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Plahte identities are monodromy relations between open string scattering amplitudes at tree level derived from the Koba-Nielsen formula. We represent these identities by polygons in the complex plane. These diagrams make manifest the appearance of sign changes and singularities in the analytic continuation of amplitudes. They provide a geometric expression of the KLT relations between closed and open string amplitudes. We also connect the diagrams to the BCFW on-shell recursion relations and generalise them to complex momenta resulting in a relation between the complex phases of partial amplitudes., 29 pages, 14 figures

We study contact interactions for long world-lines on a curved surface, focusing on the average number of times two world-lines intersect as a function of their end-points. The result can be used to extend the concept of path-ordering, as employed in the Wilson loop, from a closed curve into the interior of a surface spanning the curve. Taking this surface as a string world-sheet yields a generalisation of the string contact interaction previously used to represent the Abelian Wilson loop as a tensionless string. We also describe a supersymmetric generalisation., 28 pages, 2 figures

We evaluate self-interaction effects on the quantum correlations of field modes of opposite momenta for scalar $\lambda \phi^4$ theory in a two-dimensional asymptotically flat Robertson-Walker spacetime. Such correlations are encoded both in the von-Neumann entropy defined through the reduced density matrix in one of the modes and in the covariance expressed in terms of the expectation value of the number operators for each mode in the evolved state. The entanglement between field modes carries information about the underlying spacetime evolution., Comment: 6 pages, 3 figuras

We investigate the teleportation of a qubit between two observers Alice and Bob in an asymptotically flat Robertson-Walker expanding spacetime. We use scalar or fermionic field modes inside Alice's and Bob's ideal cavities and show the degradation of the teleportation quality, as measured by the fidelity, through a mechanism governed by spacetime expansion. This reduction is demonstrated to increase with the rapidity of the expansion and to be highly sensitive to the coupling of the field to spacetime curvature, becoming considerably stronger as it reduces from conformal to minimal. We explore a perturbative approach in the cosmological parameters to compute the Bogoliubov coefficients in order to evaluate and compare the fidelity degradation of fermionic and scalar fields.

Strings propagating in AdS_{D+1} are made Weyl invariant to leading order in large D by a ghost-matter coupling that preserves the Poincare symmetry of the boundary., LaTeX, 5pp, no figures

Using Supergravity on $AdS_7\times S^4$ we calculate the bulk one-loop contribution to the conformal anomaly of the (2,0) theory describing $N$ coincident M5 branes. When this is added to the tree-level result, and an additional subleading order contribution calculated by Tseytlin, it gives an expression for the anomaly that interpolates correctly between the large $N$ theory and the free (2,0) tensor theory corresponding to N=1. Thus we can argue that we have identified the exact $N$-dependence of the anomaly, which may have a simple protected form valid away from the large $N$ limit., Comment: LaTeX, 9 pages

We construct contact interactions for bosonic and spinning strings. In the tensionless limit of the spinning string this reproduces the super-Wilson loop that couples spinor matter to Abelian gauge theory. Adding boundary terms that quantise the motion of charges results in a string model equivalent to spinor QED. The strings represent lines of electric flux connected to the charges. The purely bosonic model is spoilt by divergences that are excluded from the spinning model by world-sheet supersymmetry, indicating a preference for spinor matter., Comment: 68 pages, 9 figures Minor corrections to Appendix C

An infra-red fixed point of ${\mathcal N}=1$ super-Yang-Mills theory is believed to be dual to a solution of five-dimensional gauged ${\mathcal N}=8$ supergravity. We test this conjecture at next to leading order in the large $N$ expansion by computing bulk one-loop corrections to the anomaly coefficient $a-c$. The one-loop corrections are non-zero for all values of the bulk mass, and not just special ones as claimed in previous work.

