Nonperturbative Effects on Seven-Brane Yukawa Couplings

Physical Review D, 2014

We provide the last missing piece of the complete non-perturbative description of the low energy effective action emerging from Calabi-Yau compactifications of type II string theory-NS5-brane instanton corrections to the hypermultiplet moduli space MH. We find them using S-duality symmetry of the type IIB formulation. The result is encoded in a set of holomorphic functions on the twistor space of MH and includes all orders of the instanton expansion.

2016

We initiate a study of corrections to the Kähler potential of N = 1 type II/Ftheory compactifications that arise from curvature terms in the action of D-branes and orientifold planes. We first show that a recently proposed correction to the Kähler coordinates, which was argued to appear at order α ′2 g s and be proportional to the intersection volume of D7-branes and O7-planes, is an artifact of an inconvenient field basis in the dual M-theory frame and can be removed by a field redefinition of the 11D metric. We then analyze to what extent curvature terms in the DBI and WZ action may still lead to corrections of a similar kind and identify two general mechanisms that can potentially modify the volume dependence of the Kähler potential in the presence of D-branes and O-planes. The first mechanism is related to an induced Einstein-Hilbert term on warped brane worldvolumes, which leads to a shift in the classical volume of the compactification manifold. The resulting corrections are generic and can appear at one-loop order on branes and O-planes of various dimensions and for configurations with or without intersections. We discuss in detail the example of intersecting D7-branes/O7-planes, where a correction can appear already at order α ′2 g 2 s in the Kähler potential. Due to an extended no-scale structure, however, it is then still subleading in the scalar potential. We also discuss a second mechanism, which is due to an induced D3-brane charge in the WZ action of D7-branes. Contrary to the first type of corrections, it appears at open string tree-level and shifts the definition of the Kähler coordinates in terms of the classical volume but leaves the volume itself uncorrected. Our work has implications for moduli stabilization and model building and suggests interesting generalizations to F-theory.

Journal of High Energy Physics, 2004

There are two known sources of nonperturbative superpotentials for Kähler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux:

Journal of High Energy Physics, 2007

We investigate, at the microscopic level, the compatibility between D-term potentials from world-volume fluxes on D7-branes and non-perturbative superpotentials arising from gaugino condensation on a different stack of D7-branes. This is motivated by attempts to construct metastable de Sitter vacua in type IIB string theory via D-term uplifts. We find a condition under which the Kähler modulus, T , of a Calabi-Yau 4-cycle gets charged under the anomalous U (1) on the branes with flux. If in addition this 4-cycle is wrapped by a stack of D7-branes on which gaugino condensation takes place, the question of U (1)-gauge invariance of the (Tdependent) non-perturbative superpotential arises. In this case an index theorem guarantees that strings, stretching between the two stacks, yield additional charged chiral fields which also appear in the superpotential from gaugino condensation. We check that the charges work out to make this superpotential gauge invariant, and we argue that the mechanism survives the inclusion of higher curvature corrections to the D7-brane action.

2001

We study relevant deformations of the N = 2 superconformal theory on the world-volume of N D3 branes at an A k−1 singularity. In particular, we determine the vacuum structure of the mass-deformed theory with N = 1 supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular covariant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero-Moser integrable system.

Journal of High Energy Physics, 2004

At the leading order, the low-energy effective field equations in string theory admit solutions of the form of products of Minkowski spacetime and a Ricci-flat Calabi-Yau space. The equations of motion receive corrections at higher orders in α ′ , which imply that the Ricci-flat Calabi-Yau space is modified. In an appropriate choice of scheme, the Calabi-Yau space remains Kähler, but is no longer Ricci-flat. We discuss the nature of these corrections at order α ′ 3 , and consider the deformations of all the known cohomogeneity one non-compact Kähler metrics in six and eight dimensions. We do this by deriving the first-order equations associated with the modified Killing-spinor conditions, and we thereby obtain the modified supersymmetric solutions. We also give a detailed discussion of the boundary terms for the Euler complex in six and eight dimensions, and apply the results to all the cohomogeneity one examples.

Communications in …, 2004

We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and

Physics Letters B, 1987

We present the O(a' 3) heterotic string corrections to the supersymmetry transformation rules of D= 10, N= I supergravity multiplet, which satisfy the on-shell closure of supersymmetry. We also generalize this result to higher orders in a', assuming a natural form of the leading O (o~'") heterotic string corrections to the effective action of the supergravity multiplet. We find no modification to the Killing spinor equations for the gravitino and dilatino at O(a' 5) or higher, whenever fermionic condensates are absent. 1. Introduction. One of the most important features of ten-dimensional string theories [ 1 ] is the possibility of non-trivial (chiral) compactification into four-dimensional space-time (D=4) in the point field theory limit. In particular, in the heterotic string theory with the gauge group Es × E8 [2], the compactification on Calabi-Yau manifolds with SU(3) holonomy gives rise to D= 4, N= 1 surviving supersymmetry with the grand unification group E 6 [31. The analysis in ref. [ 3 ] was based on the tree-level O(c~') correction to the D= 10, N= 1 supergravity, that arise from the Green-Schwarz anomaly cancellation mechanism [4]. Recently, higher order corrections have been obtained by tree-level string amplitude calculations in D= 10 [5,6], and by amodel fl-function calculations in D = 2 [ 7 ]. Essential agreement between these two kinds of calculations has been found up to O(a'4). It is also claimed that the Calabi-Yau manifold is the solution of the treelevel field equations in D = 10 to all orders in ce' [ 8 ]. The original motivation [3] of considering the Calabi-Yau manifold for surviving supersymmetry, however, has become obscure, because the covariant supersymmetry transformation rules in D = 10 with higher order corrections in or' needed for Killing spi

2010

We consider string vacua formed by compactifying Type II string theories on toroidal orbifolds and generalised Calabi-Yau manifolds and their transformations under a set of non-perturbative dualities. The dualities are the Type IIA-IIB exchanging T duality, the self-symmetry of Type IIB S duality, the non-trivial combination of the two, U duality, and the generalisation of T duality to include Calabi-Yaus, mirror symmetry. The requirement of the effective theory superpotential being invariant under these dualities is used to justify additional fluxes which do not descend via compactification from the ten dimensional action, which form an N = 2 theory. Their non-geometric structures, Bianchi constraints and tadpoles are determined and then classified in terms of modular S duality induced multiplets. The Z2 Z2 orientifold is used as an explicit example of the general methods, with N = 1 Type IIB non-geometric vacua which possess T and S duality invariance also constructed. These are t...

Fortschritte der Physik, 2011

The fermion mass textures are discussed in the context of F-theory SU (5) GUT. The tree-level up, down and charged lepton Yukawa couplings are computed in terms of the integrals of overlapping wavefunctions at the intersection points of three matter curves. All remaining entries in the fermion mass matrices can also be reliably estimated from higher order non-renormalizable Yukawa couplings mediated by heavy string modes and/or Kaluza-Klein states.