Eleven Dimensional Origin of String/String Duality: A One Loop Test

Membrane/fivebrane duality in D=11 implies Type IIA string/Type IIA fivebrane duality in D=10, which in turn implies Type IIA string/heterotic string duality in D=6. To test the conjecture, we reproduce the corrections to the 3-form field equations of the D=10 Type IIA string (a mixture of tree-level and one-loop effects) starting from the Chern-Simons corrections to the 7-form Bianchi identities of the D=11 fivebrane (a purely tree-level effect). K3 compactification of the latter then yields the familiar gauge and Lorentz Chern-Simons corrections to 3-form Bianchi identities of the heterotic string. We note that the absence of a dilaton in the D=11 theory allows us to fix both the gravitational constant and the fivebrane tension in terms of the membrane tension. We also comment on an apparent conflict between fundamental and solitonic heterotic strings and on the puzzle of a fivebrane origin of S-duality.Comment: 30 pages (including 5 postscript figures included), LaTeX, Footnote 8 has been removed; the apparent disagreement with Townsend is only one of semantics, not substanc

Duality in Fractional Programming Involving Locally Arcwise Connected and Related Functions

A nonlinear fractional programming problem is considered, where the functions involved are diferentiable with respect to an arc.Necessary and su±cient optimality conditions are obtained in terms of the right diferentials with respect to an arc of the functions. A dual is formulated and duality results are proved using concepts of locally arcwise connected, locally Q-connected and locally P-connected functions .Our results generalize the results obtained by Lyall, Suneja and Aggarwal, Kaul and Lyall and Kaul et.al.Generalized convexity; Fractional programming; Optimality conditions, Duality

Heterotic flux backgrounds and their IIA duals

We study four-dimensional heterotic flux vacua with N=2 spacetime supersymmetry. A worldsheet perspective is used to clarify quantization conditions associated to the fluxes and the constraints these place on the moduli spaces of resulting compactifications. We propose that these vacua fit naturally in the context of heterotic/IIA duality as heterotic duals to compactifications on K3-fibered but not elliptically fibered Calabi-Yau three-folds. We present some examples of such potential dual pairs

Topological strings on noncommutative manifolds

We identify a deformation of the N=2 supersymmetric sigma model on a Calabi-Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkahler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the noncommutativity and the B-field, properties of the topologically twisted sigma-models can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigma-model is localized on generalized holomorphic maps, whereas for the A-model and the B-model it is localized on holomorphic and constant maps, respectively. The geometry of topological D-branes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological D-branes, which includes A-branes and B-branes as special cases.Comment: 36 pages, AMS latex. v2: a reference to a related work has been added. v3: An error in the discussion of the Fourier-Mukai transform for twisted coherent sheaves has been fixed, resulting in several changes in Section 2. The rest of the paper is unaffected. v4: an incorrect statement concerning Lie algebroid cohomology has been fixe

The M5-Brane Elliptic Genus: Modularity and BPS States

The modified elliptic genus for an M5-brane wrapped on a four-cycle of a Calabi-Yau threefold encodes the degeneracies of an infinite set of BPS states in four dimensions. By holomorphy and modular invariance, it can be determined completely from the knowledge of a finite set of such BPS states. We show the feasibility of such a computation and determine the exact modified elliptic genus for an M5-brane wrapping a hyperplane section of the quintic threefold.Comment: 21 page

A Note on the Geometry of CHL Heterotic Strings

We present a few remarks on disconnected components of the moduli space of heterotic string compactifications on $T_2$. We show in particular how the eight dimensional CHL heterotic string can be understood in terms of topologically non-trivial $E_8\times E_8$ and \Spin(32)/Z_2 vector bundles over the torus, and that the respective moduli spaces coincide