We test the Maldacena conjecture for type IIB String Theory/ N=4 Yang-Mills by calculating the one-loop corrections in the bulk theory to the Weyl anomaly of the boundary CFT when the latter is coupled to a Ricci-flat metric. The contributions cancel within each supermultiplet, in agreement with the conjecture., Comment: LaTeX, 8 pages. Explanatory note added about boundary conditions. Typographical errors in table 2 corrected

We discuss the functional representation of fermions, and obtain exact expressions for wave-functionals of the Schwinger model. Known features of the model such as bosonization and the vacuum angle arise naturally. Contrary to expectations, the vacuum wave-functional does not simplify at large distances, but it may be reconstructed as a large time limit of the corresponding Schrodinger functional, which has an expansion in local terms. The functional Schrodinger equation reduces to a set of algebraic equations for the coefficients of these terms. These ideas generalize to a numerical approach to QCD in higher dimensions., LaTeX, 19 pages

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schr\"odinger equation from which the expansion coefficents can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counter-terms. We also describe an approximate simplification that occurs for the Sine-Gordon and Sinh-Gordon vacuum functionals., Comment: 21 pages, LaTeX, 8 figures

We show that the one-instanton sector moduli-space divergence of the O (3) sigma model leads to an unacceptable dependence of Green functions on the arbitrary way that the field is split into a quantum fluctuation about a classical background. In particular the rotational symmetry of the model is spoilt. Since the divergence is associated with the degeneration of field configurations to those of the zero-instanton sector this arbitrariness may be cancelled by modifying the zero-instanton functional integral. We explicitly construct this modification.

For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional of a massive quantum field theory can be expanded in terms of local functionals satisfying a form of the Schrodinger equation, the principal ingredient of which is a regulated functional Laplacian. We construct to leading order a Laplacian for the O(N) sigma-model that acts on such local functionals. It is determined by imposing rotational invariance in the internal space together with closure of the Poincare algebra.

We reformulate classical electromagnetism as the statistical mechanics of lines of electric flux with dynamics described by the string action in four dimensions. The retarded solution to Maxwell's equations emerges naturally as an average over a microcanonical ensemble of these lines of force at high temperature., 18 pages, some typos corrected and explanations expanded

We construct infinite-dimensional symmetries of the two dimensional equation which results from the dimensional reduction of the self-duality condition in (2, 2) signature space-time. These are symmetries of the dimensionally reduced Chalmers-Siegel action and so hold off-shell., Comment: Consists of 9 pages. Version 2: Further emphasis made on various points and some equations added, some references added and typing errors corrected

We construct symmetries of the Chalmers-Siegel action describing self-dual Yang-Mills theory using a canonical transformation to a free theory. The symmetries form an infinite dimensional Lie algebra in the group algebra of isometries., 29 pages, 8 figures

The canonical transformation that maps light-cone Yang-Mills theory to a Lagrangian description of the MHV rules is non-local, consequently the two sets of fields do not necessarily generate the same S-matrix. By deriving a new recursion relation for the canonical transformation expansion coefficients, we find a direct map between these coefficients and tree level light-cone diagrams. We use this to show that, at least up to one-loop with dimensionally regularised MHV vertices, the only difference is the omission of the one-loop amplitudes in which all gluons have positive helicity., 36 pages, JHEP3 style, published version, discussions on rational parts and supersymmetry added

The usual Toda theories based on Lie algebras have an inadequate spectrum of primary fields to describe the minimal models. We remedy this by generalising them to a class of new, conformally invariant, lagrangian field theories. We obtain operator solutions to the Heisenberg equations of motion that provide explicit decompositions of primary fields into conformal blocks. Their fusion rules follow the Clebsch-Gordan series for combining the representations of the Lie algebra with which they are labelled. For the case of A n the cyclic symmetry of the extended Dynkin diagram leads to a picture-changing operation that converts physically equivalent primary fields into each other, and results in the closure of a subalgebra of the primary fields, thus providing a lagrangian formulation of the minimal models and their generalisations.

We consider the quantization of non-affine Toda field theories in the light-cone and lattice formalisms. The vertex operators are constructed and their braiding is found to be a consequence of the fundamental commutation relations satisfied by the monodromy matrix. For certain values of the coupling, which correspond to the minimal models, the truncation of the operator algebra is closely tied to the quantum group structure.

