{
  "id": "1612.06295",
  "version": "v1",
  "published": "2016-12-19T18:01:51.000Z",
  "updated": "2016-12-19T18:01:51.000Z",
  "title": "A construction of Frobenius manifolds from stability conditions",
  "authors": [
    "Anna Barbieri",
    "Jacopo Stoppa",
    "Tom Sutherland"
  ],
  "comment": "44 pages",
  "categories": [
    "math.AG",
    "hep-th",
    "math.DG"
  ],
  "abstract": "A finite quiver $Q$ without loops or 2-cycles defines a 3CY triangulated category $D(Q)$ and a finite heart $A(Q)$. We show that if $Q$ satisfies some (strong) conditions then the space of stability conditions $Stab(A(Q))$ supported on this heart admits a natural family of semisimple Frobenius manifold structures, constructed using the invariants counting semistable objects in $D(Q)$. In the case of $A_n$ evaluating the family at a special point we recover a branch of the Saito Frobenius structure of the $A_n$ singularity $y^2 = x^{n+1}$. We give examples where applying the construction to each mutation of $Q$ and evaluating the families at a special point yields a different branch of the maximal analytic continuation of the same semisimple Frobenius manifold. In particular we check that this holds in the case of $A_n$, $n \\leq 5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-19T18:01:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stability conditions",
      "construction",
      "semisimple frobenius manifold structures",
      "saito frobenius structure",
      "special point yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}