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Paul Mansfield

Publications and source records attributed to Paul Mansfield.

At least 37 records · Page 2Linked to original sources
arXiv2003

Order $1/N^2$ test of the Maldacena conjecture II: the full bulk one-loop contribution to the boundary Weyl anomaly

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 $δ{\cal A}=(E+I)/(2π^2)$, reproduces the subleading term in the exact expression ${\cal A}=-(N^2-1)(E+I)/(2π^2)$ 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.

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arXiv2003

Order ${\bf 1/N^3}$ corrections to the conformal anomaly of the (2,0) theory in six dimensions

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.

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arXiv2001

The critical dimension of bosonic string theory in AdS space-time

The Polyakov bosonic string is quantised in Euclidean Anti-de Sitter space-time using functional methods. Regularisation of the functional determinants using both heat-kernel and zeta function techniques shows that the AdS_{D+1} string reduces to the Liouville field theory, as in the flat space-time case. A Feynman graph expansion is used to evaluate (approximately) the coefficient multiplying the Liouville action; this then gives the critical dimension for this space-time as 22 (that is, 21 flat directions plus one radial direction).

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arXiv2001

Test of gauged N=8 SUGRA / N=1 SYM duality at sub-leading order

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.

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arXiv2000

Calculating the infra-red limit of quantum field theory using analyticity of correlation functions

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.

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arXiv1999

The Schrodinger Representation for Fermions and a Local Expansion of the Schwinger Model

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.

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arXiv1999

One-loop Conformal Anomalies From AdS/CFT in the Schrodinger Representation

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.

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arXiv1998

Yang-Mills beta-function from a large-distance expansion of the Schroedinger functional

For slowly varying fields the Yang-Mills Schroedinger functional can be expanded in terms of local functionals. We show how analyticity in a complex scale parameter enables the Schroedinger functional for arbitrarily varying fields to be reconstructed from this expansion. We also construct the form of the Schroedinger equation that determines the coefficients. Solving this in powers of the coupling reproduces the results of the `standard' perturbative solution of the functional Schroedinger equation which we also describe. In particular the usual result for the beta-function is obtained illustrating how analyticity enables the effects of rapidly varying fields to be computed from the behaviour of slowly varying ones.

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arXiv1997

Short Distance Properties from Large Distance Behaviour

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 Schrödinger 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.

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arXiv1996

Boundary conformal field theories on random surfaces and the non-critical open string

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.

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arXiv1996

A Large Distance Expansion for Quantum Field Theory

Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the Hamiltonian to be reduced to algebraic equations. Applied to Yang-Mills theory this expansion leads to a confining force between quarks.

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arXiv1995

The O(N) sigma-model Laplacian

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 Schrödinger 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 Poincaré algebra.

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arXiv1995

Reconstructing the Vacuum Functional of Yang-Mills from its Large Distance Behaviour

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.

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arXiv1995

The Vacuum Functional at Large Distances

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 Schrödinger equation. For $φ^4$ 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.

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