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Paul Mansfield

Publications and source records attributed to Paul Mansfield.

At least 19 recordsLinked to original sources
arXiv2021

Effective Lagrangian for Non-Abelian Two-Dimensional Topological Field Theory

We develop a systematic approach to obtain an effective Lagrangian for 2D non-Abelian topological BF theory. A general expression is presented in a diagrammatic representation containing solely scalar fields. Expressions for the SU(2) and SU(3) effective actions are explicitly stated. In the case of SU(2), we show that the effective action can be interpreted as a winding number. By using the SU(2) effective action, the partition function on a sphere for SU(2) Yang-Mills theory is calculated. Moreover, we generalise the theory to include a source term for the gauge field as well as calculate the vacuum expectation value of the Wilson loop based on the effective theory.

hep-th↗
arXiv2021

Producing Liveness: The Trials of Moving Folk Clubs Online During the Global Pandemic

The global pandemic has driven musicians online. We report an ethnographic account of how two traditional folk clubs with little previous interest in digital platforms transitioned to online experiences. They followed very different approaches: one adapted their existing singaround format to video conferencing while the other evolved a weekly community-produced, pre-recorded show that could be watched together. However, despite their successes, participants ultimately remained unable to sing in chorus due to network constraints. We draw on theories of liveness from performance studies to explain our findings, arguing that HCI might orientate itself to online liveness as being co-produced through rich participatory structures that dissolve traditional distinctions between live and recorded and performer and audience. We discuss how participants appropriated existing platforms to achieve this, but these in turn shaped their practices in unforeseen ways. We draw out implications for the design and deployment of future live performance platforms.

cs.HC↗
arXiv2021

Plahte Diagrams for String Scattering Amplitudes

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.

hep-th↗
arXiv2018

Mandelstam formulae for generalised Wilson loops

We derive Mandelstam formulae for two generalisations of the Wilson loop. In these generalisations path-ordering of Lie algebra generators is replaced by an anti-commuting one dimensional field theory along the loop. We extend the calculation to the N=1 super-Wilson loop by introducing a superpartner for the additional field.

hep-th↗
arXiv2018

Intersection of world-lines on curved surfaces and path-ordering of the Wilson loop

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.

hep-th↗
arXiv2016

Entanglement of self interacting scalar fields in an expanding spacetime

We evaluate self-interaction effects on the quantum correlations of field modes of opposite momenta for scalar $λϕ^4$ 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.

hep-th↗
arXiv2014

Delta-function Interactions for the Bosonic and Spinning Strings and the Generation of Abelian Gauge Theory

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.

hep-th↗
arXiv2014

The Fermion Content of the Standard Model

We describe a simple model that automatically generates the sum over gauge group representations and chiralities of a single generation of fermions in the Standard Model, augmented by a sterile neutrino. The model is a modification of the world-line approach to chiral fermions.

hep-ph↗
arXiv2014

QED as the tensionless limit of the spinning string with contact interaction

We outline how QED with spinor matter can be described by the tensionless limit of spinning strings with contact interactions. The strings represent electric lines of force with charges at their ends. The contact interaction is constructed from a delta-function on the world-sheet which, although off-shell, decouples from the world-sheet metric. Integrating out the string degrees of freedom with fixed boundary generates the super-Wilson loop that couples spinor matter to electromagnetism in the world-line formalism. World-sheet and world-line, but not spacetime, supersymmetry underpin the model.

hep-th↗
arXiv2012

Faraday's Lines of Force as Strings: from Gauss' Law to the Arrow of Time

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.

hep-th↗
arXiv2009

Infinite Dimensional Symmetries of Self-Dual Yang-Mills

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.

hep-th↗
arXiv2007

A Modified Borel Summation Technique

We compare and contrast three different perturbative expansions for the quartic anharmonic oscillator wavefunction and apply a modified Borel summation technique to determine the energy eigenvalues. In the first two expansions this provides the energy eigenvalues directly however in the third method we tune the wavefunctions to achieve the correct large x behaviour. This tuning technique allows us to determine the energy eigenvalues up to an arbitrary level of accuracy with remarkable efficiency. We give numerical evidence to explain this behaviour. We also refine the modified Borel summation technique to improve its accuracy. The main sources of error are investigated with reasonable error corrections calculated.

quant-ph↗
arXiv2007

Solving the Anharmonic Oscillator: Tuning the Boundary Condition

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.

quant-ph↗
arXiv2005

The Lagrangian origin of MHV rules

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.

hep-th↗
arXiv2005

Time Evolution in String Field Theory and T-duality

The time evolution operator (Schrödinger 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.

hep-th↗
arXiv2004

Solving the Functional Schroedinger Equation: Yang-Mills String Tension and Surface Critical Scaling

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).

hep-th↗
arXiv2003

The Boundary Weyl Anomaly in the ${\cal N}=4$ SYM/Type IIB Supergravity Correspondence

We give a complete account of the Schrödinger 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.

hep-th↗