We outline a remarkably efficient method for generating solutions to quantum anharmonic oscillators with an x^{2M} potential. We solve the Schroedinger equation in terms of a free parameter which is then tuned to give the correct boundary condition by generating a power series expansion of the wavefunction in x and applying a modified Borel resummation technique to obtain the large x behaviour. The process allows us to calculate energy eigenvalues to an arbitrary level of accuracy. High degrees of precision are achieved even with modest computing power. Our technique extends to all levels of excitation and produces the correct solution to the double well oscillators even though they are dominated by non-perturbative effects., 10 pages, 4 figures. V3 contains minor changes made before final publication

We demonstrate that the canonical change of variables that yields the MHV lagrangian, also provides contributions to scattering amplitudes that evade the equivalence theorem. This `ET evasion' in particular provides the tree-level (-++) amplitude, which is non-vanishing off shell, or on shell with complex momenta or in (2,2) signature, and is missing from the MHV (aka CSW) rules. At one loop there are ET-evading diagrammatic contributions to the amplitudes with all positive helicities. We supply the necessary regularisation in order to define these contributions (and quantum MHV methods in general) by starting from the light-cone Yang-Mills lagrangian in D dimensions and making a canonical change of variables for all D-2 transverse degrees of freedom of the gauge field. In this way, we obtain dimensionally regularised three- and four-point MHV amplitudes. Returning to the one-loop (++++) amplitude, we demonstrate that its quadruple cut coincides with the known result, and show how the original light-cone Yang-Mills contributions can in fact be algebraically recovered from the ET-evading contributions. We conclude that the canonical MHV lagrangian, supplemented with the extra terms brought to correlation functions by the non-linear field transformation, provide contributions which are just a rearrangement of those from light-cone Yang-Mills and thus coincide with them both on and off shell., Comment: 32 pages, 9 figures. v2: corrects typos and Fig. 8; adds further citations and acknowledgements

We construct a canonical transformation that takes the usual Yang-Mills action into one whose Feynman diagram expansion generates the MHV rules. The off-shell continuation appears as a natural consequence of using light-front quantisation surfaces. The construction extends to include massless fermions.

The time evolution operator (Schr\"odinger functional) of quantum field theory can be expressed in terms of first quantised particles moving on the orbifold $S^1/Z_2$. We give a graphical derivation of this that generalises to second quantised string theory. T-duality then relates evolution through time t with evolution through 1/t and an interchange of string fields and backgrounds., Comment: 11 Pages, 10 .eps figures; revised version includes discussion of BRST symmetry

Motivated by a heuristic model of the Yang-Mills vacuum that accurately describes the string-tension in three dimensions we develop a systematic method for solving the functional Schroedinger equation in a derivative expansion. This is applied to the Landau-Ginzburg theory that describes surface critical scaling in the Ising model. A Renormalisation Group analysis of the solution yields the value eta=1.003 for the anomalous dimension of the correlation function of surface spins which compares well with the exact result of unity implied by Onsager's solution. We give the expansion of the corresponding beta-function to 17-th order (which receives contributions from up to 17-loops in conventional perturbation theory)., Comment: 31 pages, 7 Postscript figures

We give a complete account of the Schr\"odinger representation approach to the calculation of the Weyl anomaly of ${\cal N}=4$ SYM from the AdS/CFT correspondence. On the AdS side, the $1/N^2$ correction to the leading order result receives contributions from all the fields of Type IIB Supergravity, the contribution of each field being given by a universal formula. The correct matching with the CFT result is thus a highly non-trivial test of the correspondence., Comment: 30 pages

