Equivariant Cohomotopy implies orientifold tadpole cancellation

Sati, Hisham; Schreiber, Urs

doi:10.1016/j.geomphys.2020.103775

Cited by 28 publications

(13 citation statements)

References 103 publications

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“…While we have only discussed abelian gauge fields here, their appearance (by the construction in §5, §7) via the M2/M5 super-cocycle µ M2/M5 (2) means that the super-cohomotopical gauge enhancement mechanism found in [BSS18] applies. Together with the constraints of half-integral flux quantization and tadpole cancellation, which we demonstrate in [FSS19b] and [SS19], respectively, to follow from C-field charge quantization in full Cohomotopy (114), this should generate the expected types of nonabelian gauge fields, both for heterotic M-theory as well as for coincident 5-branes, in the form discussed in [Sat10a][Sat10b][FSS12a] [FSS12b]. While the details remain to be worked out, this opens up the possibility of a concrete strategy for systematically deriving the non-abelian D=6 M5-brane theory from first principles.…”

Section: Discussionsupporting

confidence: 59%

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

Fiorenza

Sati

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.

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Section: Discussionsupporting

confidence: 59%

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

Fiorenza

Sati

Schreiber

2020

J. High Energ. Phys.

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“…Given that M-theory is supposedly the pinnacle of fundamental physics, we suspect that M-brane charge quantization corresponds not to random but rather to the deep phenomena seen in algebraic topology. This idea has been the guiding light for investigations into M-theory in (c) ... in K-theory [SS19a][BSS19], under the Hurewicz-Boardman homomorphism. (d) ... in equivariant Cobordism [SS19a], under the Pontrjagin construction.…”

Section: Generalized Cohomology Y Ymentioning

confidence: 99%

M/F-Theory as Mf-Theory

Sati¹,

Schreiber²

2021

Preprint

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In the quest for mathematical foundations of M-theory, the Hypothesis H, that fluxes are quantized in Cohomotopy theory, implies, on flat but possibly singular spacetimes, that M-brane charges locally organize into equivariant homotopy groups of spheres. Here we show how this leads to a correspondence between phenomena conjectured in M-theory and fundamental mathematical concepts/results in stable homotopy, generalized cohomology and Cobordism theory Mf :-stems of homotopy groups correspond to charges of probe p-branes near black b-branes; -stabilization within a stem is the boundary-bulk transition; -the Adams d-invariant measures G 4 -flux; -trivialization of the d-invariant corresponds to H 3 -flux; -refined Toda brackets measure H 3 -flux; -the refined Adams e-invariant sees the H 3 -charge lattice; -vanishing Adams e-invariant implies consistent global C 3 -fields; -Conner-Floyd's e-invariant is the H 3 -flux seen in the Green-Schwarz mechanism; -the Hopf invariant is the M2-brane Page charge ( G 7 -flux); -the Pontrjagin-Thom theorem associates the polarized brane worldvolumes sourcing all these charges. In particular, spontaneous K3-reductions with 24 branes are singled out from first principles:-Cobordism in the third stable stem witnesses spontaneous KK-compactification on K3-surfaces; -the order of the third stable stem implies the 24 NS5/D7-branes in M/F-theory on K3. Finally, complex-oriented cohomology emerges from Hypothesis H, connecting it to all previous proposals for brane charge quantization in the chromatic tower: K-theory, elliptic cohomology, etc.:-quaternionic orientations correspond to unit H 3 -fluxes near M2-branes; -complex orientations lift these unit H 3 -fluxes to heterotic M-theory with heterotic line bundles. In fact, we find quaternionic/complex Ravenel-orientations bounded in dimension; and we find the bound to be 10, as befits spacetime dimension 10+1. S 3 S 3 S 3 K3\(24 • D 4

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“…However, as indicated above (see [Sa13]), one would ultimately like to use as the target the actual 4-sphere rather than its rationalization, even though we are content with the latter in this paper. See [SS19a][SS19b][SS21] for recent developments in that direction.…”

Section: M-theory Dynamics and S 4 Via Hypothesis Hmentioning

confidence: 99%

Mysterious Triality and Rational Homotopy Theory

Sati¹,

Voronov²

2021

Preprint

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Mysterious duality has been discovered by Iqbal, Neitzke, and Vafa [INV02] as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series E k .It turns out that the sequence of del Pezzo surfaces is not the only sequence of objects in mathematics which gives rise to the same E k symmetry pattern. We present a sequence of topological spaces, starting with the four-sphere S 4 , and then forming its iterated cyclic loop spaces L k c S 4 , within which we discover the E k symmetry pattern via rational homotopy theory. For this sequence of spaces, the correspondence between its E k symmetry pattern and that of toroidal compactifications of M-theory is no longer a mystery, as each space L k c S 4 is naturally related to the compactification of M-theory on the k-torus via identification of the equations of motion of (11 − k)-dimensional supergravity as the defining equations of the Sullivan minimal model of L k c S 4 . This gives an explicit duality between algebraic topology and physics.Thereby, we extend Iqbal-Neitzke-Vafa's mysterious duality between algebraic geometry and physics into a triality, also involving algebraic topology. Via this triality, duality between physics and mathematics is demystified, and the mystery is transferred to the mathematical realm as duality between algebraic geometry and algebraic topology. Now the question is: is there an explicit relation between the del Pezzo surfaces B k and iterated cyclic loop spaces of S 4 which would explain the common E k symmetry pattern?

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Equivariant Cohomotopy implies orientifold tadpole cancellation

Cited by 28 publications

References 103 publications

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

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

M/F-Theory as Mf-Theory

Mysterious Triality and Rational Homotopy Theory

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