<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math>-forms on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mi>d</mml:mi></mml:math>-spherical tessellations

Dowker, J. S.

doi:10.1016/j.geomphys.2007.01.001

Cited by 5 publications

(10 citation statements)

References 45 publications

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“…An alternative technique, which avoids the need to sum over classes and angles, is to describe the polytope groups in terms of their integer degrees, as in [13,34] and use a twisted generating function. This is left for another time.…”

Section: Discussionmentioning

confidence: 99%

Analytic torsion on spherical factors and tessellations

Dowker,

Chang

2009

Preprint

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Section: Discussionmentioning

confidence: 99%

Analytic torsion on spherical factors and tessellations

Dowker,

Chang

2009

Preprint

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“…5 The computation is given in [2,1] but I develope a few essentials here. 6 The important fact for the furtherance of the analysis is that B and C have linear eigenvalues, a + 1 + m , m = 0, 1, 2, . .…”

Section: The Calculationmentioning

confidence: 99%

“…The degeneracy is best encoded in a generating function which acts as a squareroot 'heat kernel' and allows the construction of the auxiliary ζ-function, (6), by Mellin transform directly. The details are given in [2] and result in a linear combination of Barnes ζ-functions, ζ d ,…”

Section: The Calculationmentioning

confidence: 99%

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

Dowker

2020

Preprint

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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 → 0 and compared with known results written as alternating sums over scalar values.

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“…propagating) degrees of freedom are represented by co-exact p-forms on M (q p denotes the coupling constant). During the last years several aspects of the topological Casimir effect in p-form Maxwell theory were discussed on different manifolds at zero [45,46,47,48,49,50] and at finite temperature [51,52,53]. However, antisymmetric tensor fields represent just a special class of higher-abelian gauge fields.…”

Section: Introduction and Summary 1motivation And Objectivementioning

confidence: 99%

Aspects of higher-abelian gauge theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops

Kelnhofer

2019

Nuclear Physics B

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Higher-abelian gauge theories associated with Cheeger-Simons differential characters are studied on compact manifolds without boundary. The paper consists of two parts: First the functional integral formulation based on zeta function regularization is revisited and extended in order to provide a general framework for further applications. A field theoretical model -called extended higher-abelian Maxwell theory -is introduced, which is a higher-abelian version of Maxwell theory of electromagnetism extended by a particular topological action. This action is parametrized by two non-dynamical harmonic forms and generalizes the θ-term in usual gauge theories. In the second part the general framework is applied to study the topological Casimir effect in higher-abelian gauge theories at finite temperature at equilibrium. The extended higher-abelian Maxwell theory is discussed in detail and an exact expression for the free energy is derived. A non-trivial topology of the background space-time modifies the spectrum of both the zero-point fluctuations and the occupied states forming the thermal ensemble. The vacuum (Casimir) energy has two contributions: one related to the propagating modes and the second one related to the topologically inequivalent configurations of higher-abelian gauge fields. In the high temperature limit the leading term is of Stefan-Boltzmann type and the topological contributions are suppressed. With a particular choice of parameters extended higher-abelian Maxwell theories of different degrees are shown to be dual. On the n-dimensional torus we provide explicit expressions for the thermodynamic functions in the low-and high temperature regimes, respectively. Finally, the impact of the background topology on the two-point correlation function of a higher-abelian variant of the Polyakov loop operator is analyzed.1 The reviews [2, 3, 4, 5, 6, 7] and the references therein cover also further aspects of the topological Casimir effect. Due to the vast amount of literature we are well aware that our selection may by no means be complete.

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p-forms on d-spherical tessellations

Cited by 5 publications

References 45 publications

Analytic torsion on spherical factors and tessellations

Analytic torsion on spherical factors and tessellations

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

Aspects of higher-abelian gauge theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops

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