E. Gava

Topological amplitudes in string theory

We show that certain type II string amplitudes at genus g are given by the topological partition function Fg discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional effective action of the form ΣgFgW2g, where W is the chiral superfield of N = 2 supergravitational multiplet. The holomorphic anomaly of Fg is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings.

Moduli corrections to gauge and gravitational couplings in four-dimensional superstrings

We study one-loop, moduli-dependent corrections to gauge and gravitational couplings in supersymmetric vacua of the heterotic string. By exploiting their relation to the integrability condition for the associated CP-odd couplings, we derive general expressions for them, both for (2, 2) and (2, 0) models, in terms of tree-level four-point functions in the internal N = 2 superconformal theory. The (2, 2) case, in particular symmetric orbifolds, is discussed in detail.

Perturbative prepotential and monodromies in N = 2 heterotic superstring

We discuss the prepotential describing the effective field theory of N=2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic singularities due to the appearance of charged massless states at particular surfaces in the moduli space of vector multiplets. These singularities modify the classical duality symmetry group which now becomes a representation of the fundamental group of the moduli space minus the singular surfaces. For the simplest two-moduli case, this fundamental group turns out to be a certain braid group and we determine the resulting full duality transformations of the prepotential, which are exact in perturbation theory.

Effective μ-term in superstring theory☆

Abstract In four-dimensional compactifications of the heterotic superstring theory the Kahler potential has a form which generilly induces a superpotential mass term for Higgs particles once supersymmetry is broken at low energies. This “μ-term” is analyzed in a model-independent way at the tree level and in the one-loop approximation, and explicit expressions are obtained for orbifold compactifications. Additional contributions which arise in the case of supersymmetry breaking induced by gaugino condensation are also discussed.

Superstring threshold corrections to Yukawa couplings

Abstract A general method of computing string corrections to the Kahler metric and Yukawa couplings is developed at the one-loop level for a general compactification of the heterotic superstring theory. It also provides a direct determination of the so-called Green-Schwarz term. The matter metric has an infrared divergent part which reproduces the field-theoretical anomalous dimensions, and a moduli-dependent part which gives rise to threshold corrections in the physical Yukawa couplings. Explicit expressions are derived for symmetric orbifold compactifications.

Schwinger-Dyson equations for the two-matrix model and W3 algebra

Abstract The continuum Schwinger-Dyson equations for the two-matrix model, around the Ising critical point, are derived for operators involving one of the two matrices. It is shown that, within the space of the corresponding couplings, the resulting constraints obey a W 3 algebra.

Topological Amplitudes in Heterotic Superstring Theory

Abstract We show that certain heterotic string amplitudes are given in terms of correlators of the twisted topological (2,0) SCFT, corresponding to the internal sector of the N = 1 space-time supersymmetric background. The genus g topological partition function Fg corresponds to a term in the effective action of the form W2g, where W is the gauge or gravitational superfield. We study also recursion relations related to holomorphic anomalies, showing that, contrary to the type II case, they involve correlators of anti-chiral superfields. The corresponding terms in the effective action are of the form W2gΠn, where Π is a chiral superfield obtained by chiral projection of a general superfield. We observe that the structure of the recursion relations is that of N = 1 spacetime supersymmetry Ward identity. We give also a solution of the tree-level recursion relations and discuss orbifold examples.

Bound states of type I D-strings

Abstract We study the infrared limit of the O ( N ) gauge theory that describes the low energy modes of a system of N type I D-strings and provide some support to the conjecture that, in this limit, the theory flows to an orbiford conformal theory. We compute the elliptic genus of the orbifold theory and argue that its longest string sector describes the bound states of D-strings. We show that, as a result, the masses and multiplicities of the bound states are in agreement with the predictions of heterotic-type I duality in nine dimensions, for all the BPS charges in the lattice Γ (1,17) .We study the infra-red limit of the O(N) gauge theory that describes the low energy modes of a system of

N = 2 gauge theories on the hemisphere HS 4

N

Duality symmetries in N = 2 heterotic superstring

type I D-strings and provide some support to the conjecture that, in this limit, the theory flows to an orbifold conformal theory. We compute the elliptic genus of the orbifold theory and argue that its longest string sector describes the bound states of D-strings. We show that, as a result, the masses and multiplicities of the bound states are in agreement with the predictions of heterotic-type I duality in 9 dimensions, for all the BPS charges in the lattice