{
  "id": "1709.06238",
  "version": "v1",
  "published": "2017-09-19T03:45:30.000Z",
  "updated": "2017-09-19T03:45:30.000Z",
  "title": "Zero-energy states in conformal field theory with sine-square deformation",
  "authors": [
    "Shota Tamura",
    "Hosho Katsura"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of finite norm for the Hamiltonian of a CFT with SSD, except for the zero-energy vacuum state $|0\\rangle$. We then introduce a regularized version of the SSD Hamiltonian which is related to the undeformed Hamiltonian via a unitary transformation corresponding to the Mobius quantization. The unitary equivalence of the two Hamiltonians allows us to obtain zero-energy states of the deformed Hamiltonian in a systematic way. The regularization also provides a way to compute the expectation values of observables in zero-energy states that are not necessarily normalizable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-19T03:45:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal field theory",
      "zero-energy states",
      "sine-square deformation",
      "hamiltonian",
      "two-dimensional conformal field theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}