The operator algebra of the discrete state operators in 2D gravity with non-vanishing cosmological constant

Remarks are given to the structure of physical states in 2D gravity coupled to $C\leq 1$ matter. The operator algebra of the discrete state operators is calculated for the theory with non-vanishing cosmological constant.Comment: 17 page

Pair Interaction Potentials of Colloids by Extrapolation of Confocal Microscopy Measurements of Collective Structure

A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilution to yield an estimate of the pair interaction potential, $U(r)$. We use Monte Carlo (MC) simulation to test and establish our methodology as well as to explore the effects of polydispersity on the accuracy. We use poly-12-hydroxystearic acid-stabilized poly(methyl methacrylate) (PHSA-PMMA) particles dispersed in the solvent dioctyl phthalate (DOP) to test the method and assess its accuracy for three different repulsive systems for which the range has been manipulated by addition of electrolyte.Comment: 35 pages, 14 figure

Duality and replicas for a unitary matrix model

In a generalized Airy matrix model, a power $p$ replaces the cubic term of the Airy model introduced by Kontsevich. The parameter $p$ corresponds to Witten's spin index in the theory of intersection numbers of moduli space of curves. A continuation in $p$ down to $p= -2$ yields a well studied unitary matrix model, which exhibits two different phases in the weak and strong coupling regions, with a third order critical point in-between. The application of duality and replica to the $p$-th Airy model allows one to recover both the weak and strong phases of the unitary model, and to establish some new results for these expansions. Therefore the unitary model is also indirectly a generating function for intersection numbers.Comment: 18 page, add referece

Non-homogenous disks in the chain of matrices

We investigate the generating functions of multi-colored discrete disks with non-homogenous boundary conditions in the context of the Hermitian multi-matrix model where the matrices are coupled in an open chain. We show that the study of the spectral curve of the matrix model allows one to solve a set of loop equations to get a recursive formula computing mixed trace correlation functions to leading order in the large matrix limit.Comment: 25 pages, 4 figure

Large Representation Recurrences in Large N Random Unitary Matrix Models

In a random unitary matrix model at large N, we study the properties of the expectation value of the character of the unitary matrix in the rank k symmetric tensor representation. We address the problem of whether the standard semiclassical technique for solving the model in the large N limit can be applied when the representation is very large, with k of order N. We find that the eigenvalues do indeed localize on an extremum of the effective potential; however, for finite but sufficiently large k/N, it is not possible to replace the discrete eigenvalue density with a continuous one. Nonetheless, the expectation value of the character has a well-defined large N limit, and when the discreteness of the eigenvalues is properly accounted for, it shows an intriguing approximate periodicity as a function of k/N.Comment: 24 pages, 11 figure

Double Field Theory Formulation of Heterotic Strings

We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under O(D,D+n), where n denotes the number of gauge vectors, and n additional coordinates are introduced together with a covariant constraint that locally removes these new coordinates. For the abelian subsector, the action takes the same structural form as for the bosonic string, but based on the enlarged generalized metric, thereby featuring a global O(D,D+n) symmetry. After turning on non-abelian gauge couplings, this global symmetry is broken, but the action can still be written in a fully O(D,D+n) covariant fashion, in analogy to similar constructions in gauged supergravities.Comment: 28 pages, v2: minor changes, version published in JHE

Dual Identities inside the Gluon and the Graviton Scattering Amplitudes

Recently, Bern, Carrasco and Johansson conjectured dual identities inside the gluon tree scattering amplitudes. In this paper, we use the properties of the heterotic string and open string tree scattering amplitudes to refine and derive these dual identities. These identities can be carried over to loop amplitudes using the unitarity method. Furthermore, given the $M$-gluon (as well as gluon-gluino) tree amplitudes, $M$-graviton (as well as graviton-gravitino) tree scattering amplitudes can be written down immediately, avoiding the derivation of Feynman rules and the evaluation of Feynman diagrams for graviton scattering amplitudes.Comment: 43 pages, 3 figures; typos corrected, a few points clarified

Chiral Generations on Intersecting 5-branes in Heterotic String Theory

We show that there exist two 27 and one 27 bar of E6, net one D=4, N=1 chiral matter supermultiplet as zero modes localized on the intersection of two 5-branes in the E8 x E8 heterotic string theory. The smeared intersecting 5-brane solution is used via the standard embedding to construct a heterotic background, which provides, after a compactification of some of the transverse dimensions, a five-dimensional Randall-Sundrum II like brane-world set-up in heterotic string theory. As a by-product, we present a new proof of anomaly cancellation between those from the chiral matter and the anomaly inflow onto the brane without small instanton.Comment: 26 pages, 5 figures; references added, typo correcte

Quantum gravitational contributions to quantum electrodynamics

Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. But that claim has been very controversial with the situation inconclusive. Here I report an analysis (free from earlier controversies) demonstrating that that quantum gravity corrections to quantum electrodynamics have a quadratic energy dependence that result in the reduction of the electric charge at high energies, a result known as asymptotic freedom.Comment: To be published in Nature. 19 pages LaTeX, no figure

Global AdS Picture of 1/2 BPS Wilson Loops

We study the holographic dual string configuration of 1/2 BPS circular Wilson loops in N=4 super Yang-Mills theory by using the global coordinate of AdS. The dual string worldsheet is given by the Poincare disk AdS_2 sitting at a constant global time slice of AdS_5. We also analyze the correlator of two concentric circular Wilson loops from the global AdS perspective and study the phase transition associated with the instability of annulus worldsheet connecting the two Wilson loops.Comment: 14 pages, 3 figures, v2: discussion on two branches corrected, v3: reference adde