Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory

Schreiber

2020

J. High Energ. Phys.

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In the quest for the mathematical formulation of M-theory, we consider three major open problems: a first-principles construction of the single (abelian) M5-brane Lagrangian density, the origin of the gauge field in heterotic M-theory, and the supersymmetric enhancement of exceptional M-geometry. By combining techniques from homotopy theory and from supergeometry to what we call super-exceptional geometry within super-homotopy theory, we present an elegant joint solution to all three problems. This leads to a unified description of the Nambu-Goto, Perry-Schwarz, and topological Yang-Mills Lagrangians in the topologically nontrivial setting. After explaining how charge quantization of the C-field in Cohomotopy reveals D'Auria-Fré's "hidden supergroup" of 11d supergravity as the super-exceptional target space, in the sense of Bandos, for M5brane sigma-models, we prove, in exceptional generalization of the doubly-supersymmetric super-embedding formalism, that a Perry-Schwarz-type Lagrangian for single (abelian) N = (1, 0) M5-branes emerges as the super-exceptional trivialization of the M5-brane cocycle along the super-exceptional embedding of the "half" M5-brane locus, super-exceptionally compactified on the Hořava-Witten circle fiber. From inspection of the resulting 5d super Yang-Mills Lagrangian we find that the extra fermion field appearing in super-exceptional M-geometry, whose physical interpretation had remained open, is the M-theoretic avatar of the gaugino field.

Section: Discussionmentioning

confidence: 68%

Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5

Fiorenza

Schreiber

2020

J. High Energ. Phys.

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“…✷ As we saw above, these obstructions mostly vanish for dimension reasons in our range of dimensions. However, we will consider bundles other than the tangent bundle; for example bundles with structure group SO(32) rather than SO (10) or SO (11).…”

Section: Bo 10 and Bo 11 Structuresmentioning

confidence: 99%

Ninebrane structures

Int. J. Geom. Methods Mod. Phys.

2015

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String structures in degree four are associated with cancellation of anomalies of string theory in ten dimensions. Fivebrane structures in degree eight have recently been shown to be associated with cancellation of anomalies associated to fivebranes in string theory and M-theory. We introduce and describe Ninebrane structures in degree twelve and demonstrate how they capture some anomaly cancellation phenomena in M-theory. Along the way we also define certain variants, considered as intermediate cases in degree nine and ten, which we call 2-Orientation and 2-Spin structures, respectively. As in the lower degree cases, we also discuss the natural twists of these structures and characterize the corresponding topological groups associated to each of the structures, which likewise admit refinements to differential cohomology.

“…In algebraic topology, String structures play a role of orientation for elliptic cohomology [1] [34] [35]. In differential geometry, String connections play a role in geometrically describing bundles with the String group as a structure group [31] [26] [39] [6] [7]. In mathematical physics, conditions for having String structures arise as anomaly cancellation conditions [16] [30] [31].…”

Section: Introductionmentioning

confidence: 99%

“…Since then many models of the String group have appeared, each having different desirable features (see e.g. the appendix of [7] for seven such models). For instance, in one model [23], String(n) is constructed as an extension as in eq.…”

Section: Introductionmentioning

confidence: 99%

String structures associated to indefinite Lie groups

Journal of Geometry and Physics

Shim

2019

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String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend the description of String structures from connected covers of the definite-signature orthogonal group O(n) to the indefinite-signature orthogonal group O(p, q), i.e. from the Riemannian to the pseudo-Riemannian setting. This requires that we work at the unstable level, which makes the discussion more subtle than the stable case. Similar, but much simpler, constructions hold for other noncompact Lie groups such as the unitary group U(p, q) and the symplectic group Sp(p, q). This extension provides a starting point for an abundance of constructions in (higher) geometry and applications in physics.