scholarly journals A Systematic Approach to Consistent Truncations of Supergravity Theories

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 485
Author(s):  
Michela Petrini
Keyword(s):  
Systematic Approach ◽  
Five Dimensions ◽  
Gauge Transformations ◽  
Higher Rank ◽  
Consistent Truncations ◽  
Extended Notion

Exceptional generalised geometry is a reformulation of eleven/ten-dimensional supergravity that unifies ordinary diffeomorphisms and gauge transformations of the higher-rank potentials of the theory in an extended notion of diffeormorphisms. These features make exceptional generalised geometry a very powerful tool to study consistent truncations of eleven/ten-dimensional supergravities. In this article, we review how the notion of generalised G-structure allows us to derive consistent truncations to supergravity theories in various dimensions and with different amounts of supersymmetry. We discuss in detail the truncations of eleven-dimensional supergravity to N=4 and N=2 supergravity in five dimensions.

scholarly journals $$ \mathcal{N} $$ = 2 consistent truncations from wrapped M5-branes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Davide Cassani ◽  
Grégoire Josse ◽  
Michela Petrini ◽  
Daniel Waldram
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Tangent Bundle ◽  
Dimensional Manifold ◽  
Five Dimensions ◽  
Intrinsic Torsion ◽  
Consistent Truncations

Abstract We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold M, preserving minimal $$ \mathcal{N} $$ N = 2 supersymmetry in five dimensions. These are based on GS ⊆ USp(6) structures for the generalised E6(6) tangent bundle on M, such that the intrinsic torsion is a constant GS singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS5×wM solutions arising from M5-branes wrapped on a Riemann surface. The generalised U(1) structure associated with the $$ \mathcal{N} $$ N = 2 solution of Maldacena-Nuñez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and SO(3) × U(1) × ℝ gauge group. The generalised structure associated with “BBBW” solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.

scholarly journals The index conjecture for symmetric spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jürgen Berndt ◽  
Carlos Olmos
Keyword(s):  
Symmetric Spaces ◽  
Systematic Approach ◽  
Riemannian Symmetric Space ◽  
Totally Geodesic Submanifold ◽  
Totally Geodesic ◽  
Geodesic Submanifolds ◽  
Geodesic Submanifold ◽  
Totally Geodesic Submanifolds ◽  
Higher Rank ◽  
Differential Geom

AbstractIn 1980, Oniščik [A. L. Oniščik, Totally geodesic submanifolds of symmetric spaces, Geometric methods in problems of algebra and analysis. Vol. 2, Yaroslav. Gos. Univ., Yaroslavl’ 1980, 64–85, 161] introduced the index of a Riemannian symmetric space as the minimal codimension of a (proper) totally geodesic submanifold. He calculated the index for symmetric spaces of rank {\leq 2}, but for higher rank it was unclear how to tackle the problem. In [J. Berndt, S. Console and C. E. Olmos, Submanifolds and holonomy, 2nd ed., Monogr. Res. Notes Math., CRC Press, Boca Raton 2016], [J. Berndt and C. Olmos, Maximal totally geodesic submanifolds and index of symmetric spaces, J. Differential Geom. 104 2016, 2, 187–217], [J. Berndt and C. Olmos, The index of compact simple Lie groups, Bull. Lond. Math. Soc. 49 2017, 5, 903–907], [J. Berndt and C. Olmos, On the index of symmetric spaces, J. reine angew. Math. 737 2018, 33–48], [J. Berndt, C. Olmos and J. S. Rodríguez, The index of exceptional symmetric spaces, Rev. Mat. Iberoam., to appear] we developed several approaches to this problem, which allowed us to calculate the index for many symmetric spaces. Our systematic approach led to a conjecture, formulated first in [J. Berndt and C. Olmos, Maximal totally geodesic submanifolds and index of symmetric spaces, J. Differential Geom. 104 2016, 2, 187–217], for how to calculate the index. The purpose of this paper is to verify the conjecture.

scholarly journals $$ \mathcal{N} $$ = 2 extended MacDowell-Mansouri supergravity

