Linguistics

Contains research objectives and reports on four research projects.National Institutes of Health (Grant 5 TO1 HD00111-08)National Institute of Mental Health (Grant 2 P01 MH13390-06

M-theory and Characteristic Classes

In this note we show that the Chern-Simons and the one-loop terms in the M-theory action can be written in terms of new characters involving the M-theory four-form and the string classes. This sheds a new light on the topological structure behind M-theory and suggests the construction of a theory of `higher' characteristic classes.Comment: 8 pages. Error in gravitational term fixed; minor corrections; reference and acknowledgement adde

A Pair of Disjoint 3-GDDs of type g^t u^1

Pairwise disjoint 3-GDDs can be used to construct some optimal constant-weight codes. We study the existence of a pair of disjoint 3-GDDs of type $g^t u^1$ and establish that its necessary conditions are also sufficient.Comment: Designs, Codes and Cryptography (to appear

From E_8 to F via T

We argue that T-duality and F-theory appear automatically in the E_8 gauge bundle perspective of M-theory. The 11-dimensional supergravity four-form determines an E_8 bundle. If we compactify on a two-torus, this data specifies an LLE_8 bundle where LG is a centrally-extended loopgroup of G. If one of the circles of the torus is smaller than sqrt(alpha') then it is also smaller than a nontrivial circle S in the LLE_8 fiber and so a dimensional reduction on the total space of the bundle is not valid. We conjecture that S is the circle on which the T-dual type IIB theory is compactified, with the aforementioned torus playing the role of the F-theory torus. As tests we reproduce the T-dualities between NS5-branes and KK-monopoles, as well as D6 and D7-branes where we find the desired F-theory monodromy. Using Hull's proposal for massive IIA, this realization of T-duality allows us to confirm that the Romans mass is the central extension of our LE_8. In addition this construction immediately reproduces the conjectured formula for global topology change from T-duality with H-flux.Comment: 25 pages, 4 eps figure

K-Theory and S-Duality: Starting Over from Square 3

Recently Maldacena, Moore, and Seiberg (MMS) have proposed a physical interpretation of the Atiyah-Hirzebruch spectral sequence, which roughly computes the K-homology groups that classify D-branes. We note that in IIB string theory, this approach can be generalized to include NS charged objects and conjecture an S-duality covariant, nonlinear extension of the spectral sequence. We then compute the contribution of the MMS double-instanton configuration to the derivation d_5. We conclude with an M-theoretic generalization reminiscent of 11-dimensional E_8 gauge theory.Comment: 27 pages, 3 figure

A handlebody calculus for topology change

We consider certain interesting processes in quantum gravity which involve a change of spatial topology. We use Morse theory and the machinery of handlebodies to characterise topology changes as suggested by Sorkin. Our results support the view that that the pair production of Kaluza-Klein monopoles and the nucleation of various higher dimensional objects are allowed transitions with non-zero amplitude.Comment: Latex, 32 pages, 7 figure

Regge calculus from a new angle

In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show such a formulation allows to replace the length variables by 3d or 4d dihedral angles as basic variables. Moreover we will introduce a first order formulation, which in contrast to using flat simplices, does not require any constraints. These considerations could be useful for the construction of quantum gravity models with a cosmological constant.Comment: 8 page

On Flux Quantization in F-Theory

We study the problem of four-form flux quantization in F-theory compactifications. We prove that for smooth, elliptically fibered Calabi-Yau fourfolds with a Weierstrass representation, the flux is always integrally quantized. This implies that any possible half-integral quantization effects must come from 7-branes, i.e. from singularities of the fourfold. We subsequently analyze the quantization rule on explicit fourfolds with Sp(N) singularities, and connect our findings via Sen's limit to IIB string theory. Via direct computations we find that the four-form is half-integrally quantized whenever the corresponding 7-brane stacks wrap non-spin complex surfaces, in accordance with the perturbative Freed-Witten anomaly. Our calculations on the fourfolds are done via toric techniques, whereas in IIB we rely on Sen's tachyon condensation picture to treat bound states of branes. Finally, we give general formulae for the curvature- and flux-induced D3 tadpoles for general fourfolds with Sp(N) singularities.Comment: 46 page

Fragmentation production of doubly heavy baryons

Baryons with a single heavy quark are being studied experimentally at present. Baryons with two units of heavy flavor will be abundantly produced not only at future colliders, but also at existing facilities. In this paper we study the production via heavy quark fragmentation of baryons containing two heavy quarks at the Tevatron, the LHC, HERA, and the NLC. The production rate is woefully small at HERA and at the NLC, but significant at $pp$ and $p\bar{p}$ machines. We present distributions in various kinematical variables in addition to the integrated cross sections at hadron colliders.Comment: 13 pages, macro package epsfig needed, 6 .eps figure files in a separate uuencoded, compressed and tarred file; complete paper available at http://www.physics.carleton.ca/~mad/papers/paper.p