Moduli spaces of type  $$\mathcal {B}$$ B surfaces with torsion

Gilkey, Peter Β.

doi:10.1007/s00022-016-0364-9

Cited by 3 publications

(2 citation statements)

References 43 publications

(49 reference statements)

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“…In this section our tools for doing this are standard calculations using the Gilkey‐DeWitt heat‐kernel coefficients, [ 40–43 ] that give the effects of integrating out heavy particles at one loop order. These tools show that such loops contribute local shifts to the effective Lagrangian of the form

{\cal L}_{\scriptscriptstyle I}= {\cal L}_u + \delta {\cal L}

with

\begin{eqnarray} \frac{\delta {\cal L}}{\sqrt {-g}} &=& a_{cc}^{(s)} m^4 + a_{eh}^{(s)} \, m^2 \, R + \frac{a_{rs}^{(s)} m^2}{M_p^2}\, i\epsilon ^{\mu \nu \lambda \rho } {\overline{\psi }}_\mu \gamma _5 \gamma _\nu D_\lambda \psi _\rho \nonumber\\ && +\ \frac{a_{gm}^{(s)} m^3}{M_p^2} \, {\overline{\psi }}_\mu \gamma ^{\mu \nu } \psi _\nu + \cdots \end{eqnarray}

where

a_{cc}^{(s)}

a_{eh}^{(s)}

a_{r s}^{(s}

…”

Section: Wilsonian Flowmentioning

confidence: 99%

Who's Afraid of the Supersymmetric Dark? The Standard Model vs Low‐Energy Supergravity

Burgess

Quevedo

2022

Fortschritte der Physik

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Use of supergravity equations in astronomy and late-universe cosmology is often criticized on three grounds: (i) phenomenological success usually depends on the supergravity form for the scalar potential applying at the relevant energies; (ii) the low-energy scalar potential is extremely sensitive to quantum effects involving very massive particles and so is rarely well-approximated by classical calculations of its form; and (iii) almost all Standard Model particles count as massive for these purposes and none of these are supersymmetric. Why should Standard Model loops preserve the low-energy supergravity form even if supersymmetry is valid at energies well above the electroweak scale? We use recently developed tools for coupling supergravity to non-supersymmetric matter to estimate the loop effects of heavy non-supersymmetric particles on the low-energy effective action, and provide evidence that the supergravity form is stable against integrating out such particles (and so argues against the above objection). This suggests an intrinsically supersymmetric picture of Nature where supersymmetry survives to low energies within the gravity sector but not the visible sector (for which supersymmetry is instead non-linearly realized). We explore the couplings of both sectors in this picture and find that the presence of auxiliary fields in the gravity sector makes the visible sector share many features usually attributed to linearly realized supersymmetry although (unlike for the MSSM) a second Higgs doublet is not required for all Yukawa couplings to be non-vanishing and changes the dimension of the operator generating the Higgs mass. We discuss the naturalness of this picture and some of the implications it might have when searching for dark-sector physics.

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{\cal L}_{\scriptscriptstyle I}= {\cal L}_u + \delta {\cal L}

with

\begin{eqnarray} \frac{\delta {\cal L}}{\sqrt {-g}} &=& a_{cc}^{(s)} m^4 + a_{eh}^{(s)} \, m^2 \, R + \frac{a_{rs}^{(s)} m^2}{M_p^2}\, i\epsilon ^{\mu \nu \lambda \rho } {\overline{\psi }}_\mu \gamma _5 \gamma _\nu D_\lambda \psi _\rho \nonumber\\ && +\ \frac{a_{gm}^{(s)} m^3}{M_p^2} \, {\overline{\psi }}_\mu \gamma ^{\mu \nu } \psi _\nu + \cdots \end{eqnarray}

where

a_{cc}^{(s)}

a_{eh}^{(s)}

a_{r s}^{(s}

…”

Section: Wilsonian Flowmentioning

confidence: 99%

Who's Afraid of the Supersymmetric Dark? The Standard Model vs Low‐Energy Supergravity

Burgess

Quevedo

2022

Fortschritte der Physik

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“…This structure is the Lorentzian-hyperbolic plane; it isometrically embeds in the pseudo-sphere which is affine complete. We refer to [2] for a further discussion of these two geometries and to [8] for a discussion of the pseudo-group of isometries. Case 3c.…”

Section: The Proof Of Theorem 110mentioning

confidence: 99%

Affine Killing complete and geodesically complete homogeneous affine surfaces

Gilkey

Park

Valle-Regueiro

2019

Journal of Mathematical Analysis and Applications

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Aspects of Differential Geometry IV

Calviño-Louzao

Garcı́a-Rı́o

Gilkey³

et al. 2019

Synthesis Lectures on Mathematics and Statistics

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Book IV continues the discussion begun in the first three volumes. Although it is aimed at firstyear graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces which are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group R 2 is Abelian and the ax C b group is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type A surfaces. These are the left-invariant affine geometries on R 2 . Associating to each Type A surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue D 1 turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type B surfaces; these are the left-invariant affine geometries on the ax C b group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere S 2 . The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension.

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Moduli spaces of type $$\mathcal {B}$$ B surfaces with torsion

Abstract: We examine moduli spaces of locally homogeneous surfaces of Type B with torsion where the symmetric Ricci tensor is non-degenerate. We also determine the space of affine Killing vector fields in this context.2010 Mathematics Subject Classification. 53C21.

Cited by 3 publications

References 43 publications

Who's Afraid of the Supersymmetric Dark? The Standard Model vs Low‐Energy Supergravity

Who's Afraid of the Supersymmetric Dark? The Standard Model vs Low‐Energy Supergravity

Affine Killing complete and geodesically complete homogeneous affine surfaces

Aspects of Differential Geometry IV

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