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Pedro D. Alvarez ◽  
Lucas Delage ◽  
Mauricio Valenzuela ◽  
Jorge Zanelli
Keyword(s):  
Equations Of Motion ◽  
Outer Automorphism ◽  
Chiral Fermion ◽  
Reducible Representation ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Broken Symmetries ◽  
Hodge Operator ◽  
Translation Type ◽  
Extended Notion

Abstract We construct a gauge theory based in the supergroup G = SU(2, 2|2) that generalizes MacDowell-Mansouri supergravity. This is done introducing an extended notion of Hodge operator in the form of an outer automorphism of su(2, 2|2)-valued 2-form tensors. The model closely resembles a Yang-Mills theory — including the action principle, equations of motion and gauge transformations — which avoids the use of the otherwise complicated component formalism. The theory enjoys H = SO(3, 1) × ℝ × U(1) × SU(2) off-shell symmetry whilst the broken symmetries G/H, translation-type symmetries and supersymmetry, can be recovered on surface of integrability conditions of the equations of motion, for which it suffices the Rarita-Schwinger equation and torsion-like constraints to hold. Using the matter ansatz —projecting the 1 ⊗ 1/2 reducible representation into the spin-1/2 irreducible sector — we obtain (chiral) fermion models with gauge and gravity interactions.

Reading Longer Words: Insights Into Multisyllabic Word Reading

2017 ◽  
Vol 2 (1) ◽  
pp. 86-94 ◽  
Author(s):  
Lindsay Heggie ◽  
Lesly Wade-Woolley
Keyword(s):  
Systematic Approach ◽  
Word Reading ◽  
Explicit Instruction ◽  
Working Memory Capacity ◽  
Reading Difficulties ◽  
Instructional Programs ◽  
Morphological Knowledge ◽  
Morphological Complexity ◽  
Reading Accuracy ◽  
Grade 3

Students with persistent reading difficulties are often especially challenged by multisyllabic words; they tend to have neither a systematic approach for reading these words nor the confidence to persevere (Archer, Gleason, & Vachon, 2003; Carlisle & Katz, 2006; Moats, 1998). This challenge is magnified by the fact that the vast majority of English words are multisyllabic and constitute an increasingly large proportion of the words in elementary school texts beginning as early as grade 3 (Hiebert, Martin, & Menon, 2005; Kerns et al., 2016). Multisyllabic words are more difficult to read simply because they are long, posing challenges for working memory capacity. In addition, syllable boundaries, word stress, vowel pronunciation ambiguities, less predictable grapheme-phoneme correspondences, and morphological complexity all contribute to long words' difficulty. Research suggests that explicit instruction in both syllabification and morphological knowledge improve poor readers' multisyllabic word reading accuracy; several examples of instructional programs involving one or both of these elements are provided.

Coming Together Through Falling Apart

2019 ◽  
Vol 40 (2) ◽  
pp. 151-168
Author(s):  
Heather Churchill ◽  
Jeremy M. Ridenour
Keyword(s):  
Data Analysis ◽  
Qualitative Data ◽  
Structural Changes ◽  
Systematic Approach ◽  
Qualitative Approach ◽  
Psychological Assessments ◽  
Transference And Countertransference ◽  
Testing Data ◽  
Psychoanalytically Oriented Psychotherapy

Abstract. Assessing change during long-term psychotherapy can be a challenging and uncertain task. Psychological assessments can be a valuable tool and can offer a perspective from outside the therapy dyad, independent of the powerful and distorting influences of transference and countertransference. Subtle structural changes that may not yet have manifested behaviorally can also be assessed. However, it can be difficult to find a balance between a rigorous, systematic approach to data, while also allowing for the richness of the patient’s internal world to emerge. In this article, the authors discuss a primarily qualitative approach to the data and demonstrate the ways in which this kind of approach can deepen the understanding of the more subtle or complex changes a particular patient is undergoing while in treatment, as well as provide more detail about the nature of an individual’s internal world. The authors also outline several developmental frameworks that focus on the ways a patient constructs their reality and can guide the interpretation of qualitative data. The authors then analyze testing data from a patient in long-term psychoanalytically oriented psychotherapy in order to demonstrate an approach to data analysis and to show an example of how change can unfold over long-term treatments.

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