7 research outputs found
A Note on Real Tunneling Geometries
In the Hartle-Hawking ``no boundary'' approach to quantum cosmology, a real
tunneling geometry is a configuration that represents a transition from a
compact Riemannian spacetime to a Lorentzian universe. I complete an earlier
proof that in three spacetime dimensions, such a transition is ``probable,'' in
the sense that the required Riemannian geometry yields a genuine maximum of the
semiclassical wave function.Comment: 5 page
On 3d extensions of AGT relation
An extension of the AGT relation from two to three dimensions begins from
connecting the theory on domain wall between some two S-dual SYM models with
the 3d Chern-Simons theory. The simplest kind of such a relation would
presumably connect traces of the modular kernels in 2d conformal theory with
knot invariants. Indeed, the both quantities are very similar, especially if
represented as integrals of the products of quantum dilogarithm functions.
However, there are also various differences, especially in the "conservation
laws" for integration variables, which hold for the monodromy traces, but not
for the knot invariants. We also discuss another possibility: interpretation of
knot invariants as solutions to the Baxter equations for the relativistic Toda
system. This implies another AGT like relation: between 3d Chern-Simons theory
and the Nekrasov-Shatashvili limit of the 5d SYM.Comment: 23 page
From the twilight of cultural memory: the 'Bumah' in the mosques of central Oman
We give a short introduction to the theory of twisted Alexander polynomials
of a 3--manifold associated to a representation of its fundamental group. We
summarize their formal properties and we explain their relationship to twisted
Reidemeister torsion. We then give a survey of the many applications of twisted
invariants to the study of topological problems. We conclude with a short
summary of the theory of higher order Alexander polynomials.Comment: 42 pages, final version of the survey paper to be published by the
proceedings of the conference `The Mathematics of Knots: Theory and
Application' in Heidelberg in December 2008. In the final version we updated
references and fixed a few typo