Corners in M-theory

Sati, Hisham

doi:10.1088/1751-8113/44/25/255402

Cited by 10 publications

(26 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Open question of brane charge quantization . The first statement above resonates with established folklore, while the second matches with an observation about the charge structure of the C‐field in 11‐dimensional supergravity that was made only more recently, in [, Sec. 2.5].…”

Section: Brane Charge Quantizationmentioning

confidence: 99%

“…These equations governing the Sullivan model of the 4‐sphere

\begin{matrix} true \\ right normald G_{4} & left = 0 \\ right normald G_{7} & left = - 0false \frac{1}{2} G_{4} \land G_{4} \end{matrix}

are also precisely the equations of motion of the

C_{3} / C_{6}

‐field in

D = 11

supergravity. This alone shows that, rationally, the unified M2/M5‐brane charge is in the non‐Abelian generalized cohomology theory classified by the 4‐sphere [, Sec. 2.5].…”

Section: Brane Charge Quantizationmentioning

confidence: 99%

“…First observe the classical fact that, by Pontryagin–Thom theory plain 4‐cohomotopy (before equivariant enhancement) classifies cobordism classes of co‐dimension 4 submanifolds in space‐time (see e.g. [, Ch.…”

Section: Outlook – Beyond Rationalmentioning

confidence: 99%

See 2 more Smart Citations

The Rational Higher Structure of M‐theory

Fiorenza

Sati

Schreiber

2019

Fortschritte der Physik

Self Cite

View full text Add to dashboard Cite

We review how core structures of string/M‐theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approximation which ignores torsion‐subgroups in brane charges and focuses on tangent spaces of super space‐time. Already at this level, super homotopy theory discovers all super p‐brane species, their intersection laws, their M/IIA‐, T‐ and S‐duality relations, their black brane avatars at ADE‐singularities, including their instanton contributions, and, last not least, Dirac charge quantization: for the D‐branes it recovers twisted K‐theory, rationally, but for the M‐branes it gives cohomotopy cohomology theory. We close with an outlook on the lift of these results beyond the rational/infinitesimal approximation to a candidate formalization of microscopic M‐theory in super homotopy theory.

show abstract

Section: Brane Charge Quantizationmentioning

confidence: 99%

“…These equations governing the Sullivan model of the 4‐sphere

\begin{matrix} true \\ right normald G_{4} & left = 0 \\ right normald G_{7} & left = - 0false \frac{1}{2} G_{4} \land G_{4} \end{matrix}

are also precisely the equations of motion of the

C_{3} / C_{6}

‐field in

D = 11

supergravity. This alone shows that, rationally, the unified M2/M5‐brane charge is in the non‐Abelian generalized cohomology theory classified by the 4‐sphere [, Sec. 2.5].…”

Section: Brane Charge Quantizationmentioning

confidence: 99%

See 1 more Smart Citation

The Rational Higher Structure of M‐theory

Fiorenza

Sati

Schreiber

2019

Fortschritte der Physik

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, our techniques could be applied to primitive homotopy quantum field theories, and to Dai-Freed theories which are related to η-invariants; such a formalism would be based on the Dai-Freed theorem [DF95] rather than the Atiyah-Patodi-Singer index theorem and would enable constructions with chiral or Majorana fermions and unoriented manifolds, which are applicable to other symmetry-protected states of quantum matter such as topological superconductors [Wit16a] as well as to anomalies in M-theory [Wit16b]. Another application involves repeating our constructions with Dirac operators replaced by signature operators, which would lead to an extended quantum field theory describing anomalies in Reshetikhin-Turaev theories based on modular tensor categories [Tur10]; these theories should also have applications to anomalies in M-theory along the lines considered in [Sat11].…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…An alternative approach can be found in [Bun09]. The most important concepts from b-geometry for the ensuing formalism are summarised in Appendix A.4; a detailed introduction can be found in [Mel93], see also [Sat11] for a more physics oriented introduction.…”

Section: Extended Quantum Field Theory and The Parity Anomalymentioning

confidence: 99%

Extended Quantum Field Theory, Index Theory, and the Parity Anomaly

Müller

Szabo

2018

Commun. Math. Phys.

View full text Add to dashboard Cite

We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit construction of a geometric cobordism bicategory which incorporates general background fields in a stack, and together with the theory of symmetric monoidal bicategories we use it to provide the concrete forms of invertible extended quantum field theories which capture anomalies in both the path integral and Hamiltonian frameworks. Specialising this situation by using the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners due to Loya and Melrose, we obtain a new Hamiltonian perspective on the parity anomaly. We compute explicitly the 2-cocycle of the projective representation of the gauge symmetry on the quantum state space, which is defined in a parity-symmetric way by suitably augmenting the standard chiral fermionic Fock spaces with Lagrangian subspaces of zero modes of the Dirac Hamiltonian that naturally appear in the index theorem. We describe the significance of our constructions for the bulkboundary correspondence in a large class of time-reversal invariant gauge-gravity symmetryprotected topological phases of quantum matter with gapless charged boundary fermions, including the standard topological insulator in 3 + 1 dimensions. • Dai-Freed theories describing chiral anomalies in odd dimensions d have been sketched in [Mon15]. They are an extended version of the field theories constructed in [DF95].• Wess-Zumino theories describing the anomaly in self-dual field theories have been constructed in [Mon15].• The theory describing the anomaly of the worldvolume theory of M5-branes has been constructed as an unextended quantum field theory in [Mon17].

show abstract

Parametrised Homotopy Theory and Gauge Enhancement

Braunack-Mayer

2019

Fortschritte der Physik

View full text Add to dashboard Cite

show abstract

Corners in M-theory

Cited by 10 publications

References 54 publications

The Rational Higher Structure of M‐theory

The Rational Higher Structure of M‐theory

Extended Quantum Field Theory, Index Theory, and the Parity Anomaly

Parametrised Homotopy Theory and Gauge Enhancement

Contact Info

Product

Resources

About