K.S. Narain

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.

R4 couplings in M- and type II theories on Calabi-Yau spaces

We discuss several implications of R^4 couplings in M theory when compactified on Calabi-Yau (CY) manifolds. In particular, these couplings can be predicted by supersymmetry from the mixed gauge-gravitational Chern-Simons couplings in five dimensions and are related to the one-loop holomorphic anomaly in four-dimensional N=2 theories. We find a new contribution to the Einstein term in five dimensions proportional to the Euler number of the internal CY threefold, which corresponds to a one-loop correction of the hypermultiplet geometry. This correction is reproduced by a direct computation in type II string theories. Finally, we discuss a universal non-perturbative correction to the type IIB hyper-metric.Abstract We discuss several implications of R4 couplings in M-theory when compactified on Calabi-Yau (CY) manifolds. In particular, these couplings can be predicted by supersymmetry from the mixed gauge-gravitational Chem-Simons couplings in five dimensions and are related to the one-loop holomorphic anomaly in four-dimensional N = 2 theories. We find a new contribution to the Einstein term in five dimensions proportional to the Euler number of the internal CY threefold, which corresponds to a one-loop correction of the hypermultiplet geometry. This correction is reproduced by a direct computation in type 11 string theories. Finally, we discuss a universal non-perturbative correction to the type IIB hyper-metric.

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.

On subleading contributions to the AdS / CFT trace anomaly

In the context of the AdS/CFT correspondence, we perform a direct computation in AdS5 supergravity of the trace anomaly of a d = 4, = 2 SCFT. We find agreement with the field theory result up to next to leading order in the 1/N expansion. In particular, the order N gravitational contribution to the anomaly is obtained from a Riemann tensor squared term in the 7-brane effective action deduced from heterotic - type I duality. We also discuss, in the AdS/CFT context, the order N corrections to the trace anomaly in d = 4, = 4 SCFTs involving SO or Sp gauge groups.

Moduli corrections to gravitational couplings from string loops

We study moduli dependent threshold corrections to gravitational couplings in the case of the heterotic string compactified on a symmetric orbifold, for untwisted moduli, extending the previous analysis on gauge couplings. Like in the gauge case, the contribution comes entirely from the spacetime N = 2 sector. As a byproduct, this calculation provides a simple derivation of the trace anomaly coefficients for the different fields coupled to gravity.

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.

Structure constants of planar Script N = 4 Yang Mills at one loop

We study structure constants of gauge invariant operators in planar = 4 Yang-Mills at one loop with the motivation of determining features of the string dual of weak coupling Yang-Mills. We derive a simple renormalization group invariant formula characterizing the corrections to structure constants of any primary operator in the planar limit. Applying this to the scalar SO(6) sector we find that the one loop corrections to structure constants of gauge invariant operators is determined by the one loop anomalous dimension hamiltonian in this sector. We then evaluate the one loop corrections to structure constants for scalars with arbitrary number of derivatives in a given holomorphic direction. We find that the corrections can be characterized by suitable derivatives on the four point tree function of a massless scalar with quartic coupling. We show that individual diagrams violating conformal invariance can be combined together to restore it using a linear inhomogeneous partial differential equation satisfied by this function.

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.

Deformed topological partition function and Nekrasov backgrounds

A deformation of the N = 2 topological string partition function is analyzed by considering higher dimensional F-terms of the type W 2gn , where W is the chiral Weyl superfield and eachfactor stands for the chiral projection of a real function of N = 2 vector multiplets. These terms generate physical amplitudes involving two anti-self-dual Riemann tensors, 2g − 2 anti-self-dual graviphoton field strengths and 2n self-dual field strengths from the matter vector multiplets. Their coefficients Fg,n generalizing the genus g partition function Fg,0 of the topological twisted type II theory, can be used to define a generating functional by introducing deformation parameters besides the string coupling. Choosing all matter field strengths to be that of the dual heterotic dilaton supermultiplet, one obtains two parameters that we argue should correspond to the deformation parameters of the Nekrasov partition function in the field theory limit, around the conifold singularity. Its perturbative part can be obtained from the one loop analysis on the heterotic side. This has been computed in (1) and in the field theory limit shown to be given by the radius deformation of c = 1 CFT coupled to two-dimensional gravity. Quite remarkably this result reproduces the gauge theory answer up to a phase difference that may be attributed to the regularization procedure. The type II results are expected to be exact and should also capture the part that is non-perturbative in heterotic dilaton.