scholarly journals Conformally soft fermions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Yorgo Pano ◽  
Sabrina Pasterski ◽  
Andrea Puhm
Keyword(s):  
Gauge Theory ◽  
Inner Product ◽  
Conformal Dimension ◽  
Infinite Dimensional ◽  
Primary Operator ◽  
Left And Right ◽  
Symmetry Generators ◽  
Goldstone Modes ◽  
Asymptotic Symmetries

Abstract Celestial diamonds encode the global conformal multiplets of the conformally soft sector, elucidating the role of soft theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat the soft charges associated to the fermionic layers that tie this structure together. This extends the analysis of conformally soft currents for photons and gravitons which have been shown to generate asymptotic symmetries in gauge theory and gravity to infinite-dimensional fermionic symmetries. We construct fermionic charge operators in 2D celestial CFT from a suitable inner product between 4D bulk field operators and spin s = $$ \frac{1}{2} $$ 1 2 and $$ \frac{3}{2} $$ 3 2 conformal primary wavefunctions with definite SL(2, ℂ) conformal dimension ∆ and spin J where |J| ≤ s. The generator for large supersymmetry transformations is identified as the conformally soft gravitino primary operator with ∆ = $$ \frac{1}{2} $$ 1 2 and its shadow with ∆ = $$ \frac{3}{2} $$ 3 2 which form the left and right corners of the celestial gravitino diamond. We continue this analysis to the subleading soft gravitino and soft photino which are captured by degenerate celestial diamonds. Despite the absence of a gauge symmetry in these cases, they give rise to conformally soft factorization theorems in celestial amplitudes and complete the celestial pyramid.

scholarly journals Celestial diamonds: conformal multiplets in celestial CFT

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Sabrina Pasterski ◽  
Andrea Puhm ◽  
Emilio Trevisani
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Explicit Construction ◽  
Conformal Dimension ◽  
Massless Particles ◽  
Special Values ◽  
Left And Right ◽  
Opposite Helicity ◽  
Asymptotic Symmetries

Abstract We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin s = $$ \left\{0,\frac{1}{2},1,\frac{3}{2},2\right\} $$ 0 1 2 1 3 2 2 we classify and construct all SL(2,ℂ) primary descendants which are organized into ‘celestial diamonds’. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,ℂ) conformal dimension ∆ and spin J. Radiative conformal primary wavefunctions have J = ±s and give rise to conformally soft theorems for special values of ∆ ∈ $$ \frac{1}{2}\mathbb{Z} $$ 1 2 ℤ . They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have |J| ≤ s. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.

scholarly journals Asymptotic symmetries and celestial CFT

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Laura Donnay ◽  
Sabrina Pasterski ◽  
Andrea Puhm
Keyword(s):  
Principal Series ◽  
Finite Energy ◽  
Continuous Series ◽  
Asymptotic Symmetry ◽  
Null Infinity ◽  
Conformal Dimension ◽  
Contour Integrals ◽  
Celestial Sphere ◽  
Goldstone Modes ◽  
Asymptotic Symmetries

Abstract We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension ∆. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series ∆ ∈ 1 + iℝ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S2) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.

scholarly journals Gravitational breathing memory and dual symmetries

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ali Seraj
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Scalar Field ◽  
Memory Effects ◽  
Balance Equations ◽  
Symmetry Principle ◽  
Dual Formulation ◽  
Physical Role ◽  
Asymptotic Symmetries

Abstract Brans-Dicke theory contains an additional propagating mode which causes homogeneous expansion and contraction of test bodies in transverse directions. This “breathing” mode is associated with novel memory effects in addition to those of general relativity. Standard tensor mode memories are related to a symmetry principle: they are determined by the balance equations corresponding to the BMS symmetries. In this paper, we show that the leading and subleading breathing memory effects are determined by the balance equations associated with the leading and “overleading” asymptotic symmetries of a dual formulation of the scalar field in terms of a two-form gauge field. The memory effect causes a transition in the vacuum of the dual gauge theory. These results highlight the significance of dual charges and the physical role of overleading asymptotic symmetries.