We compute the complete bulk one-loop contribution to the Weyl anomaly of the boundary theory for IIB Supergravity compactified on $ AdS_5\times S^5$. The result, that $\delta {\cal A}=(E+I)/(2\pi^2)$, reproduces the subleading term in the exact expression ${\cal A}=-(N^2-1)(E+I)/(2\pi^2)$ for the Weyl anomaly of ${\cal N}=4$ Super-Yang-Mills theory, confirming the Maldacena conjecture. The anomaly receives contributions from all multiplets casting doubt on the possibility of describing the boundary theory beyond leading order in $N$ by a consistent truncation to the `massless' multiplet of IIB Supergravity., Comment: LaTeX, 6pp

We compute the conformal anomalies of boundary CFTs for scalar and fermionic fields propagating in AdS spacetime at one-loop. The coefficients are quantized, with values related to the mass-spectra for Kaluza-Klein compactifications of Supergravity on AdS5xS5 and AdS7xS4. Our approach interprets the boundary partition function of fields propagating on AdS spacetime in terms of wave-functionals that satisfy the functional Schrodinger equation., LaTeX, 28 pages, 3 figures, minor corrections, reference added

We describe a general method for calculating the infra-red limit of physical quantities in unitary quantum field theories. Using analyticity of Green functions in a complex scale parameter, the infra-red limit is expressed as a contour integral entirely in the ultra-violet region. The infra-red limit is shown to be the limit of the Borel transform of the physical quantity. The method is illustrated by calculating the central charge of the perturbed unitary minimal models and the critical exponents of phi^4 theory in three dimensions. We obtain approximate values for the central charge which are very close to the exact values using only a one loop perturbative calculation. For phi^4 theory we obtain estimates which are within the errors of other more elaborate approaches., Comment: 32 pages, 8 figures, Journal reference added and 3 new references

We illustrate a method for improving Renormalisation Group improved perturbation theory by calculating the infrared central charge of a perturbed conformal field theory. The additional input is a dispersion relation that exploits analyticity of the energy-momentum tensor correlator., Comment: 9 pages, 3 Postscript figures, uses AMS-LaTeX

We show how to compute vacuum expectation values from derivative expansions of the vacuum wave functional. Such expansions appear to be valid only for slowly varying fields, but by exploiting analyticity in a complex scale parameter we can reconstruct the contribution from rapidly varying fields., 39 pages, 16 figures, LaTeX2e using package graphicx

We analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov`s non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville field imply that the metric is discontinuous as the boundary is approached. We consider the semi-classical limit and argue how it singles out the free boundary conditions on the Liouville field. We define the open string susceptibility, the anomalous gravitational scaling dimensions and a new Yang-Mills Feynman mass critical exponent., Comment: 32 pages, latex, no figures. Text reorganised. A note, a new subsection, 2 apendices and 3 references added. Version to be published in Nuclear Physics B

For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional can be expanded as a sum of local functionals, however this does not satisfy the obvious form of the Schr\"odinger equation. For $\varphi^4$ theory we construct the appropriate equation that this expansion does satisfy. This reduces the eigenvalue problem for the Hamiltonian to a set of algebraic equations. We suggest two approaches to their solution. The first is equivalent to the usual semi-classical expansion whilst the other is a new scheme that may also be applied to theories that are classically massless but in which mass is generated quantum mechanically., Comment: 11 pages, latex

For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional can be expanded as a sum of local functionals. For Yang-Mills theory the leading term in the expansion dominates large distance effects and leads to an area law for the Wilson loop. However, this expansion cannot be expected to converge for fields that vary more rapidly. By studying the analyticity of the vacuum functional under scale transformations we show how to re-sum this series so as to reconstruct the vacuum functional for arbitrary fields., Comment: 7 pages, latex

We solve Schr\"odinger's equation for the ground-state of {\it four}-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading order approximation are reduced to a calculation in {\it two}-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass-scale goes to zero., Comment: 18 pages, DTP-93-43 [original version corrupted by mailer]

