Construction of matryoshka nested indecomposable N-replications of Kac-modules of quasi-reductive Lie superalgebras, including the sl(m/n) and osp(2/2n) series

We construct a new class of finite dimensional indecomposable representations of simple superalgebras which may explain, in a natural way, the existence of the heavier elementary particles. In type I Lie superalgebras sl(m/n) and osp(2/2n), one of the Dynkin weights labeling the finite dimensional irreducible representations is continuous. Taking the derivative, we show how to construct indecomposable representations recursively embedding N copies of the original irreducible representation, coupled by generalized Cabibbo angles, as observed among the three generations of leptons and quarks of the standard model. The construction is then generalized in the appendix to quasi-reductive Lie superalgebras.Comment: Revised version 2 with minor modifications. On the suggestion of the referee, we show that the construction does not apply to the psl(n/n) superalgebras. 15 pages, 32 references Revised version 3 no modification except reformatting the bibliography and adding do

Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials

We describe a conjectural formula via intersection numbers for the Masur-Veech volumes of strata of quadratic differentials with prescribed zero orders, and we prove the formula for the case when the zero orders are odd. For the principal strata of quadratic differentials with simple zeros, the formula reduces to compute the top Segre class of the quadratic Hodge bundle, which can be further simplified to certain linear Hodge integrals. An appendix proves that the intersection of this class with $\psi$-classes can be computed by Eynard-Orantin topological recursion. As applications, we analyze numerical properties of Masur-Veech volumes, area Siegel-Veech constants and sums of Lyapunov exponents of the principal strata for fixed genus and varying number of zeros, which settles the corresponding conjectures due to Grivaux-Hubert, Fougeron, and elaborated in [the7]. We also describe conjectural formulas for area Siegel-Veech constants and sums of Lyapunov exponents for arbitrary affine invariant submanifolds, and verify them for the principal strata

On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1} \otimes Cl_{1,1}. The general case used in quantum field theory lacks this feature. Theories with non-symmetric bilinear forms are however needed in the analysis of multi-particle states in interacting theories. A connection to q-deformed structures through nontrivial vacuum states in quantum theories is outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 27 - July 4, 199

A limiting velocity for quarkonium propagation in a strongly coupled plasma via AdS/CFT

We study the dispersion relations of mesons in a particular hot strongly coupled supersymmetric gauge theory plasma. We find that at large momentum k the dispersion relations become omega = v_0 k + a + b/k + ..., where the limiting velocity v_0 is the same for mesons with any quantum numbers and depends only on the ratio of the temperature to the quark mass T/m_q. We compute a and b in terms of the meson quantum numbers and T/m_q. The limiting meson velocity v_0 becomes much smaller than the speed of light at temperatures below but close to T_diss, the temperature above which no meson bound states at rest in the plasma are found. From our result for v_0, we find that the temperature above which no meson bound states with velocity v exist is T_diss(v) \simeq (1-v^2)^(1/4) T_diss, up to few percent corrections.We thus confirm by direct calculation of meson dispersion relations a result inferred indirectly in previous work via analysis of the screening length between a static quark and antiquark in a moving plasma. Although we do not do our calculations in QCD, we argue that the qualitative features of the dispersion relation we compute, including in particular the relation between dissociation temperature and meson velocity, may apply to bottomonium and charmonium mesons propagating in the strongly coupled plasma of QCD. We discuss how our results can contribute to understanding quarkonium physics in heavy ion collisions.Comment: 57 pages, 12 figures; references adde

Double Counting Ambiguities in the Linear Sigma Model

We study the dynamical consequences imposed on effective chiral field theories such as the quark-level SU(2) linear $\sigma$ model (L$\sigma$M) due to the fundamental constraints of massless Goldstone pions, the normalization of the pion decay constant and form factor, and the pion charge radius. We discuss quark-level double counting L$\sigma$M ambiguities in the context of the Salam-Weinberg $Z = 0$ compositeness condition. Then SU(3) extensions to the kaon are briefly considered.Comment: 23 pages To be published in Journal of Physics