scholarly journals Dimensional Enhancement via Supersymmetry

2011 ◽  
Vol 2011 ◽  
pp. 1-45 ◽  
Author(s):  
M. G. Faux ◽  
K. M. Iga ◽  
G. D. Landweber
Keyword(s):  
Quantum Mechanics ◽  
Representation Theory ◽  
Gauge Invariance ◽  
Extra Dimensions ◽  
Field Theories ◽  
Consistency Test ◽  
One Dimensional ◽  
Supersymmetric Field Theories ◽  
Higher Dimensional ◽  
Supersymmetric Models

We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describes “shadows” of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can “enhance” to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of “phantoms” which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.

Lorentz violation and super-symmetry

2006 ◽  
Vol 84 (6-7) ◽  
pp. 669-675
Author(s):  
M Pospelov
Keyword(s):  
Standard Model ◽  
Supersymmetric Standard Model ◽  
Gauge Invariance ◽  
Recent Progress ◽  
Lorentz Violation ◽  
Field Theories ◽  
Constant Vector ◽  
Natural Explanation ◽  
Supersymmetric Field Theories ◽  
Super Symmetry

We review recent progress in constructing supersymmetric field theories modified by the presence of constant vector and tensor backgrounds, or in other words SUSY field theories with Lorentz violation (LV). We show that the requirement of supersymmetry and gauge invariance limits the LV in the minimal supersymmetric Standard Model to dimension five and higher levels, giving a natural explanation to the smallness of the Lorentz violation. We show main phenomenological features of such models, among which is the absence of large LV corrections to dispersion relations, and include radiative corrections. We show that 1/MPlanck normalized corrections are ruled out at the 10–10 level. PACS Nos.: 11.30.Cp, 11.30.Pb, 11.10.Hi

scholarly journals Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections

2019 ◽  
Vol 34 (04) ◽  
pp. 1950028
Author(s):  
R. D. Mota ◽  
D. Ojeda-Guillén ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Supersymmetric Quantum Mechanics ◽  
Type Model ◽  
One Dimensional ◽  
The Third ◽  
Derivative Formula ◽  
Supersymmetric Models ◽  
Oscillator Type ◽  
The Creation

By modifying and generalizing known supersymmetric models, we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of [Formula: see text]. Also, by changing the derivative [Formula: see text] by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator [Formula: see text], we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.

scholarly journals Extended Supersymmetries in One Dimension

10.14311/965 ◽  
2008 ◽  
Vol 48 (2) ◽  
Author(s):  
F. Toppan
Keyword(s):  
Summer School ◽  
Clifford Algebras ◽  
Irreducible Representations ◽  
One Dimension ◽  
One Dimensional ◽  
Supersymmetric Field Theories ◽  
Fusion Algebra ◽  
Higher Dimensional ◽  
Extract Information

This work covers part of the material presented at the Advanced Summer School in Prague. It is mostly devoted to the structural properties of Extended Supersymmetries in One Dimension. Several results are presented on the classification of linear, irreducible representations realized on a finite number of time-dependent fields. The connections between supersymmetry transformations, Clifford algebras and division algebras are discussed. A manifestly supersymmetric framework for constructing invariants without using the notion of superfields is presented. A few examples of one-dimensional, N-extended, off-shell invariant sigma models are computed. The relation between supersymmetry transformations and graph theory is outlined. The notion of the fusion algebra of irreps tensor products is presented. The relevance of one-dimensional Supersymmetric Quantum Mechanics as a way to extract information on higher dimensional supersymmetric field theories is discussed. 

scholarly journals Hearing the shape of a drum for light: isospectrality in photonics

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Seungkyun Park ◽  
Ikbeom Lee ◽  
Jungmin Kim ◽  
Namkyoo Park ◽  
Sunkyu Yu
Keyword(s):  
Quantum Mechanics ◽  
Research Topic ◽  
Complex Structures ◽  
Inhomogeneous Materials ◽  
Independent Control ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Wave Phenomena ◽  
Spectral Responses ◽  
Many Particles

Abstract The independent tailoring of wave quantities lays the foundation for controlling wave phenomena and designing wave devices. The concept of isospectrality, which suggests the existence of systems that provide identical spectra, has inspired a novel route to the spectrum-preserved engineering of wave–matter interactions in photonics, acoustics, and quantum mechanics. Recently, in photonics, constructing isospectral optical structures has become an emerging research topic to handle the intricate spectral responses of the systems composed of many-particles or inhomogeneous materials. The cornerstones in this field have stimulated the realization of non-Hermitian systems with real eigenspectra, one-dimensional structures exhibiting higher-dimensional physics, and novel engineering methodologies for broadband devices such as phase-matched multiplexers and multimodal lasing platforms. Here we review recent achievements based on isospectrality in photonics. We outline milestones in two different subfields of supersymmetric photonics and interdimensional isospectrality. We illustrate that isospectrality has paved the way for the independent control of wave quantities, showing great potential for the analytical and platform-transparent design of photonic systems with complex structures and materials.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals Unitarity in KK-graviton production, a case study in warped extra-dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. de Giorgi ◽  
S. Vogl
Keyword(s):  
Extra Dimensions ◽  
Sum Rules ◽  
Effective Theory ◽  
Higher Dimensional ◽  
Massive Spin ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Warped Extra Dimensions ◽  
Kaluza Klein

Abstract The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-tower leads to an early breakdown of perturbative unitarity. However, by considering the full tower we obtain a set of sum rules for the couplings between the different KK-fields that restore unitarity up to the scale of the 5D theory. We prove analytically that these are fulfilled in the model under consideration and present numerical tests of their convergence. This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions.

scholarly journals AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Riemann Surface ◽  
Central Charge ◽  
Global Solutions ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

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