Nonperturbative Yukawa Couplings from String Instantons

Abstract

Nonperturbative D-brane instantons can generate perturbatively absent though phenomenologically relevant couplings for type II orientifold compactifications with D-branes. We discuss the generation of the perturbatively vanishing SU(5) GUT Yukawa coupling of type (10 10 5 H ). Moreover, for a simple globally consistent intersecting D6-brane model, we discuss the generation of mass terms for matter fields. This can serve as a mechanism for decoupling exotic matter. Introduction.-Nonperturbative mass generation by gauge instantons is essential to explain the pattern of meson masses in QCD. Specifically, QCD instantons generate a nonperturbative, effective fermion interaction [1] that involves N f flavors of quark fields and breaks the perturbative U1 A axial symmetry to a discrete Z 2N F subgroup. In this way the mass of the 0 meson gets generated [2,3]. In addition, gauge instantons of the weak SU2 gauge group are responsible for baryon number violating processes in the standard model of particle physics. DisciplinesFollowing these observations, it would be very interesting if also some of the quark and lepton masses are of nonperturbative origin in theories beyond the standard model. For instance, Weinberg [4] suggested that quark masses could be due to gauge instantons of some hypercolor interactions in subquark models.Also in string theory compactifications, quark and lepton masses, or rather the respective Yukawa couplings, can be generated by nonperturbative effects, more precisely by string world-sheet [5] or by spacetime instantons. Most importantly, string theory opens up some new perspectives in that nonperturbative effects do not only include gauge instantons of the effective gauge theory, but also entirely stringy instantons not related to effective gauge interactions. In fact, during the last year there has been some progress towards a better understanding of nonperturbative effects in N 1 supersymmetric four-dimensional string compactifications on Calabi-Yau orientifolds ([6 -9] and further developments in [10 -19]; for closely related earlier work see [20,21]). Type IIA orientifolds with intersecting D6-branes (see, e.g., the recent reviews [22,23] for references) receive nonperturbative corrections from Euclidean D2-brane instantons, short E2-instantons, wrapping special Lagrangian three-cycles of the internal Calabi-Yau space.Once a conformal field theory (CFT) description of the background is available, the induced nonperturbative couplings can be studied using methods from open string theory. An analysis of the zero mode structure of such instantons shows that so-called O(1)-instantons [14 -17] can

Progress in D‐brane model building

“…The relevant Euclidean D-branes in the latter case are those which intersect the space-filling D-branes of a given model, generating a non-perturbative superpotential for the chiral matter fields. The phenomenological consequences of these instanton effects have been recently analyzed in [155][156][157] (see also [158,159]), with the result that they provide new sources for moduli stabilization, generation of µ-terms and neutrino Majorana masses. Just like all the other developments described in this review, instantonic D-branes represent a piece of progress in approaching string theory to particle physics.…”

Gauge theory analog of some “stringy” D-instantons

“…Such D-branes are usually refered to as "stringy" instantons. Especially, they can lead to phenomenologically desirable couplings as for example Majorana mass terms [1,2] or Yukawa couplings [4] and turned out as well to be useful for constructing models which feature dynamically supersymmetry breaking [5][6][7][8]. The conditions under which a non-perturbative contribution to the low-energy effective gauge theory can be generated by a "stringy" instanton are quite restrictive.…”

Rigid D6-branes on $ {{{{T^6}}} \left/ {{\left( {{Z_2} \times {Z_{2M}} \times \Omega \mathcal{R}} \right)}} \right.} $ with discrete torsion

“…Rigid branes also admit non-vanishing instanton contributions to the superpotential, Kähler potential [35,36] and gauge kinetic function due to their minimal number of zero modes (see e.g. the review [37] and references therein), which can generate non-perturbative neutrino masses [38,39], µ-terms [40], perturvatively forbidden Yukawa couplings [41,42] or might even trigger supersymmetry breaking [43].…”