The Elliptic curves in gauge theory, string theory, and cohomology

Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the reduction of M-theory to) type IIA and as the elliptic fiber leading to F-theory for type IIB. In this paper we elaborate on the physical setting for various generalized cohomology theories, including elliptic cohomology, and we note that the above two seemingly unrelated descriptions can be unified using Sen's picture of the orientifold limit of F-theory compactification on K3, which unifies the Seiberg-Witten curve with the F-theory curve, and through which we naturally explain the constancy of the modulus that emerges from elliptic cohomology. This also clarifies the orbifolding performed in the previous work and justifies the appearance of the w_4 condition in the elliptic refinement of the mod 2 part of the partition function. We comment on the cohomology theory needed for the case when the modular parameter varies in the base of the elliptic fibration.Comment: 23 pages, typos corrected, minor clarification

Duality symmetry and the form fields of M-theory

In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this paper, we propose the extention of these characters to include the dual fields. The unified treatment of the M-theory four-form field strength and its dual leads to several observations. In particular we elaborate on the possibility of a twisted cohomology theory with a twist given by degrees greater than three.Comment: 12 pages, modified material on the differentia

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 mathematical formalism for the Kondo effect in WZW branes

In this paper, we show how to adapt our rigorous mathematical formalism for closed/open conformal field theory so that it captures the known physical theory of branes in the WZW model. This includes a mathematically precise approach to the Kondo effect, which is an example of evolution of one conformally invariant boundary condition into another through boundary conditions which can break conformal invariance, and a proposed mathematical statement of the Kondo effect conjecture. We also review some of the known physical results on WZW boundary conditions from a mathematical perspective.Comment: Added explanations of the settings and main result

Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky vs. Hanamura

We describe the Voevodsky's category $DM^{eff}_{gm}$ of motives in terms of Suslin complexes of smooth projective varieties. This shows that Voeovodsky's $DM_{gm}$ is anti-equivalent to Hanamura's one. We give a description of any triangulated subcategory of $DM^{eff}_{gm}$ (including the category of effective mixed Tate motives). We descibe 'truncation' functors $t_N$ for $N>0$. $t=t_0$ generalizes the weight complex of Soule and Gillet; its target is $K^b(Chow_{eff})$; it calculates $K_0(DM^{eff}_{gm})$, and checks whether a motive is a mixed Tate one. $t_N$ give a weight filtration and a 'motivic descent spectral sequence' for a large class of realizations, including the 'standard' ones and motivic cohomology. This gives a new filtration for the motivic cohomology of a motif. For 'standard realizations' for $l,s\ge 0$ we have a nice description of $W_{l+s}H^i/W_{l-1}H^i(X)$ in terms of $t_s(X)$. We define the 'length of a motif' that (modulo standard conjectures) coincides with the 'total' length of the weight filtration of singular cohomology. Over a finite field $t_0Q$ is (modulo Beilinson-Parshin conjecture) an equivalence.Comment: Several linguistic corrections made; section 2.3 was corrected als

Twisted topological structures related to M-branes

Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tower of the orthogonal group, and demonstrate the relations to M-branes.Comment: 17 pages, title changed on referee's request, minor changes to improve presentation, typos correcte

Loop Groups, Kaluza-Klein Reduction and M-Theory

We show that the data of a principal G-bundle over a principal circle bundle is equivalent to that of a \hat{LG} = U(1) |x LG bundle over the base of the circle bundle. We apply this to the Kaluza-Klein reduction of M-theory to IIA and show that certain generalized characteristic classes of the loop group bundle encode the Bianchi identities of the antisymmetric tensor fields of IIA supergravity. We further show that the low dimensional characteristic classes of the central extension of the loop group encode the Bianchi identities of massive IIA, thereby adding support to the conjectures of hep-th/0203218.Comment: 26 pages, LaTeX, utarticle.cls, v2:clarifications and refs adde

Long-term evolution of antigen repertoires among carried meningococci

Most studies of bacterial pathogen populations have been based on isolates collected from individuals with disease, or their contacts, over short time periods. For commensal organisms that occasionally cause disease, such as Neisseria meningitidis, however, the analysis of isolates from long-term asymptomatic carriage is necessary to elucidate their evolution and population structure. Here, we use mathematical models to analyse the structuring and dynamics of three vaccine-candidate antigens among carried meningococcal isolates collected over nearly 30 years in the Czech Republic. The data indicate that stable combinations of antigenic alleles were maintained over this time period despite evidence for high rates of recombination, consistent with theoretical models in which strong immune selection can maintain non-overlapping combinations of antigenic determinants in the presence of recombination. We contrast this antigenic structure with the overlapping but relatively stable combinations of the housekeeping genes observed among the same isolates, and use a novel network approach to visualize these relationships

emm typing and validation of provisional M types for group A streptococci.

This report discusses the following issues related to typing of group A streptococci (GAS): The development and use of the 5' emm variable region sequencing (emm typing) in relation to the existing serologic typing system; the designation of emm types in relation to M types; a system for validation of new emm types; criteria for validation of provisional M types to new M-types; a list of reference type cultures for each of the M-type or emm-type strains of GAS; the results of the first culture exchange program for a quality control testing system among the national and World Health Organization collaborating centers for streptococci; and dissemination of new approaches to typing of GAS to the international streptococcal community