Vadim S. Kaplunovsky

Moduli dependence of string loop corrections to gauge coupling constants

We consider one-loop corrections 4Δa to inverse gauge couplings ga−2 in supersymmetric vacua of the heterotic string. The form of these corrections plays an important role in scenarios for dynamical supersymmetry breaking in string theory. Specifically, we calculate the exact functional dependence of Δa(U) on any untwisted modulus field U of an orbifold vacuum; it has the universal form Δa(U, U)=Aa·log(|η(U)|4·lm U)+const., where Aa are easily computable rational constants. The dependence is nontrivial (Aa≠0) only if some sectors of the orbifold Hilbert space have precisely N=2 space-time supersymmetry. The expression for Δa has an expected invariance under modular transformations of U, since these are symmetries of the orbifold vacuum state. However, Δa is not the real part of a holomorphic function, in seeming contradiction with the existence of a supersymmetric effective lagrangian. The apparent paradox is an infrared problem, and can occur not just in string theory but in renormalizable supersymmetric field theories as well. We show how the paradox is resolved in the field theory case and argue that the same resolution applies also to the string theory case.

Model-independent analysis of soft terms in effective supergravity and in string theory

Abstract We discuss supersymmetry breakdown in effective supergravities such as emerge in the low-energy limit of superstring theory. Without specifying the precise trigger of the breakdown, we analyse the soft parameters in the Lagrangian of the supersymmetrized Standard Model.

One-loop threshold effects in string unification

Like grand unification of old, string unification predicts simple tree-level relations between the couplings of all unbroken gauge groups such as SU(3)C or SU(2)W. I show here how to compute one-loop corrections to these relations for any four-dimensional model based on a classical vacuum of the heterotic string. The result can be used to calculate both sin2θWand ΛQCD in terms of αQCD and MPlanck.

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

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 E6 ⊗ E8, 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 273 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 Kahler manifolds of restricted type, spanned by the moduli related respectively to the 27 and 27 matter fields. The holomorphic functions of the moduli generating the two restricted Kahler metrics also determine the Yukawa couplings of the matter fields. We derive explicit formulae 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 E6 ⊗ E8; this phenomenon is illustrated using the examples of (2, 2) orbifolds and tensor products of minimal N = 2 theories.

Perturbative couplings of vector multiplets in N = 2 heterotic string vacua

Abstract We study the low-energy effective Lagrangian of N = 2 heterotic string vacua at the classical and quantum level. The couplings of the vector multiplets are uniquely determined at the tree level, while the loop corrections are severely constrained by the exact discrete symmetries of the string vacuum. We evaluate the general transformation law of the perturbative prepotential and determine its form for the toroidal compactifications of six-dimensional N = 1 supersymmetric vacua.

Field dependent gauge couplings in locally supersymmetric effective quantum field theories

Abstract We investigate the field dependence of the gauge couplings of locally supersymmetric effective quantum field theories. We find that the Weyl rescaling of supergravity gives rise to Wess-Zumino terms that affect the gauge couplings at the one-loop level. These Wess-Zumino terms are crucial in assuring supersymmetric consistency of both perturbative and non-perturbative gauge interactions. At the perturbative level, we distinguish between the holomorphic wilsonian gauge couplings and the physically-measurable momentum-dependent effective gauge couplings; the latter are affected by the Konishi and the super-Weyl anomalies and their field-dependence is non-holomorphic. At the non-perturbative level, we show how consistency of the scalar potential generated by infrared-strong gauge interactions with the local supersymmetry requires a very specific form of the effective superpotential. We use this superpotential to determine the dependence of the supersymmetric condensates of a strongly interacting gauge theory on its (field-dependent) wilsonian gauge coupling and the Yukawa couplings of the matter fields. The article concludes with the discussion of the field-dependent non-perturbative phenomena in the context of string unification.We investigate the field dependence of the gauge couplings of locally supersymmetric effective quantum field theories. We find that the Weyl rescaling of supergravity gives rise to Wess-Zumino terms that affect the gauge couplings at the one-loop level. These Wess-Zumino terms are crucial in assuring supersymmetric consistency of both perturbative and non-perturbative gauge interactions. At the perturbative level, we distinguish between the holomorphic Wilsonian gauge couplings and the physically-measurable momentum-dependent effective gauge couplings; the latter are affected by the Konishi and the super-Weyl anomalies and their field-dependence is non-holomorphic. At the non-perturbative level, we show how consistency of the scalar potential generated by infrared-strong gauge interactions with the local supersymmetry requires a very specific form of the effective superpotential. We use this superpotential to determine the dependence of the supersymmetric condensates of a strongly interacting gauge theory on its (field-dependent) Wilsonian gauge coupling and the Yukawa couplings of the matter fields. The article concludes with the discussion of the field-dependent non-perturbative phenomena in the context of string unification.

