On effective field theories describing (2, 2) vacua of the heterotic string

Abstract

Classical vacua of the heterotic string corresponding to c = 9, N = (2,2) superconformal theories on the world sheet yield low-energy effective field theories with N = 1 space-time supersymmetry in four dimensions, gauge group EC @ Es, several families of 27 and 27 matter fields, and moduli fields. String theory relates matter fields to moduli; in this article we relate the kinetic terms in the effective Lagrangian for both moduli and matter fields to the 273 and z3 Yukawa couplings.Geometrically, we recover the result (obtained previously via the type II superstring and N = 2 supergravity) that moduli space is a direct product of two Mahler manifolds of restricted type, spanned by the moduli related respectively to the 27 and 27 matter fields. The holomorphic functions of the moduli genera,ting the' two restricted Kahler metrics also determine the Yukawa couplings of the matter fields. We derive explicit formulaa for the metric for the matter fields in terms of the metric for the corresponding moduli; the two metrics are not identical to each other.The precise relation between moduli and matter metrics takes a slightly different form on subspaces of the moduli space where the unbroken gauge symmetry is enhanced beyond Es @ E8 ; this phenomenon is illustrated using the examples of (2,2) orbifolds and tensor products of minimal N = 2 theories.

Recent efforts in the computation of string couplings

“…As expected, these constraints on the Kähler structure are inherited from the Wardidentities of the underlying (2,2) super-conformal algebra [9].…”

“…It is given by the two-point function of the corresponding truely marginal operators. Using superconformal Ward identities it was shown in [9] that the moduli manifold has the direct product structure…”

“…Let us denote the charged matter field by A and include it in the Kähler potential in the -3-following form: K = − log (t +t) 3 − AĀ(t +t) . (This is the lowest order appearance of the charged matter fields in the twisted sector of simple orbifold compactifications [9], [10].) For the Kähler potential to be invariant (up to a Kähler transformation), we need to require the following transformation properties for the matter fields: A → A (ict+d) 2 .…”

Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces

“…In these coordinates the 27 3 Yukawa couplings on X are simply the third derivatives with respect to the moduli of a prepotential from which the Kähler potential can also be derived. Whereas the left-moving N = 2 superconformal symmetry of (2,2) compactifications is necessary for having N = 1 space-time supersymmetry, it is the additional right-moving symmetry which is responsible for the special structure [29]. The paper is organized as follows.…”

Model-independent analysis of soft masses in heterotic string models with anomalous U(1) symmetry

“…The supergravity theory (SUGRA) is effectively constructed from 4-dimensional (4D) string model using several methods [1,2,3]. The structure of SUGRA is constrained by gauge symmetries including an anomalous U(1) symmetry (U(1) A ) [4] and stringy symmetries such as duality [5].…”