Observations on the Moduli Space of Superconformal Field Theories

Abstract Some aspects of the moduli space of superconformal field theories are discussed. It is helpful to consider the conformal field theory as a background for propagation of strings and to exploit the space-time interpretation. Using this point of view we show that the metric on the moduli space of N = 4 superconformal field theory with c = 6 is locally that of O(20,4)/O(20) × O(4). We also discover some properties of the moduli space of N = 2 superconformal field theories with c = 9. Particular examples of these conformal field theories are sigma models on four- and six-dimensional Calabi-Yau spaces. Therefore, we can use this technique to learn about the moduli space of these spaces. For c = 6 we recover the known moduli space of K3. Our analysis of the c = 9 system leads to a new coupling in four dimensional supergravity. As a by-product, we prove that gauge couplings cannot depend on the moduli of N = 1 space-time supersymmetric compactifications.

[1]  Strings in background fields , 1985 .

[2]  Nathan Seiberg,et al.  Comments on the N = 2,3,4 superconformal algebras in two dimensions , 1987 .

[3]  M. D. Roo,et al.  Matter coupling in N = 4 supergravity , 1985 .

[4]  L. Girardello,et al.  The effective interactions of chiral families in four-dimensional superstrings☆ , 1987 .

[5]  A. Sen.  Central charge of the Virasoro algebra for supersymmetric sigma models on Calabi-Yau manifolds , 1986 .

[6]  Dine,et al.  Nonrenormalization theorems in superstring theory. , 1986, Physical review letters.

[7]  P. Vecchia,et al.  N=2 Extended Superconformal Theories in Two-Dimensions , 1985 .

[8]  D. Gross,et al.  Superstring Modifications of Einstein's Equations , 1986 .

[9]  S. Ferrara,et al.  General Dimensional Reduction of Ten-Dimensional Supergravity and Superstring , 1986 .

[10]  L. Girardello,et al.  Vector multiplets coupled to N=2 supergravity: Super-Higgs effect, flat potentials and geometric structure , 1985 .

[11]  E. Witten.  Dimensional Reduction of Superstring Models , 1985 .

[12]  E. Witten.  New Issues in Manifolds of SU(3) Holonomy , 1986 .

[13]  C. Vafa,et al.  On Four-Dimensional Gauge Theories from Type II Superstrings , 1987 .

[14]  K. Narain.  New Heterotic String Theories in Uncompactified Dimensions < 10 , 1986 .

[15]  A. Sen.  (2, 0) Supersymmetry and Space-Time Supersymmetry in the Heterotic String Theory , 1986 .

[16]  L. Girardello,et al.  Effective Lagrangians for Four-dimensional Superstrings , 1987 .

[17]  T. Eguchi,et al.  Unitary representations of the N=4 superconformal algebra , 1987 .

[18]  A. Proeyen,et al.  Structure of N=2 Supergravity , 1981 .

[19]  P. G. Lauwers,et al.  GAUGE AND MATTER FIELDS COUPLED TO N = 2 SUPERGRAVITY , 1984 .

[20]  A. Todorov.  Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surfaces , 1980 .

[21]  E. Witten,et al.  Matter couplings in N = 2 supergravity , 1983 .

[22]  P. Ginsparg,et al.  Finiteness of Ricci flat supersymmetric non-linear σ-models , 1985 .

[23]  M. Dine,et al.  Couplings and scales in superstring models , 1985 .

[24]  Some properties of O(32) superstrings , 1984 .

[25]  T. Banks,et al.  Non-perturbative infinities , 1986 .

[26]  C. Hull.  Ultra-violet finiteness of supersymmetric non-linear sigma models , 1985 .

[27]  P. Vecchia,et al.  On the unitary representations of N = 2 superconformal theory , 1986 .

[28]  M. Dine,et al.  Microscopic knowledge from macroscopic physics in string theory , 1988 .

[29]  The Conformal Field Theory of Orbifolds , 1987 .

[30]  P. Vecchia,et al.  Explicit construction of unitary representations of the N = 2 superconformal algebra , 1986 .

[31]  Vacuum configurations for superstrings , 1985 .

[32]  Michael B. Green,et al.  Anomaly-free chiral theories in six dimensions , 1985 .

[33]  A. Sen,et al.  Conformal invariance of supersymmetric σ-models on Calabi-Yau manifolds , 1986 .

[34]  C. Lovelace.  Stability of string vacua: (I). A new picture of the renormalization group , 1986 .

[35]  A. Kent,et al.  Determinant Formulae and Unitarity for the N=2 Superconformal Algebras in Two-Dimensions or Exact Results on String Compactification , 1986 .

[36]  P. G. Lauwers,et al.  Lagrangians of N = 2 supergravity-matter systems , 1985 .

[37]  A. Sen.  Heterotic string theory on Calabi-Yau manifolds in the Green-Schwarz formalism☆ , 1987 .

[38]  E. Witten,et al.  Nonperturbative Effects on the String World Sheet , 1987 .

[39]  C. Lovelace.  Strings in Curved Space , 1984 .

[40]  A. Proeyen,et al.  Potentials and symmetries of general gauged N = 2 supergravity-Yang-Mills models , 1984 .

[41]  E. Martinec,et al.  The Renormalization Group and String Field Theory , 1987 .