Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTwisted Cohomotopy implies M5-brane anomaly cancellation
166
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then we prove that this subtlety is resolved under the hypothesis that the C-field flux is charge-quantized in the generalized cohomology theory called J-twisted Cohomotopy.
rate research
Read More
We show that charge-quantization of the M-theory C-field in J-twisted Cohomotopy implies emergence of a higher Sp(1)-gauge field on single heterotic M5-branes, which exhibits worldvolume twisted String structure.
We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Horava-Wittens proposal for the extension of the Green-Schwarz mechanism from heterotic string theory to heterotic M-theory. We discuss how this squares with the Hypothesis H that the elusive mathematical foundation of M-theory is based on charge quantization in J-twisted Cohomotopy theory.
There are fundamental open problems in the precise global nature of RR-field tadpole cancellation conditions in string theory. Moreover, the non-perturbative lift as M5/MO5-anomaly cancellation in M-theory had been based on indirect plausibility arguments,lacking a microscopic underpinning in M-brane charge quantization. We provide a framework for answering these questions, crucial not only for mathematical consistency but also for phenomenological accuracy of string theory, by formulating the M-theory C-field on flat M-orientifolds in the generalized cohomology theory called Equivariant Cohomotopy. This builds on our previous results for smooth but curved spacetimes, showing in that setting that charge quantization in twisted Cohomotopy rigorously implies a list of expected anomaly cancellation conditions. Here we further expand this list by proving that brane charge quantization in unstable equivariant Cohomotopy implies the anomaly cancellation conditions for M-branes and D-branes on flat orbi-orientifolds. For this we (a) use an unstable refinement of the equivariant Hopf-tom Dieck theorem to derive local/twisted tadpole cancellation, and (b) the lift to super-differential cohomology to establish global/untwisted tadpole cancellation. Throughout, we use (c) the unstable Pontrjagin-Thom theorem to identify the brane/O-plane configurations encoded in equivariant Cohomotopy and (d) the Boardman homomorphism to equivariant K-theory to identify Chan-Paton representations of D-brane charge. We find that unstable equivariant Cohomotopy, but not its image in K-theory, distinguishes D-brane charge from the finite set of types of O-plane charges.
The celebrated Green-Schwarz mechanism in heterotic string theory has been suggested to secretly underly a higher gauge theoretic phenomenon, embodying a higher Bianchi identity for a higher-degree analog of a curvature form of a higher gauge field. Here we prove that the non-perturbative Horava-Witten Green-Schwarz mechanism for heterotic line bundles in heterotic M-theory with M5-branes parallel to MO9-planes on $A_1$-singularities is accurately encoded in the higher gauge theory for higher gauge group of the equivariant homotopy type of the Z/2-equivariant A-infinity-loop group of twistor space. In this formulation, the flux forms of the heterotic gauge field, the B-field on the M5-brane, and of the C-field in the M-theory bulk are all unified into the character image of a single cocycle in equivariant twistorial Cohomotopy theory; and that cocycle enforces the quantization condition on all fluxes: the integrality of the gauge flux, the half-shifted integrality of the C-field flux and the integrality of the dual C-field flux (i.e., of the Page charge in the bulk and of the Hopf-WZ term on the M5-brane). This result is in line with the Hypothesis H that M-brane charges are quantized in J-twisted Cohomotopy theory. The mathematical essence of our proof is, first, the construction of the equivariant twisted non-abelian character map via an equivariant twisted non-abelian de Rham theorem, which we prove; and, second, the computation of the equivariant relative minimal model of the Z/2-equivariant Sp(1)-parametrized twistor fibration. We lay out the relevant background in equivariant rational homotopy theory and explain how this brings about the subtle flux quantization relations in heterotic M-theory.
We introduce a differential refinement of Cohomotopy cohomology theory, defined on Penrose diagram spacetimes, whose cocycle spaces are unordered configuration spaces of points. First we prove that brane charge quantization in this differential 4-Cohomotopy theory implies intersecting p/(p+2)-brane moduli given by ordered configurations of points in the transversal 3-space. Then we show that the higher (co-)observables on these brane moduli, conceived as the (co-)homology of the Cohomotopy cocycle space, are given by weight systems on horizontal chord diagrams and reflect a multitude of effects expected in the microscopic quantum theory of Dp/D(p+2)-brane intersections: condensation to stacks of coincident branes and their Chan-Paton factors, BMN matrix model and fuzzy funnel states, M2-brane 3-algebras, the Hanany-Witten rules, AdS3-gravity observables, supersymmetric indices of Coulomb branches as well as gauge/gravity duality between all these. We discuss this in the context of the hypothesis that the M-theory C-field is charge-quantized in Cohomotopy theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
