Codimension-2 black hole solutions on a thin 3-brane and their extension into the bulk

In this talk we discuss black hole solutions in six-dimensional gravity with a Gauss- Bonnet term in the bulk and an induced gravity term on a thin 3-brane of codimension-2. It is shown that these black holes can be localized on the 3-brane, and they can further be extended into the bulk by a warp function. These solutions have regular horizons and no other curvature singularities appear apart from the string-like ones. The projection of the Gauss-Bonnet term on the brane imposes a constraint relation which requires the presence of matter in the extra dimensions, in order to sustain our solutions.Comment: 9 pages, Talk given at the conference "NEB-XIII:Recent developments in gravity" held at Thessaloniki, Greece in June 200

Fuzzy dimensions and Planck's Uncertainty Principle for p-branes

The explicit form of the quantum propagator of a bosonic p-brane, previously obtained by the authors in the quenched-minisuperspace approximation, suggests the possibility of a novel, unified, description of p-branes with different dimensionality. The background metric that emerges in this framework is a quadratic form on a Clifford manifold. Substitution of the Lorentzian metric with the Clifford line element has two far reaching consequences. On the one hand, it changes the very structure of the spacetime fabric since the new metric is built out of a Minimum Length below which it is impossible to resolve the distance between two points; on the other hand, the introduction of the Clifford line element extends the usual relativity of motion to the case of Relative Dimensionalism of all p-branes that make up the spacetime manifold near the Planck scale.Comment: 11 pages, LaTex, no figures; in print on Class.& Quantum Gra

Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime

A theory in which 4-dimensional spacetime is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza-Klein theory. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U(1)xSU(2)xSU(3) of the standard model. The generalized spin connection in C-space has the properties of Yang-Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb-Ramond fields.Comment: 57 pages; References added, section 2 rewritten and expande

A Novel View on the Physical Origin of E8

We consider a straightforward extension of the 4-dimensional spacetime $M_4$ to the space of extended events associated with strings/branes, corresponding to points, lines, areas, 3-volumes, and 4-volumes in $M_4$. All those objects can be elegantly represented by the Clifford numbers $X\equiv x^A \gamma_A \equiv x^{a_1 ...a_r} \gamma_{a_1 ...a_r}, r=0,1,2,3,4$. This leads to the concept of the so-called Clifford space ${\cal C}$, a 16-dimensional manifold whose tangent space at every point is the Clifford algebra ${\cal C \ell }(1,3)$. The latter space besides an algebra is also a vector space whose elements can be rotated into each other in two ways: (i) either by the action of the rotation matrices of SO(8,8) on the components $x^A$ or (ii) by the left and right action of the Clifford numbers $R=$exp [\alpha^A \gam_A] and $S=$exp [\beta^A \gam_A] on $X$. In the latter case, one does not recover all possible rotations of the group SO(8,8). This discrepancy between the transformations (i) and (ii) suggests that one should replace the tangent space ${\cal C \ell}(1,3)$ with a vector space $V_{8,8}$ whose basis elements are generators of the Clifford algebra ${\cal C \ell}(8,8)$, which contains the Lie algebra of the exceptional group E$_8$ as a subspace. E$_8$ thus arises from the fact that, just as in the spacetime $M_4$ there are $r$-volumes generated by the tangent vectors of the spacetime, there are $R$-volumes, $R=0,1,2,3,...,16$, in the Clifford space ${\cal C}$, generated by the tangent vectors of ${\cal C}$.Comment: 14 page