No abstract

Invariant polynomials for torus links are obtained in the framework of the Chern-Simons topological gauge theory. The polynomials are computed as vacuum expectation values on the three-sphere of Wilson line operators representing the Verlinde algebra of the corresponding rational conformal field theory. In the case of the SU(2) gauge theory our results provide explicit expressions for the Jones polynomial as well as for the polynomials associated to the N-state (N > 2) vertex models (Akutsu-Wadati polynomials). By means of the Chern-Simons coset construction, the minimal unitary models are analyzed, showing that the corresponding link invariants factorize into two SU(2) polynomials. A method to obtain skein rules from the Chern-Simons knot operators is developed. This procedure yields the eigenvalues of the braiding matrix of the corresponding conformal field theory.

Quantum mechanics emergesà la Verlinde from a foliation of R 3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k B . The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on R 3 . The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant from Boltzmann's constant k B .

The evidence for neutrino masses in atmospheric and solar neutrino experiments provides further support for the embedding of the Standard Model fermions in the chiral 16 SO(10) representation. Such an embedding is afforded by the realistic free fermionic heterotic-string models. In this paper we advance the study of these string models toward a non-perturbative analysis by generalizing the work of Donagi, Pantev, Ovrut and Waldram from the case of G = SU (2n + 1) to G = SU (2n) stable holomorphic vector bundles on elliptically fibered Calabi-Yau manifolds with fundamental group Z 2 . We demonstrate existence of G = SU (4) solutions with three generations and SO(10) observable gauge group over Hirzebruch base surface, whereas we show that certain classes of del Pezzo base surface do not admit such solutions. The SO(10) symmetry is broken to SU (5) × U (1) by Wilson line. The overlap with the realistic free fermionic heterotic-string models is discussed. * faraggi@thphys.ox.ac.uk

The conformal field theory for the gl(N, N) affine Lie superalgebra in two space-time dimensions is studied. The energy-momentum tensor of the model, with vanishing Virasoro anomaly, is constructed. This theory has a topological symmetry generated by operators of dimensions 1, 2 and 3, which are represented as normal-ordered products of gl(N, N) currents. The topological algebra they satisfy is linear and differs from the one obtained by twisting the N = 2 superconformal models. It closes with a set of gl(N) bosonic and fermionic currents.The Wess-Zumino-Witten model for the supergroup GL(N, N) provides an explicit realization of this symmetry and can be used to obtain a free-field representation of the different generators. In this free-field representation, the theory decomposes into two uncoupled components with sl(N) and U(1) symmetries. The non-abelian component is responsible for the extended character of the topological algebra, and it is shown to be equivalent to an SL(N)/SL(N) coset model. In the light of these results, the G/G coset models are interpreted as topological sigma models for the group manifold of G.

We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al . Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e. an effective description of some underlying degrees of freedom.

We elaborate a full superfield description of the interacting system of dynamical Dϭ4, Nϭ1 supergravity and a dynamical superstring. As far as a minimal formulation of simple supergravity is used, such a system should contain as well the tensor ͑real linear͒ multiplet which describes the dilaton and the two-superform gauge field whose pullback provides the Wess-Zumino term for the superstring. The superfield action is given by the sum of the Wess-Zumino action for Dϭ4, Nϭ1 superfield supergravity, the superfield action for the tensor multiplet in curved superspace, and the Green-Schwarz superstring action. The latter includes the coupling to the tensor multiplet both in the Nambu-Goto and in the Wess-Zumino terms. We derive superfield equations of motion including, besides the superfield supergravity equations with the source, the source-full superfield equations for the linear multiplet. The superstring equations keep the same form as for the superstring in supergravity and 2-superform background. The analysis of gauge symmetries shows that the superfield description of the interacting system is gauge equivalent to the dynamical system described by the sum of the spacetime, component action for supergravity interacting with the tensor multiplet, and of the purely bosonic string action.

A new method to obtain the Picard-Fuchs equations of effective, N = 2 supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding N = 2 theory.