scholarly journals On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

2020 ◽  
Vol 80 (1) ◽  
Author(s):  
Ricardo Caroca ◽  
Patrick Concha ◽  
Octavio Fierro ◽  
Evelyn Rodríguez
Keyword(s):  
Virasoro Algebra ◽  
Expansion Method ◽  
Superconformal Algebra ◽  
Supersymmetric Extension ◽  
Infinite Dimensional ◽  
Gravity Theories ◽  
Symmetry Generators ◽  
Asymptotic Symmetries ◽  
R Symmetry

AbstractIn this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-$$BMS_3$$BMS3, the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the $$\mathfrak {so}(2,2)\oplus \mathfrak {so}(2,1)$$so(2,2)⊕so(2,1) gravity theories. We extend our results to the $$\mathcal {N}=2$$N=2 and $$\mathcal {N}=4$$N=4 cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit $$\ell \rightarrow \infty $$ℓ→∞.

scholarly journals Effect of corpus callosum agenesis on the language network in children and adolescents

2021 ◽  
Author(s):  
Lisa Bartha-Doering ◽  
Ernst Schwartz ◽  
Kathrin Kollndorfer ◽  
Florian Ph. S. Fischmeister ◽  
Astrid Novak ◽  
...  
Keyword(s):  
Functional Connectivity ◽  
Corpus Callosum ◽  
Network Connectivity ◽  
Functional Language ◽  
Healthy Controls ◽  
Language Abilities ◽  
Verbal Abilities ◽  
Left And Right ◽  
Language Network

AbstractThe present study is interested in the role of the corpus callosum in the development of the language network. We, therefore, investigated language abilities and the language network using task-based fMRI in three cases of complete agenesis of the corpus callosum (ACC), three cases of partial ACC and six controls. Although the children with complete ACC revealed impaired functions in specific language domains, no child with partial ACC showed a test score below average. As a group, ACC children performed significantly worse than healthy controls in verbal fluency and naming. Furthermore, whole-brain ROI-to-ROI connectivity analyses revealed reduced intrahemispheric and right intrahemispheric functional connectivity in ACC patients as compared to controls. In addition, stronger functional connectivity between left and right temporal areas was associated with better language abilities in the ACC group. In healthy controls, no association between language abilities and connectivity was found. Our results show that ACC is associated not only with less interhemispheric, but also with less right intrahemispheric language network connectivity in line with reduced verbal abilities. The present study, thus, supports the excitatory role of the corpus callosum in functional language network connectivity and language abilities.

The role of visual experience for spatial numerical associations

2012 ◽  
Vol 25 (0) ◽  
pp. 222 ◽  
Author(s):  
Michael J. Proulx ◽  
Achille Pasqualotto ◽  
Shuichiro Taya
Keyword(s):  
Visual Experience ◽  
Opposite Effect ◽  
Random Number Generation ◽  
Number Line ◽  
Mental Number Line ◽  
Generation Task ◽  
Congenitally Blind ◽  
Left And Right ◽  
The Right

The topographic representation of space interacts with the mental representation of number. Evidence for such number–space relations have been reported in both synaesthetic and non-synaesthetic participants. Thus far most studies have only examined related effects in sighted participants. For example, the mental number line increases in magnitude from left to right in sighted individuals (Loetscher et al., 2008, Curr. Biol.). What is unclear is whether this association arises from innate mechanisms or requires visual experience early in life to develop in this way. Here we investigated the role of visual experience for the left to right spatial numerical association using a random number generation task in congenitally blind, late blind, and blindfolded sighted participants. Participants orally generated numbers randomly whilst turning their head to the left and right. Sighted participants generated smaller numbers when they turned their head to the left than to the right, consistent with past results. In contrast, congenitally blind participants generated smaller numbers when they turned their head to the right than to the left, exhibiting the opposite effect. The results of the late blind participants showed an intermediate profile between that of the sighted and congenitally blind participants. Visual experience early in life is therefore necessary for the development of the spatial numerical association of the mental number line.

