Lectures on Higher Structures in M-theory

Saemann, Christian

doi:10.1142/9789813144613_0004

Cited by 10 publications

(8 citation statements)

References 73 publications

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“…definition based on quantum mechanics on the moduli space of instantons [16,17], a definition based on deconstruction from four dimensional superconformal, quiver field theories [18], and the conjecture that the (2,0) theory compactified on a circle is equivalent to the five dimensional maximally supersymmetric Yang-Mills theory [19,20]. And despite an extensive amount of work on this topic, see for example, [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], the field theoretic description of the multiple M5-branes system remains mysterious. In addition to consistency and symmetry requirement, the fundamental theory, no matter how it is defined, should reproduce properties that are expected of the multiple M5-branes system.…”

Section: Introductionmentioning

confidence: 99%

Boundary string current & Weyl anomaly in six-dimensional conformal field theory

Chu

Miao

2019

J. High Energ. Phys.

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It was recently discovered that for a boundary system in the presence of a background magnetic field, the quantum fluctuation of the vacuum would create a non-uniform magnetization density for the vacuum and a magnetization current is induced in the vacuum [1]. It was also shown that this "magnetic Casimir effect" of the vacuum is closely related to another quantum effect of the vacuum, the Weyl anomaly. Furthermore, the phenomena can be understood in terms of the holography of the boundary system [2]. In this paper, we generalize this four dimensional effect to six dimensions. We use the AdS/BCFT holography to show that in the presence of a 3-form magnetic field strength H, a string current is induced in a six dimensional boundary conformal field theory. This allows us to determine the gauge field contribution to the Weyl anomaly in six dimensional conformal field theory in a H-flux background. For the (2,0) superconformal field theory of N M5-branes, the current has a magnitude proportional to N 3 for large N . This suggests that the degree of freedoms scales as N 3 in the (2,0) superconformal theory of N multiple M5-branes. The prediction we have for the Weyl anomaly is a new criteria that the (2,0) theory should satisfy.

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Section: Introductionmentioning

confidence: 99%

Boundary string current & Weyl anomaly in six-dimensional conformal field theory

Chu

Miao

2019

J. High Energ. Phys.

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“…[92]), but there is a more natural way out. Consider higher holomorphic Chern-Simons theory for L := L −2 ⊕ L −1 ⊕ L 0 a Lie 3-algebra as done in [93]. The higher extension of gauge potentials in this theory is merely auxiliary, and the L ∞ -algebra of the higher holomorphic Chern-Simons theory reduces to that of ordinary holomorphic Chern-Simons theory.…”

Section: Comments On (Higher) Holomorphic Chern-simons Theoriesmentioning

confidence: 99%

L_∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism

Jurčo

Raspollini

Sämann

et al. 2019

Fortschritte der Physik

221

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We review in detail the Batalin–Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. In particular, we show how a field theory gives rise to an L∞‐algebra and how quasi‐isomorphisms between L∞‐algebras correspond to classical equivalences of field theories. A few experts may be familiar with parts of our discussion, however, the material is presented from the perspective of a very general notion of a gauge theory. We also make a number of new observations and present some new results. Most importantly, we discuss in great detail higher (categorified) Chern–Simons theories and give some useful shortcuts in usually rather involved computations.

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“…The relation between these 3-algebras and L ∞ -algebras is reviewed in e.g. [36]. [37,38], which worked out a somewhat complicated noncommutative deformation of loop space.…”

Section: Nonassociativity In M-theorymentioning

confidence: 99%

An introduction to nonassociative physics

Szabo¹

2019

Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018)

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We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic monopoles, in string theory and M-theory with nongeometric fluxes, and in M-theory with non-geometric Kaluza-Klein monopoles. After a brief overview of the main historical appearences of nonassociativity in quantum mechanics, string theory and M-theory, we provide a detailed account of the classical and quantum dynamics of electric charges in the backgrounds of various distributions of magnetic charge. We apply Born reciprocity to map this system to the phase space of closed strings propagating in R-flux backgrounds of string theory, and then describe the lift to the phase space of M2-branes in R-flux backgrounds of M-theory. Applying Born reciprocity maps this M-theory configuration to the phase space of M-waves probing a non-geometric Kaluza-Klein monopole background. These four perspective systems are unified by a covariant 3-algebra structure on the M-theory phase space.

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Lectures on Higher Structures in M-theory

Cited by 10 publications

References 73 publications

Boundary string current & Weyl anomaly in six-dimensional conformal field theory

Boundary string current & Weyl anomaly in six-dimensional conformal field theory

L_∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism

An introduction to nonassociative physics

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Lectures on Higher Structures in M-theory

Cited by 10 publications

References 73 publications

Boundary string current & Weyl anomaly in six-dimensional conformal field theory

Boundary string current & Weyl anomaly in six-dimensional conformal field theory

L∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism

An introduction to nonassociative physics

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Product

Resources

About

L_∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism