Reidemeister torsion and the laplacian on lens spaces

Ray, Daniel

doi:10.1016/0001-8708(70)90018-6

Cited by 76 publications

(62 citation statements)

References 4 publications

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“…The quantity that comes into the physical calculation is actually −Tr log m 2 k,n 15) where Λ is the cutoff and R is the radius of The torsion of the lens space for the trivial representation is T O (S 3 /Z q ) = log(1/q). To compute this, we use the fact that, as described in [24], the lens space has a cell decomposition in which the chain group C k is isomorphic to Z for k = 0, . .…”

Section: Difficulties With the Modelmentioning

confidence: 99%

Unification Scale, Proton Decay, And Manifolds Of G2 Holonomy

Friedmann¹,

Witten²

2003

Advances in Theoretical and Mathematical Physics

208

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Models of particle physics based on manifolds of G 2 holonomy are in most respects much more complicated than other string-derived models, but as we show here they do have one simplification: threshold corrections to grand unification are particularly simple. We compute these corrections, getting completely explicit results in some simple cases. We estimate the relation between Newton's constant, the GUT scale, and the value of α GU T , and explore the implications for proton decay. In the case of proton decay, there is an interesting mechanism which (relative to four-dimensional SUSY GUT's) enhances the gauge boson contribution to p → π 0 e + L compared to other modes such asBecause of numerical uncertainties, we do not know whether to intepret this as an enhancement of the p → π 0 e + L mode or a suppression of the others.e-print archive: http://lanl.arXiv.org/abs/hep-th/0211269

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Section: Difficulties With the Modelmentioning

confidence: 99%

Unification Scale, Proton Decay, And Manifolds Of G2 Holonomy

Friedmann¹,

Witten²

2003

Advances in Theoretical and Mathematical Physics

208

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“…That was actually a continuation of works of Calabi, Gallot and Meyer on spectrum of spheres [25]. Ikeda used representation theory to find the spectrum of lens spaces.…”

Section: Introductionmentioning

confidence: 87%

On a relation between spectral theory of lens spaces and Ehrhart theory

Mohades

Honari

2017

Indagationes Mathematicae

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In this article Ehrhart quasi-polynomials of simplices are employed to determine isospectral lens spaces in terms of a finite set of numbers. Using the natural lattice associated with a lens space the associated toric variety of a lens space is introduced. It is proved that if two lens spaces are isospectral then the dimension of global sections of powers of a natural line bundle on these two toric varieties are equal and they have the same general intersection number. Also, harmonic polynomial representation of the group SO(n) is used to provide a direct proof for a theorem of Lauret, Miatello and Rossetti on isospectrality of lens spaces.

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“…where we characterize ω by the integer ℓ, the Ray-Singer torsion was first computed by Ray by assuming N ≥ 2 in [18]. A direct computation has been made in [19,20].…”

Section: Jhep02(2018)037 2 Flat Gauge Fields On Lens Spacesmentioning

confidence: 99%

Five-dimensional fermionic Chern-Simons theory

Bak

Gustavsson

2018

J. High Energ. Phys.

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We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This theory can be obtained from 5d maximally supersymmetric YM theory by performing the maximal topological twist. We put the theory on a five-manifold and compute the partition function. We find that it is a topological quantity, which involves the Ray-Singer torsion of the five-manifold. For abelian gauge group we consider the uplift to the 6d theory and find a mismatch between the 5d partition function and the 6d index, due to the nontrivial dimensional reduction of a selfdual two-form gauge field on a circle. We also discuss an application of the 5d theory to generalized knots made of 2d sheets embedded in 5d.

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Reidemeister torsion and the laplacian on lens spaces

Cited by 76 publications

References 4 publications

Unification Scale, Proton Decay, And Manifolds Of <i>G</i><sub>2</sub> Holonomy

Unification Scale, Proton Decay, And Manifolds Of <i>G</i><sub>2</sub> Holonomy

On a relation between spectral theory of lens spaces and Ehrhart theory

Five-dimensional fermionic Chern-Simons theory

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