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

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

A note on the dyonic D6-brane

We study the dyon electric charge of D6-branes as eleven dimensional KK-monopoles. We observe that the dyon charge is intimately related with the existence of gauge connections and antisymmetric fields on the brane world volume.Comment: 8 pages, Contribution to the 6th International Workshop on Conformal Field Theory and Integrable Models, Landau Institute, Sept. 2002, to honour A. Belavin on the occasion of his 60th birthda

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

BRS Cohomology of the Supertranslations in D=4

Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator $\delta = c^{\alpha} \sigma^{\mu}_{\alpha \dot \beta} {\overline c}^{\dot \beta} (\epsilon^{\mu})^{\dag}$. We find that the cohomology of this operator depends on a spin-orbit coupling in an SU(2) group and has a quite complicated structure. This spin-orbit type coupling will turn out to be basic in the cohomology of supersymmetric field theories in general.Comment: 14 pages, CTP-TAMU-13/9

On the Topology and Flux of T-Dual Manifolds

We present a general formula for the topology and H-flux of the T-dual of a type two compactification. Our results apply to T-dualities with respect to any free circle action. In particular we find that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of the dual H-flux over the dual circle. As a corollary we conjecture an obstruction to multiple T-dualities, generalizing an obstruction known to exist on the twisted torus. Examples include SU(2) WZW models, Lens spaces and the supersymmetric string theory on the non-spin AdS^5xCP^2xS^1 compactification.Comment: 4 Pages, No Figure

Presentations of Wess-Zumino-Witten Fusion Rings

The fusion rings of Wess-Zumino-Witten models are re-examined. Attention is drawn to the difference between fusion rings over Z (which are often of greater importance in applications) and fusion algebras over C. Complete proofs are given characterising the fusion algebras (over C) of the SU(r+1) and Sp(2r) models in terms of the fusion potentials, and it is shown that the analagous potentials cannot describe the fusion algebras of the other models. This explains why no other representation-theoretic fusion potentials have been found. Instead, explicit generators are then constructed for general WZW fusion rings (over Z). The Jacobi-Trudy identity and its Sp(2r) analogue are used to derive the known fusion potentials. This formalism is then extended to the WZW models over the spin groups of odd rank, and explicit presentations of the corresponding fusion rings are given. The analogues of the Jacobi-Trudy identity for the spinor representations (for all ranks) are derived for this purpose, and may be of independent interest.Comment: 32 pages, 3 figures, added references, minor additions to text. To be published in Rev. Math. Phy

Higher Spin BRS Cohomology of Supersymmetric Chiral Matter in D=4

We examine the BRS cohomology of chiral matter in $N=1$, $D=4$ supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators \Y_{(a,b)} are products of the elementary chiral superfields $S$ and \ov S and the derivative operators D_\a, \ov D_{\dot \b} and \pa_{\a \dot \b}. Such superfields \Y_{(a,b)} can be chosen to have `$a$' symmetrized undotted indices \a_i and `$b$' symmetrized dotted indices \dot \b_j. The result derived here is that each composite superfield \Y_{(a,b)} is subject to potential supersymmetry anomalies if $a-b$ is an odd number, which means that \Y_{(a,b)} is a fermionic superfield.Comment: 15 pages, CPT-TAMU-20/9

String loop corrections to the universal hypermultiplet

We study loop corrections to the universal dilaton supermultiplet for type IIA strings compactified on Calabi-Yau threefolds. We show that the corresponding quaternionic kinetic terms receive non-trivial one-loop contributions proportional to the Euler number of the Calabi-Yau manifold, while the higher-loop corrections can be absorbed by field redefinitions. The corrected metric is no longer Kahler. Our analysis implies in particular that the Calabi-Yau volume is renormalized by loop effects which are present even in higher orders, while there are also one-loop corrections to the Bianchi identities for the NS and RR field strengths.Comment: 30 pages, harvmac, 1 figure. v2: minor typos corrected. Version to appear in Classical and Quantum Gravit