Topological sectors for heterotic M5-brane charges under Hypothesis H

Roberts, David

doi:10.1007/jhep06(2020)052

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Our focus will be mostly on the Sullivan model, but the Quillen model is also important in our context, and we will discuss it in §2.2 and use it in §5.2. In our context, the Sullivan minimal model of the 4-sphere S 4 captures the dynamics of the fields in M-theory, as proposed in [Sa13], and developed further under the name Hypothesis H in [FSS17] [FSS19b][FSS19c] [GS21] (and applied in [Ro20]); we review this below in §2.1. Particularly, the Sullivan minimal model M(S 4 ) describes the dynamics of the fields, expressed as differential forms on spacetime.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Mysterious Triality and Rational Homotopy Theory

Sati¹,

Voronov²

2021

Preprint

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Mysterious Triality and Rational Homotopy Theory

Sati

Voronov

2023

Commun. Math. Phys.

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In previous work [SV21][SV22], we introduced Mysterious Triality, extending the Mysterious Duality [INV02] between physics and algebraic geometry to include algebraic topology in the form of rational homotopy theory. Starting with the rational Sullivan minimal model of the 4-sphere S 4 , capturing the dynamics of M-theory via Hypothesis H, this progresses to the dimensional reduction of M-theory on torus T k , k ≥ 1, with its dynamics described via the iterated cyclic loop space L k c S 4 of the 4-sphere. From this, we also extracted data corresponding to the maximal torus/Cartan subalgebra and the Weyl group of the exceptional Lie group/algebra of type E k .In this paper, we discover much richer symmetry by extending the data of the Cartan subalgebra to a maximal parabolic subalgebra p k(k) k of the split real form e k(k) of the exceptional Lie algebra of type E k by exhibiting an action, in rational homotopy category, of p k(k) k on the slightly more symmetric than L k c S 4 toroidification T k S 4 . This action universally represents symmetries of the equations of motion of supergravity in the reduction of M-theory to 11 − k dimensions.Along the way, we identify the minimal model of the toroidification T k S 4 , generalizing the results of Vigué-Poirrier, Sullivan, and Burghelea, and establish an algebraic toroidification/totalization adjunction.

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