The paper constructs arbitrary networks of 10d non-tachyonic heterotic string theories via cobordism-implied junctions and gives worldsheet realizations for graphs, higher-dimensional networks, and compact configurations with sectors on different spaces.
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Eleven-Dimensional Supergravity on a Manifold with Boundary
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abstract
In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with boundary, which is believed to be relevant to the strong coupling limit of the $E_8\times E_8$ heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of $E_8$ for each boundary component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum $M$-theory with eleven-dimensional supergravity as its low energy limit.
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Hořava-Witten theory on S¹∨S¹ is dual to a type 0B orientifold with SO(16)^4 gauge group, explaining gauge group doubling via the geometry's junction and revealing two variants from E8 wall orientations.
Explicit worldsheet constructions of 9d junctions joining several 10d string theories via generalized RG flow interpolations and closed tachyon condensation, providing dynamical realizations of multi-theory cobordisms.
Witten's conformal boundary condition admits no half-supersymmetric extension in linearized minimal supergravity because supersymmetry maps the natural gravitino datum to the trace-free extrinsic curvature left unfixed by the conformal prescription.
The Kaluza-Klein tower functions as a MIMO gravitational communication channel between branes, with modes acting as subchannels for encoding information via occupation, phases, and timing.
Under a duality symmetry assumption, minimal supergravity coupled to two vector multiplets in D=8 is uniquely fixed in the BPS sector by anomaly cancellation, uplifts, and gauge enhancement.
Proposes a refinement of the Swampland Cobordism Conjecture for duality groups, arguing that diverging commutator widths necessitate infinitely many duality defects to realize monodromies in 9d supergravity bordisms.
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
A duality web is proposed in which Z2 quotients of M-theory on S1 vee S1 and F-theory on (S1 vee S1) x S1 map to 0A/0B orientifolds and non-supersymmetric E-type and D-type heterotic strings, providing evidence for existing dualities.
Hořava-Witten theory offers a potential string embedding of the dark dimension by localizing the Standard Model on the 11th interval, with symmetric tadpole cancellation and an infinite-distance limit helping derive the scalar potential and couplings from Schwinger integrals.
A consistent set of rules from M-theory on S¹ ∨ S¹ combined with type I' enhancements reproduces the light spectra, gauge groups, and global structure of ten-dimensional heterotic string theories, with indications of junctions between them.
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The Art of Branching: Cobordism Junctions of 10d String Theories
Explicit worldsheet constructions of 9d junctions joining several 10d string theories via generalized RG flow interpolations and closed tachyon condensation, providing dynamical realizations of multi-theory cobordisms.