arXiv subjects

Hugh Osborn

Publications and source records attributed to Hugh Osborn.

24 records · Page 2Linked to original sources

arXiv2018

Structures on the Conformal Manifold in Six Dimensional Theories

The tensors which may be defined on the conformal manifold for six dimensional CFTs with exactly marginal operators are analysed by considering the response to a Weyl rescaling of the metric in the presence of local couplings. It is shown that there are three symmetric two index tensors only one of which satisfies any positivity conditions. The general results are specialised to the six dimensional conformal theory defined by free two-forms and also to the interacting scalar $ϕ^3$ theory at two loops which preserves conformal invariance to this order. All three two index tensor contributions are present.

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arXiv2016

$C_T$ for Non-unitary CFTs in Higher Dimensions

The coefficient $C_T$ of the conformal energy-momentum tensor two-point function is determined for the non-unitary scalar CFTs with four- and six-derivative kinetic terms. The results match those expected from large-$N$ calculations for the CFTs arising from the $O(N)$ non-linear sigma and Gross-Neveu models in specific even dimensions. $C_T$ is also calculated for the CFT arising from $(n-1)$-form gauge fields with derivatives in $2n+2$ dimensions. Results for $(n-1)$-form theory extended to general dimensions as a non-gauge-invariant CFT are also obtained; the resulting $C_T$ differs from that for the gauge-invariant theory. The construction of conformal primaries by subtracting descendants of lower-dimension primaries is also discussed. For free theories this also leads to an alternative construction of the energy-momentum tensor, which can be quite involved for higher-derivative theories.

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arXiv2016

Scheme Dependence and Multiple Couplings

For theories with multiple couplings the perturbative $β$-functions for scalar, Yukawa couplings are expressible in terms of contributions corresponding to one particle irreducible graphs and also contributions which are one particle reducible depending on the anomalous dimension. Here we discuss redefinitions, or changes of scheme, which preserve this structure. The redefinitions allow for IPR contributions of a specific form, as is necessary to encompass the relation between MS and momentum subtraction renormalisation schemes. Many multiply 1PR terms in the transformed $β$-function are generated but these can all be absorbed into antisymmetric contributions to the anomalous dimensions which are essentially arbitrary and can be discarded. As an illustration the results are applied to the scheme dependence of the anomalous dimension, which determines the $β$-function, for ${\cal N}=1$ supersymmetric scalar fermion theories in four dimensions up to four loops.

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arXiv2015

Diagonal Limit for Conformal Blocks in d Dimensions

Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of 3F2 functions.

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arXiv2003

Local Couplings and Sl(2,R) Invariance for Gauge Theories at One Loop

The response of the one loop effective action for a gauge theory with local couplings $g(x),θ(x)$ under a local Weyl rescaling of the background metric is calculated. Apart from terms which may be removed by local contributions to the effective action the result is compatible with $Sl(2,R)$ symmetry acting on $g,θ$. Two loop effects are also discussed.

hep-th↗

arXiv1999

N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory

The implications of N=1 superconformal symmetry for four dimensional quantum field theories are studied. Superconformal covariant expressions for two and three point functions of quasi-primary superfields of arbitrary spin are found and connected with the operator product expansion. The general formulae are specialised to cases involving a scalar superfield L, which contains global symmetry currents, and the supercurrent, which contains the energy momentum tensor, and the consequences of superconformal Ward identities analysed. The three point function of L is shown to have unique completely antisymmetric or symmetric forms. In the latter case the superspace version of the axial anomaly equation is obtained. The three point function for the supercurrent is shown to have two linearly independent forms. A linear combination of the associated coefficients for the general expression is shown to be related to the scale of the supercurrent two point function through Ward identities. The coefficients are given for the two free field superconformal theories and are also connected with the parameters present in the supercurrent anomaly for supergravity backgrounds. Superconformal invariants, which are possible even in three point functions, are discussed.

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