On gauge couplings in string theory

Abstract We investigate the field dependence of the gauge couplings of N = 1 string vacua from the point of view of the low energy effective quantum field theory. We find that field-theoretical considerations severely constrain the form of the string loop corrections; in particular, the dilaton dependence of the gauge couplings is completely universal at the one-loop level. The moduli dependence of the string threshold corrections is also constrained, and we illustrate the power of such constraints with a detailed discussion of the orbifold vacua and the (2,2) (Calabi-Yau) vacua of the heterotic string.

Aspects of duality in N = 2 string vacua

We collect further evidence for the proposed duality between N = 2 heterotic and type II string vacua in a specific model suggested by Kachru and Vafa. In the gauge sector the previous analysis is extended; it is further shown that the duality also holds for the one-loop gravitational couplings to the vector multiplets. 1. The recent advances in understanding nonperturbative aspects of N = 2 supersymmetric YangMills theories [ I] have raised the question whether similar techniques are applicable in string theory. One of the key elements in the work of Seiberg and Witten is the relation between a gauge theory at strong coupling and a ‘dual’ theory at weak coupling with magnetic monopoles (dyons) as elementary excitations. This dual theory can be analyzed in perturbation theory and, as a consequence, the exact non-perturbative low energy effective action for all values of the coupling constant is determined. In order to apply such techniques to string theory, a similar strong-weak coupling duality has to be established. For N = 2 string theories it has been conjeetured that such a duality exists between heterotic vacua

Comments on the M theory approach to N = 1 SQCD and brane dynamics

Abstract We use the M theory approach of Witten to investigate N = 1 SU( N c ) SQCD with N f flavors. We reproduce the field theoretical results and identify in M theory the gluino condensate and the eigenvalues of the meson matrix. This approach allows us to identify the constant piece of the effective field theory coupling from which the coefficient of the one-loop β-function can be identified. By studying the area of the M-theory five-brane we investigate the stability of type IIA brane configurations. We prove that in a supersymmetric setup there is no force between static D4-branes that end on NS five-branes. The force in the case that there is a relative velocity between the branes is computed. We show that at the regions of intersecting IIA branes the curvature of the M theory five-brane is singular in the type IIA limit.

On four-dimensional gauge theories from type II superstrings

We study the four-dimensional gauge theories which are associated with classical vacua of the type II superstring, i.e. which correspond to a superconformal field theory on the world sheet. Using the fact that gauge symmetry arises from a supersymmetric affine Kac-Moody algebra, and demanding unitarity of the underlying world-sheet field theory, we show that no such vacua can yield the particle spectrum of the standard model. Of the gauge theories which are permitted by unitarity, we find that many can be constructed explicitly as orbifolds which twist the left- and right-moving degrees of freedom of the string asymmetrically; among these are three N = 4 supersymmetric models – which have previously been constructed in a quite different fashion – and two N = 1 supersymmetric models with chiral gauge representations for the massless fermions.