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J. S. Dowker

Publications and source records attributed to J. S. Dowker.

At least 37 records · Page 2Linked to original sources
arXiv2022

$C_T$ for monodromy defects of fields on odd dimensional spheres for higher derivative propagation

The central charge $C_T$ is computed for scalar and Dirac fields propagating according to GJMS-type kinetic operators acting on odd $d$-dimensional spheres in the presence of a spherical monodromy. The relation of $C_T$ to the derivatives of the free energy on the conically deformed sphere via the Perlmutter factor leads to a numerical quadrature. The variation of $C_T$ with the monodromy flux, $δ$, displays sign changes, exactly as in even dimensions. Closed forms for $C_T$ are derived when $δ$ equals 0 or 1/2 with the derivative order either even or odd and shown to agree with existing, even $d$ expressions. The infinite $d$ limits are also derived in these special cases.

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arXiv2022

Entanglement entropy and $C_T$ for monodromy defects of fields on odd-dimensional spheres

The effect of a spherical monodromy defect on the entanglement entropy and central charge $C_T$ of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter, $δ$, with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the $Z_2$ monodromy ($δ=1/2$) yielding an explicit $d\to\infty$ limit, $C_T\to -6/π$

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arXiv2022

Renyi entropy for monodromy defects of higher derivative free fields on even-dimensional spheres

Explicit polynomial forms for Rényi and entanglement entropies are given on even --dimensional spheres which possess a codimension--2 U(1) monodromy defect. Free scalar and Dirac fields are treated and higher-derivative propagation operators employed. The central charge, $C_T$, is also calculated. Comparison with existing results is made and it is shown how these can be obtained from the values here.

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arXiv2022

Renyi entropy for spherical monodromy of free scalar fields in even dimensions

The effect of a co--dimension--2 spherical monodromy defect on the free--field theory of a conformal scalar is investigated. The conformal anomaly is computed (in two ways) and thence the Rényi and entanglement entropies. The $C_T$ central charge is found to be negative for a range of monodromy flux.The calculations are pursued for any even dimensional sphere. A Possible conflict with existing results is raised.

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arXiv2021

Effective actions on finite cylinders

Some free--field spectral problems on a generalised cylinder are revisited. In two dimensions, conformal scalar effective actions for various boundary conditions are written in elliptic function terms and some special values given. Fermions are then discussed in arbitrary dimensions and an analysis of the most general local (`bag') boundary conditions is given leading to an intrinsic formula for the eigenvalues which interpolate between Neveu--Schwarz and Ramond. This is used to give reasonably explicit expressions for the effective action and other values of the zeta function. It is shown that these boundary conditions are transferred as a chemical potential to the boundary spectral problem. The existence of real exponential eigenmodes along the cylinder is pointed out and a curious asymmetry between the positive and negative Dirac spectra uncovered for large cylinder length.

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arXiv2021

Casimir Domains on a sphere

A Casimir--type analysis of the effect of dividing the two--sphere by several lines of latitude is done for conformally invariant Dirichlet and Neumann scalars and for spinors. An effective action combination is shown to have minima for symmetrical arrangements of the circles. For a domain of two caps and a slice, the Dirichlet slice expands to fill the whole sphere while the Neumann one adjusts to an angular separation of 57.92 degrees. The fermion expression is written in terms of the Weber class function, $\gf$, and a connection is noted with an earlier calculation of twisted scalar effective actions on the tetrahedron.

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arXiv2021

Remarks on spherical monodromy defects for free scalar fields

The computation of the effect of a simple monodromy defect in the case of a sphere with twisted boundary conditions is revisited and streamlined using earlier calculations for a similar system. Compact and explicit expressions are found for arbitrary integer dimensions. Comments on other work are made.

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arXiv2020

Conformal anomalies for higher derivative free critical p-forms on even spheres

The conformal anomaly is computed on even $d$--spheres for a $p$--form propagating according to the Branson--Gover higher derivative, conformally covariant operators. The system is set up on a $q$--deformed sphere and the conformal anomaly is computed as a rational function of the derivative order, $2k$, and of $q$. The anomaly is shown to be an extremum at the round sphere ($q=1$) only for $k<d/2$. At these integer values, therefore, the entanglement entropy is minus the conformal anomaly, as usual. The unconstrained $p$--form conformal anomaly on the full sphere is shown to be given by an integral over the Plancherel measure for a coexact form on hyperbolic space in one dimension higher.A natural ghost sum is constructed and leads to quantities which, for critical forms, i.e. when $2k=d-2p$, are, remarkably, a simple combination of standard quantities, for usual second order, $k=1$, propagation, when these are available. Our values coincide with a recent hyperbolic computation of David and Mukherjee.Values are suggested for the Casimir energy on the Einstein cylinder from the behaviour of the conformal anomaly as $q\to0$ and compared with known results written as alternating sums over scalar values.

