M-Theory

#import "@preview/cetz:0.5.2": canvas, draw
#import draw: arc, bezier, content, merge-path, on-layer, set-style

#set page(width: auto, height: auto, margin: 10pt, fill: none)
#set text(size: 14pt)

#canvas(length: 1cm, {
  draw.scale(1.2)

  // Vertices: (position, arc-start, arc-stop)
  let vertices = (
    ((-4.5, -1.2), -34deg, 45deg),
    ((-2.8, 3.5), -90deg, -11deg),
    ((4.5, 3), 180deg, 256deg),
    ((5, -2.3), 124deg, 194deg),
    ((0, -5.2), 56deg, 124deg),
  )
  // Pentagon edge controls
  let edge-ctrls = (
    ((-3.2, 0.2), (-2.8, 1.8)),
    ((0.2, 2.8), (2.2, 2.8)),
    ((4, 0.8), (4, -0.2)),
    ((3, -2.8), (1.2, -3.5)),
    ((-1.2, -3.5), (-2.8, -2.3)),
  )
  // Arrow data: (from-off, to-off, ctrl1, ctrl2, label, label-pos, anchor)
  // Control points for moderate curvature
  let arrows = (
    (
      (-0.3, 0.3),
      (-0.3, -0.3),
      (-5.4, 0.5),
      (-4.5, 2.4),
      align(center)[compac-\ tification],
      (-4.5, 2.1),
      "east",
    ),
    (
      (0.3, 0.2),
      (-0.2, 0.3),
      (-0.1, 4.8),
      (2.2, 4.5),
      [M-theory],
      (0.6, 4.4),
      "south",
    ),
    (
      (0.3, -0.2),
      (0.3, 0.3),
      (5.8, 1.6),
      (5.9, 0.0),
      [T-duality],
      (5.8, 0.6),
      "west",
    ),
    (
      (-0.2, -0.3),
      (0.3, -0.2),
      (3.8, -4.3),
      (1.6, -5.5),
      align(center)[orientifold\ action $Omega$],
      (3.9, -4.5),
      "north",
    ),
    (
      (-0.3, -0.2),
      (-0.2, -0.3),
      (-1.6, -5.5),
      (-4.5, -3.2),
      [S-duality],
      (-4.0, -4.2),
      "north",
    ),
  )
  // Node labels: (offset, label, anchor) - positioned close to cusp tips
  let labels = (
    ((-0.6, -0.3), align(center)[heterotic\ $S O(32)$], "east"),
    ((-0.3, 0.6), align(center)[heterotic\ $E(8) times E(8)$], "south"),
    ((0.5, 0.3), [Type II A], "west"),
    ((0.5, 0), [Type II B], "west"),
    ((0, -0.5), [Type I], "north"),
  )

  let off(pt, delta) = (pt.at(0) + delta.at(0), pt.at(1) + delta.at(1))

  // Build pentagon path
  let pentagon = {
    for idx in range(5) {
      let (pt, ..) = vertices.at(idx)
      let (next, ..) = vertices.at(calc.rem(idx + 1, 5))
      let (ctrl1, ctrl2) = edge-ctrls.at(idx)
      if idx == 0 { bezier(pt, next, ctrl1, ctrl2) } else {
        bezier((), next, ctrl1, ctrl2)
      }
    }
  }

  on-layer(0, merge-path(
    pentagon,
    close: true,
    fill: gray.transparentize(70%),
    stroke: none,
  ))

  on-layer(1, {
    set-style(stroke: (paint: rgb("#00008b"), thickness: 0.8pt), fill: none)
    for (pt, start, stop) in vertices {
      for rad in (0.15, 0.3, 0.45, 0.6, 0.75, 0.9) {
        arc(pt, start: start, stop: stop, radius: rad, anchor: "origin")
      }
    }
  })

  on-layer(2, merge-path(pentagon, close: true, fill: none, stroke: (
    paint: rgb("#666"),
    thickness: 2pt,
  )))

  on-layer(3, {
    let arrow-gray = rgb("#555")
    set-style(
      stroke: (paint: arrow-gray, thickness: 1.2pt),
      mark: (
        fill: arrow-gray,
        stroke: arrow-gray,
        scale: 0.8,
        start: "stealth",
        end: "stealth",
      ),
    )

    for (
      idx,
      (off1, off2, ctrl1, ctrl2, lbl, label-pos, anchor),
    ) in arrows.enumerate() {
      let (p1, ..) = vertices.at(idx)
      let (p2, ..) = vertices.at(calc.rem(idx + 1, 5))
      bezier(off(p1, off1), off(p2, off2), ctrl1, ctrl2)
      content(label-pos, lbl, anchor: anchor)
    }

    for (idx, (delta, lbl, anchor)) in labels.enumerate() {
      content(off(vertices.at(idx).at(0), delta), lbl, anchor: anchor)
    }

    content(
      (0, -0.5),
      align(
        center,
      )[parameter space of \ #text(size: 1.4em, weight: "bold")[M-Theory]],
      anchor: "center",
    )
  })
})