John F. Wheater

D-brane recoil and logarithmic operators

Abstract We construct the pair of logarithmic operators associated with the recoil of a D -brane. This construction establishes a connection between a translation in time and a world-sheet rescaling. The problem of measuring the centre of mass coordinate of the D -brane is considered and the relation between the string uncertainty principle and the logarithmic operators is discussed.

Convergent Yang-Mills Matrix Theories

We consider the partition function and correlation functions in the bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. In the supersymmetric case, we show that the partition function converges when D = 4,6 and 10, and that correlation functions of degree k < kc = 2(D−3) are convergent independently of the group. In the bosonic case we show that the partition function is convergent when D ≥ Dc, and that correlation functions of degree k < kc are convergent, and calculate Dc and kc for each group, thus extending our previous results for SU(N). As a special case these results establish that the partition function and a set of correlation functions in the IKKT IIB string matrix model are convergent.

Boundary logarithmic conformal field theory

Abstract We discuss the effect of boundaries in boundary logarithmic conformal field theory and show, with reference to both c =−2 and c =0 models, how they produce new features even in bulk correlation functions which are not present in the corresponding models without boundaries. We show how Cardys relation between boundary states and bulk quantities is modified.

Random surfaces: from polymer membranes to strings

I review the state of knowledge about random surface ensembles in continuous embedding spaces and their possible role in defining strings in arbitrary dimensions. The application of rigorous statistical mechanics, approximate calculation and numerical simulation is described.

Electroweak radiative corrections to neutrino and electron scattering and the value of sin2θw

Abstract We describe in detail the calculation of all first-order electroweak radiative corrections to total and differential neutrino cross sections and to the parity-violating asymmetry in ed scattering. We find that leading log approximations agree well with our exact result for the shape, but not necessarily the magnitude, of the corrections to d σ ν, ν / d γ except for γ → 1. Corrections to total neutrino cross sections have also been calculated by Marciano and Sirlin; our results agree with theirs. The corrections to sin 2 θ w are experiment dependent. If sin 2 θ w is defined in the MS scheme at a scale M w , they reduce the average value found from the ratio of charged to neutral current neutrino scattering by 0.012 to 0.215 ± 0.015. They reduce the value obatained from the Paschos Wolfenstein relation by 0.008 to 0.221 ± 0.014. In ed scattering they reduce the value by 0.008 to 0.215 ± 0.015. Using a corrected value of 0.215 ± 0.015 and the first-order corrections to the mass formulae, the SU(2) × U(1) predictions for the vector boson masses are M w = 83.1 −2.8 +3.1 rmGeV and M z = 93.8 −2.2 +2.5 GeV, about five GeV larger than obtained from the lowest order analysis.

The Spectral Dimension of Generic Trees

Abstract We define generic ensembles of infinite trees. These are limits as N→∞ of ensembles of finite trees of fixed size N, defined in terms of a set of branching weights. Among these ensembles are those supported on trees with vertices of a uniformly bounded order. The associated probability measures are supported on trees with a single spine and Hausdorff dimension dh=2. Our main result is that the spectral dimension of the ensemble average is ds=4/3, and that the critical exponent of the mass, defined as the exponential decay rate of the two-point function along the spine, is 1/3.

THE SPECTRAL DIMENSION OF THE BRANCHED POLYMER PHASE OF TWO-DIMENSIONAL QUANTUM GRAVITY

Abstract The metric of two-dimensional quantum gravity interacting with conformal matter is believed to collapse to a branched polymer metric when the central charge c > 1. We show analytically that the spectral dimension, ds, of such a branched polymer phase is 4 3 . This is in good agreement with numerical simulations for large c.

Modular transformation and boundary states in logarithmic conformal field theory

Abstract We study the c =−2 model of logarithmic conformal field theory in the presence of a boundary using symplectic fermions. We find boundary states with consistent modular properties. A peculiar feature of this model is that the vacuum representation corresponding to the identity operator is a sub-representation of a “reducible but indecomposable” larger representation. This leads to unusual properties, such as the failure of the Verlinde formula. Despite such complexities in the structure of modules, our results suggest that logarithmic conformal field theories admit bona fide boundary states.

Random walks on combs

We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds, we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.

The crumpling transition of crystalline random surfaces

We investigate the crumpling transition in two different models of crystalline random surfaces with extrinsic curvature which have recently caused some confusion and find that many of the results previously obtained are erroneous. Using the Fourier acceleration technique to ameliorate critical slowing down problems we have made numerical simulations of surfaces of up to 1282 points embedded in three dimensions. The first model, which has a non-compact lattice version of the extrinsic curvature, suffers from a sickness in the non-crumpled phase which is a lattice artefact; it is smooth in one intrinsic direction and folded up on the scale of the lattice spacing in the other, so we call this phase corrugated. The crumpling transition is continuous, having a diverging persistence length with critical exponent v = 1.15 ± 0.15 and a cusp in the specific heat indicating that α ⩽ 0. The second model, in which the extrinsic curvature depends upon the cosine of the angle between normals of adjacent triangles, also has a continuous transition with v = 0.94 ± 0.20 and α = 0.53 ± 0.15. Just beyond the crumpling transition, the smooth phase is found to have Hausdorff dimension dH < 2.14 at two standard deviations and so we conclude that dH = 2 throughout this phase. A study of the correlation functions shows that, in the crumpled phase, the system is apparently described by a very simple gaussian action. If true, this result could have important implications which we discuss briefly.