scholarly journals GENERAL FRAMEWORK FOR CONSISTENT SAMPLING IN HILBERT SPACES

2005 ◽  
Vol 03 (04) ◽  
pp. 497-509 ◽  
Author(s):  
YONINA C. ELDAR ◽  
TOBIAS WERTHER
Keyword(s):  
Hilbert Spaces ◽  
General Framework ◽  
Inner Product ◽  
Riesz Bases ◽  
Oblique Projection ◽  
Dual Frames ◽  
Infinite Dimensional ◽  
Reconstruction Scheme ◽  
Linear Reconstruction ◽  
Oblique Dual

We introduce a general framework for consistent linear reconstruction in infinite-dimensional Hilbert spaces. We study stable reconstructions in terms of Riesz bases and frames, and generalize the notion of oblique dual frames to infinite-dimensional frames. As we show, the linear reconstruction scheme coincides with the so-called oblique projection, which turns into an ordinary orthogonal projection when adapting the inner product. The inner product of interest is, in general, not unique. We characterize the inner products and corresponding positive operators for which the new geometrical interpretation applies.

The structure of norm Clifford algebras

2012 ◽  
Vol 62 (6) ◽  
Author(s):  
Hans Keller ◽  
Herminia Ochsenius
Keyword(s):  
Clifford Algebra ◽  
Classical Case ◽  
Canonical Representation ◽  
Inner Product ◽  
Infinite Products ◽  
Infinite Dimensional ◽  
Significant Step ◽  
Group Of Isometries ◽  
Inner Automorphisms ◽  
Special Case

AbstractOrthomodular Hilbertian spaces are infinite-dimensional inner product spaces (E, 〈·, ·〉) with the rare property that to every orthogonally closed subspace U ⊆ E there is an orthogonal projection from E onto U. These spaces, discovered about 30 years ago, are constructed over certain non-Archimedeanly valued, complete fields and are endowed with a non-Archimedean norm derived from the inner product. In a previous work [KELLER, H. A.—OCHSENIUS, H.: On the Clifford algebra of orthomodular spaces over Krull valued fields. In: Contemp. Math. 508, Amer. Math. Soc., Providence, RI, 2010, pp. 73–87] we described the construction of a new object, called the norm Clifford algebra C̃(E) associated to E. It can be considered a counterpart of the well-established Clifford algebra of a finite dimensional quadratic space. In contrast to the classical case, C̃(E) allows to represent infinite products of reflections by inner automorphisms. It is a significant step towards a better understanding of the group of isometries, which in infinite dimension is complex and hard to grasp.In the present paper we are concerned with the inner structure of these new algebras. We first give a canonical representation of the elements, and we prove that C̃ is always central. Then we focus on an outstanding special case in which C̃ is shown to be a division ring. Moreover, in that special case we completely describe the ideals of the corresponding valuation ring $$\mathcal{A}$$. It turns out, rather unexpectedly, that every left-ideal and every right-ideal of $$\mathcal{A}$$ is in fact bilateral.

La sinistra e la destra nella Francia politica

2013 ◽  
pp. 13-22
Author(s):  
Vincent Duclert
Keyword(s):  
French Revolution ◽  
Presidential Elections ◽  
The State ◽  
Political Life ◽  
Role Of The State ◽  
Political Forces ◽  
The Future ◽  
Left And Right ◽  
The Republic

The recent presidential elections in 2012 have shown that left-right cleavage was still dominant in France. The redistribution of political forces, strongly awaited by the center (but also by the extremes) did not take place. At the same time, the major issues, such the European unification, the future of the nation, the future of the Republic, the role of the state, continue to cross left and right fields, revealing other cleavages that meet other historical or philosophical contingencies. However, the left-right opposition in France structured contemporary political life, organizing political families, determining the meaning and practice of institutions. Thence, the question is to understand what defines these two political fields and what history brings to their knowledge since the French Revolution, or they are implemented

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