Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator

The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. The paper describes an extension of this uniformity for the totally antisymmetrised n-th powers up to n=9, identifying (see Tables 3 and 6) families of representations with integer eigenvalues 5,...,9 for the quadratic Casimir operator, in each case providing a formula (see eq. (11) to (15)) for the dimensions of the representations in the family as a function of D=dim g. This generalises previous results for powers j and Casimir eigenvalues j, j<=4. Many intriguing, perhaps puzzling, features of the dimension formulas are discussed and the possibility that they may be valid for a wider class of not necessarily simple Lie algebras is considered.Comment: 16 pages, LaTeX, 1 figure, 9 tables; v2: presentation improved, typos correcte

D6-branes and torsion

The D6-brane spectrum of type IIA vacua based on twisted tori and RR background fluxes is analyzed. In particular, we compute the torsion factors of the (co)homology groups H_n and describe the effect that they have on D6-brane physics. For instance, the fact that H_3 contains Z_N subgroups explains why RR tadpole conditions are affected by geometric fluxes. In addition, the presence of torsional (co)homology shows why some D6-brane moduli are lifted, and it suggests how the D-brane discretum appears in type IIA flux compactifications. Finally, we give a clear, geometrical understanding of the Freed-Witten anomaly in the present type IIA setup, and discuss its consequences for the construction of semi-realistic flux vacua.Comment: 35 pages, 1 figure. One reference adde

Open string wavefunctions in flux compactifications

We consider compactifications of type I supergravity on manifolds with SU(3) structure, in the presence of RR fluxes and magnetized D9-branes, and analyze the generalized Dirac and Laplace-Beltrami operators associated to the D9-brane worldvolume fields. These compactifications are T-dual to standard type IIB toroidal orientifolds with NSNS and RR 3-form fluxes and D3/D7 branes. By using techniques of representation theory and harmonic analysis, the spectrum of open string wavefunctions can be computed for Lie groups and their quotients, as we illustrate with explicit twisted tori examples. We find a correspondence between irreducible unitary representations of the Kaloper-Myers algebra and families of Kaluza-Klein excitations. We perform the computation of 2- and 3-point couplings for matter fields in the above flux compactifications, and compare our results with those of 4d effective supergravity.Comment: 89 pages, 4 figures. v3: more typos corrected, version published in JHE