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arXiv2018

On $a$-$F$ dimensional interpolation

A dimensional interpolation between the free energy and conformal anomaly on spheres is derived for free scalar and spinor fields on the basis of standard field theory. The regularisation used is an extension of one by Candelas and Weinberg. It yields a (known) simple integral which is shown to be identical to the interpolations introduced by Giombi and Klebanov using earlier AdS/CFT results. The extension to GJMS--type higher derivatives is made with a hint of a possible, kinematic resolution of the non--minimal Type-B mismatch being presented. Another form of the sphere conformal anomaly is given.

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arXiv2017

a-F interpolation with boundary

A recent derivation of the interpolation between the free energy and conformal anomaly for free fields on spheres is generalised to hemispheres with Neumann (N) and Dirichlet (D) conditions at the rim for GJMS scalar fields. It is shown that the N minus D interpolation is minus a quarter of that for a higher derivative fermion on the spherical rim. In particular, since, for ordinary bosons k=1, the related fermion is irregular propagating according to a second order (pseudo) operator. (2k is the derivative order in the equation of motion.) It is suggested that the relation has a role to play in the Type--B AdS/CFT mismatch. The DN boundary value problem is enlarged upon in the context of Branson and Gover's construction of the D to N operator. Contact is made with a result of Park and Wojciechowski which is then related to a duality relation of Barvinsky and Nesterov.

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arXiv2017

Renyi entropies and C_T for higher derivative free scalars and spinors on even spheres

General expressions for the Rényi entropies and central charges for higher derivative free spinors and scalars on even spheres are obtained using a direct spectral method on a compact lune division of the sphere. Formulae and numbers are rapidly obtained for any dimension and order of derivative. The relation between the conformal anomaly and the hyperbolic free energy is briefly explored using standard expansions. A field theoretic derivation of the central charge formula for higher derivative scalars in any (even) dimension, given by Osborn and Stergiou and by Gliozzi {\it et al}, is thereby provided. The corresponding extension to spinors is made. Generalised Bernoulli polynomials play an important technical role.

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arXiv2017

Renyi entropy and C_T for p-forms on even spheres

Renyi entropy and central charge, $C_T$, are calculated for a coexact p--form on an even sphere with particular reference to the conformally invariant case. It is shown, for example, that the entanglement entropy is minus the standard conformal anomaly with no `shift' being required. The shift necessary for a conformal p--form, when using a hyperbolic technique, is predicted, on a numerical basis, to be (minus) the entanglement entropy of a conformal (p-1)-form. The central charges agree numerically with a general formula of Buchel {\it et al}.

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arXiv2016

Revivals and Casimir energy for a free Maxwell field (spin-1 singleton) on R x S^d for odd d

Earlier work on quantum revivals is extended to Maxwell fields (aka spin-one singletons). An evaluation of the Casimir energy on the generalised Einstein universe is also done to illustrate the utility of the Barnes zeta--function and generalised Bernoulli polynomials. Contact is made with some recent calculations in AdS/CFT. In particular. higher order singletons are considered with the Casimir energy being a polynomial in the order.

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arXiv2016

Quantum revivals in free field CFT

A commentary is made on the recent work by Cardy, ArXiv:1603. 08267, on quantum revivals and higher dimensional CFT. The actual expressions used here are those derived some time ago. The calculation is extended to fermion fields for which the power spectrum involves the odd divisor function. Comments are made on the equivalence of operator counting and eigenvalue methods, which is quickly verified. An explanation of the rational revivals for odd spheres is given in terms of wrongly quantised fields.

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arXiv2016

Charged Renyi entropies for free scalar fields

I first calculate the charged spherical Renyi entropy by a numerical method that does not require knowledge of any eigenvalue degeneracies, and applies to all odd dimensions. An image method is used to relate the full sphere values to those for an integer covering, n. It is shown to be equivalent to a `transformation' property of the zeta--function. The infinite limit is explicitly constructed analytically and a relation deduced between the limits of corner coefficients and the effective action (free energy) which generalises, for free fields, a result of Bueno, Myers and Witczak--Krempa and Elvang and Hadjiantonis to any dimension. Finally, the known polynomial expressions for the Renyi entropy on even spheres at zero chemical potential are re--derived in a different form and a simple formula for the conformal anomaly given purely in terms of central factorials is obtained.

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arXiv2015

Conformal weights of charged Renyi entropy twist operators for free scalar fields

I compute the conformal weights of the twist operators of free scalar fields for charged Rényi entropy in both odd and even dimensions. Explicit expressions can be found, in odd dimensions as a function of the chemical potential in the absence of a conical singularity and thence by images for all integer coverings. This method, developed some time ago, is equivalent, in results, to the replica technique. A review is given. The same method applies for even dimensions but a general form is more immediately available. For no chemical potential, the the closed form in the covering order is written in an alternative way related to old trigonometric sums. Some derivatives are obtained. An analytical proof is given of a conjecture made by Bueno, Myers and Witczac--Krempa regarding the relation between the conformal weights and a corner coefficient (a universal quantity) in the Rényi entropy.

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