Inflation from Supersymmetric Quantum Cosmology

We derive a special scalar field potential using the anisotropic Bianchi type I cosmological model from canonical quantum cosmology under determined conditions in the evolution to anisotropic variables $\beta_\pm$. In the process, we obtain a family of potentials that has been introduced by hand in the literature to explain cosmological data. Considering supersymmetric quantum cosmology, this family is scanned, fixing the exponential potential as more viable in the inflation scenario $\rm V (\phi) = V_0 \,e^{-\sqrt{3}\phi}$.Comment: 14 pages, latex2e, To appear in Phys. Rev.

Topological gauge fixing

We implement the metric-independent Fock-Schwinger gauge in the abelian quantum Chern-Simons field theory defined in ${\mathbb R}^3$. The expressions of the various components of the propagator are determined. Although the gauge field propagator differs from the Gauss linking density, we prove that its integral along two oriented knots is equal to the linking number

Differentiable Rigidity under Ricci curvature lower bound

In this article we prove a differentiable rigidity result. Let $(Y, g)$ and $(X, g_0)$ be two closed $n$-dimensional Riemannian manifolds ($n\geqslant 3$) and $f:Y\to X$ be a continuous map of degree $1$. We furthermore assume that the metric $g_0$ is real hyperbolic and denote by $d$ the diameter of $(X,g_0)$. We show that there exists a number $\varepsilon:=\varepsilon (n, d)>0$ such that if the Ricci curvature of the metric $g$ is bounded below by $-n(n-1)$ and its volume satisfies \vol_g (Y)\leqslant (1+\varepsilon) \vol_{g_0} (X) then the manifolds are diffeomorphic. The proof relies on Cheeger-Colding's theory of limits of Riemannian manifolds under lower Ricci curvature bound.Comment: 33 pages, 1 dessi

Deformed N=2 theories, generalized recursion relations and S-duality

We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental flavors or with one adjoint hypermultiplet. In both cases we explicitly compute the first few instanton corrections to the partition function and the prepotential using Nekrasov's approach. These results allow to reconstruct exact expressions involving quasi-modular functions of the bare gauge coupling constant and to show that the prepotential terms satisfy a modular anomaly equation that takes the form of a recursion relation with an explicitly epsilon-dependent term. We then investigate the implications of this recursion relation on the modular properties of the effective theory and find that with a suitable redefinition of the prepotential and of the effective coupling it is possible, at least up to the third order in the deformation parameters, to cast the S-duality relations in the same form as they appear in the Seiberg-Witten solution of the undeformed theory.Comment: 33 pages, no figures, LaTeX2

Classical solutions for exotic instantons?

We consider the D7/D(--1) system in Type I' as a prototypical "exotic" brane instanton. With respect to systems such as the D3/D(-1) ones, which correspond to gauge instantons in four dimensions, exotic systems lack the bosonic mixed moduli w of the ADHM construction, related to the instanton size, and their possible field-theoretical interpretation as classical solutions is an important open question. For the system at hand, we propose that it corresponds to the point-like limit of the eight-dimensional so-called SO(8) instanton solution. This configuration is a solution of the quartic term of the non-abelian D7 action, i.e., the term which stays finite in the limit in which alpha' goes to zero with the string coupling fixed that preserves the D(-1) effects. As a necessary consistency condition, we check that the next order term in the non-abelian effective action vanishes on the SO(8) solution so that the limit we take is well-defined.Comment: 39 pages, 3 figures. Some references added, and minor corrections: a more precise statement of eq. (3.18) and a few coefficients in eq. (3.10

Curing and post-curing luminescence in an epoxy resin

A spontaneous luminescence is reported when epoxy resin samples are heated in air. This phenomenon is very sensitive to the nature of the atmosphere. The same treatment in nitrogen leads to an extinction of the luminescence. The emission process is restored when samples are kept for a sufficient time in air. In order to better understand this phenomenon, we have investigated the luminescence of the elementary constituents of the epoxy (resin and hardener) when heated in air and nitrogen, as well as during resin curing in the same atmospheres. It appears that the emission process is linked with the presence of oxygen. Although the kinetics of the luminescence can differ depending on the nature of the sample (cured resin, resin during curing, liquid components), the emission spectra are the same during resin curing and upon heating of the cured resin and hardener. The emission spectrum of the base resin is different. It is concluded that the light results from a chemiluminescence process during oxidation.Comment: p. 1

Exotic instanton counting and heterotic/type I' duality

We compute the partition function for the exotic instanton system corresponding to D-instantons on D7 branes in Type I' theory. We exploit the BRST structure of the moduli action and its deformation by RR background to fully localize the integration. The resulting prepotential describes non-perturbative corrections to the quartic couplings of the gauge field F living on the D7's. The results match perfectly those obtained in the dual heterotic theory from a protected 1-loop computation, thus providing a non-trivial test of the duality itself.Comment: 42 pages, 3 figure

On Four-Point Functions of Half-BPS Operators in General Dimensions

We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for these correlators and present them in a universal form. We then solve these identities, employing Jack polynomial expansions. We show that the general solution is parameterized by a set of arbitrary two-variable functions, with the exception of the case d=4, where in addition functions of a single variable appear. We also discuss the operator product expansion using recent results on conformal partial wave amplitudes in arbitrary dimension.Comment: The discussion of the case d=6 expanded; references added/correcte