branes in string theory compactified on a torus can be derived by universal wrapping rules whose formulation we present. These rules even apply to branes in less than ten dimensions whose tendimensional origin is an exotic brane. In that case the wrapping rules contain an additional combinatorial factor that is related to the highest dimension in which the ten-dimensional exotic brane, after compactification, can be realized as a standard brane. We show that the wrapping rules also apply to cases with less supersymmetry. As a specific example, we discuss the compactification of IIA/IIB string theory on (T 4 /Z 2 ) × T n .

Weaving the exotic web

“…This implies that under duality transformations, the structure of the domain-wall background is not essentially changed and only the name of the mixed-symmetry potential E (n) 9,a 1 ,...,as are changed. The transformation rule (at the linearized level) is perfectly consistent with the rule [16,17], E (n) · · · y, · · · y, · · · y p Ty ↔ E (n) · · · y, · · · y, · · · y n−p .…”

“…Here, the subscript "9, 2" represents that the field strength is the mixed-symmetry tensor with 9 antisymmetric indices and 2 antisymmetric indices, and the Hodge star operator * 10 is associated with the dual metricg mn . By introducing the associated potential Q 9,2 ≡ dD 8,2 , we can find a connection between the non-geometric Q-flux and the mixed-symmetry potential D 8,2 introduced in a series of works [8][9][10][11][12][13][14][15][16][17] (see [12,79] for a similar Hodge duality between Q-flux and the mixed-symmetry potential D 8,2 ). In the 5 2 2 (12345, 67) background, we obtain…”

“…Just like the Dp-brane is electrically coupled to the Ramond-Ramond (R-R) (p + 1)-form potential, in general, exotic branes are electrically coupled to mixed-symmetry potentials. In a series of works [8][9][10][11][12][13][14][15][16][17], it has been shown that there exists a one-to-one correspondence between exotic branes and some mixed-symmetry potentials that are defined in ten dimensions. A classification of mixed-symmetry potentials (and thus of exotic branes) has been done by considering different arguments.…”

“…This prediction is based on the analysis of roots and weights of the U-duality group at any dimension [25][26][27][28][29][30]. Lately, the so-called wrapping rules were formulated [11,17,[31][32][33]. This set of rules allows one to construct a set of mixed-symmetry potentials, depending on the type of T -and S-duality transformations that one performs.…”

“…For example, the F1 and the pp-wave (electrically) couple to the B-field B 2 and the graviphoton A m 1 , and Dp-branes couple to the R-R potentials C p+1 . Following a series of works [8][9][10][11][12][13][14][15][16][17], we call F1 and the pp-wave the F(undamental)-branes. There are also the S(olitonic)-branes, which consist of 5 2 -brane (NS5-brane), 5 1 2 -brane (KK monopole), 5 2 2 -brane, 5 3 2 -brane, and 5 4 2brane.…”