Many field theories of physical interest have configuration spaces consisting of disconnected components. Quantum mechanical amplitudes are then expressed as sums over these components. We use the Faddeev-Popov approach to write the terms in this topological expansion as moduli space integrals. A cut-off is needed when these integrals diverge. This introduces a dependence on the choice of parametrisation of configuration space which must be removed if the theory is to make physical sense. For theories that have a local symmetry this also leads to a breakdown in BRST invariance. We discuss in detail the cases of Bosonic Strings and Yang-Mills theory, showing how this arbitrariness may be removed by the use of a counter-term in the former case, and by compactification on $S\sp 4$ in the latter., Comment: 19 pages, DTP-93-45 [original version corrupted by mailer]

Timelike T-duality of string theory appears as a symmetry of time evolution in string field theory, exchanging evolution through times t and 1/t, and exchanging boundary states with backgrounds. This is demonstrated by constructing the string field Schrodinger functional, the generator of time evolution, based on Feynman diagram arguments and in analogy with quantum field theory. There, the functional can be described using only properties of first quantised particles on a timelike orbifold. Using new sewing rules applicable to both open and closed strings we generalise this approach to bosonic string theory and express the string field Schrodinger functional in terms of strings on S^1/Z_2., Comment: 49 pages, 39 .eps figures. Replaced with published version

The Toda field is a multicomponent field in two space-time dimensions satisfying a generalisation of the Liouville equation ϖ2ϕ + exp ϕ = 0. We define the quantum field theory, and solve for the fields in terms of their initial values on a forward light-cone, demonstrating that our solution is regular. We give an explicit result for the Liouville equation which is the quantum version of the well-known classical solution. We also discuss the energy-momentum spectrum, and the conformal properties of the theory.

We show that the amplitude for N open and M closed strings on a disc may be written as a sum of amplitudes with N+2M open strings, with appropriate orderings and phases. This form may be simplified using Plahte identities which relate open string amplitudes with different orderings. We demonstrate that these also hold for type I superstrings.

The measure for integrating over instanton degrees of freedom in the euclidean functional integrals for non-abelian gauge theories is discussed within the context of the construction of Atiyah, Drinfeld, Hitchin and Manin, and evaluated for the SU(2) two-instanton solution of 't Hooft.

We do mean-field perturbation theory for U(1) lattice gauge theory in the axial gauge, and evaluate corrections from fluctuations up to fourth order for the free energy and plaquette energy. Comparing with similar results previously obtained in the Feynman gauge we find, to those orders studied, a gauge dependence of the size of the first correction term neglected with one exception. This gauge dependence decreases rapidly as the order of the approximation is increased. To any finite order, results in axial gauge are better approximations than results in the Feynman gauge. We speculate why. Assuming it to be generally true, we evaluate the first correction beyond the one-loop mean-field approximation to the free energy of SU(2) gauge theory with Wilson action in the axial gauge. This correction brings the mean-field result very close to Monte Carlo results for β > 1.6. It also makes the mean-field result identical, within a narrow margin, to ressumed strong coupling results in the interval 1.6 < β < 2.4, thus showing the absence of a phase transition. For both groups studied, we find that the asymptotic series of mean-field perturbation theory give much better approximations than do ordinary weak coupling series.

The Toda field is a multicomponent field in two space-time dimensions, satisfying a generalisation of the Liouville equation ∂2φ + exp φ = 0. We define and solve non-perturbatively a quantum Toda field theory and its classical limit. Our technique generates an infinite number of conservation laws. By restricting the fields to one dimension we also solve the quantum mechanics and the classical mechanics of the Toda lattice.

Recently, Zamolodchikov has shown that certain minimal conformal field theories preserve their integrability away from the critical point. In an attempt to understand these results we consider a class of integrable field theories, namely two-dimensional Toda field theories. It is found that for particular values of the coupling constant these theories describe minimal models, in particular the Ising model can be described both by an E 8 and A 1 Toda field theory. The affine versions of these theories then represent the model away from criticality, for instance the Ising model in a magnetic field is described by the affine E 8 Toda field theory, whereas the affine A 1 theory describes a thermal perturbation. This generalizes to a deformation of all minimal models.