Non-perturbative Superpotentials Research Articles

The supersymmetric CP problem in orbifold compactifications

The possibility of spontaneous breaking of CP symmetry by the expectation values of orbifold moduli is investigated with particular reference to CP-violating phases in soft supersymmetry-breaking terms. The effect of different mechanisms for stabilizing the dilaton and the form of the non-perturbative superpotential on the existence and size of these phases is studied. Models with modular symmetries which are subgroups of PSL(2, Z) , as well as the single overall modulus T case with the full PSL(2, Z) modular symmetry, are discussed. Non-perturbative superpotentials involving the absolute modular invariant j(T), such as may arise from F-theory compactifications, are considered.

Aspects of N=1 string dynamics

We review several topics of interest in the study of 4d N=1 supersymmetric compactifications of the heterotic string. After a brief introduction to the construction of such models, our focus is on the novel physics which occurs at singularities in the moduli space of vacua. Among the phenomena we discuss are nonperturbative superpotentials, dynamical generation of poles in various low-energy couplings, and phase transitions which change the net number of chiral generations.

Fayet-Iliopoulos potentials from four-folds

We show how certain non-perturbative superpotentials W, which are the two-dimensional analogs of the Seiberg-Witten prepotential in 4d, can be computed via geometric engineering from 4-folds. We analyze an explicit example for which the relevant compact geometry of the 4-fold is given by $P^1$ fibered over $P^2$. In the field theory limit, this gives an effective U(1) gauge theory with N=(2,2) supersymmetry in two dimensions. We find that the analog of the SW curve is a K3 surface, and that the complex FI coupling is given by the modular parameter of this surface. The FI potential itself coincides with the middle period of a meromorphic differential. However, it only shows up in the effective action if a certain 4-flux is switched on, and then supersymmetry appears to be non-perturbatively broken. This can be avoided by tuning the bare FI coupling by hand, in which case the supersymmetric minimum naturally corresponds to a singular K3.

CP violation by soft supersymmetry breaking terms in orbifold compactifications

The possibility of spontaneous breaking of CP symmetry by the expectation values of orbifold moduli is investigated with particular reference to $CP$ violating phases in soft supersymmetry breaking terms. The effect of different mechanisms for stabilizing the dilaton and the form of the non-perturbative superpotential on the existence and size of these phases is studied. Non-perturbative superpotentials involving the absolute modular invariant $j(T)$, such as may arise from F-theory compactifications, are considered.

Singularities, gauge dynamics, and non-perturbative superpotentials in string theory

We describe a class of 4D N = 1 compactifications of the SO(32) heterotic/type I string theory which are destabilized by non-perturbatively generated superpotentials. In the type I description, the destabilizing superpotential is generated by a one instanton effect or gaugino condensation in a non-perturbative SU(2) gauge group. The dual, heterotic description involves destabilization due to world-sheet instanton or half world-sheet instanton effects in the two cases. A genericity argument suggests that a (global) supersymmetry-breaking model of Intriligator and Thomas might be typical in a class of string theory models. Our analysis also suggests that the tensionless strings which arise in the E 8 × E 8 theory in six dimensions when an instanton shrinks to zero size should, in some cases, have supersymmetry breaking dynamics upon further compactification to four dimensions. We provide explicit examples, constructed using F-theory, of the two cases of dynamically generated superpotentials.

Supersymmetry breaking and duality in SU( N) × SU( N − M) theories

We consider a class of N = 1 supersymmetric Yang-Mills theories, with gauge group SU( N) × SU( N − M) and fundamental matter content. Duality plays an essential role in analyzing the nonperturbative infrared dynamics of these models. We find that Yukawa couplings drive these theories into the confining phase, and show how the nonperturbative superpotentials arise in the dual picture. We show that the odd- N, M = 2 models with an appropriate tree-level superpotential break supersymmetry.

Non-perturbative superpotentials in string theory

The non-perturbative superpotential can be effectively calculated in M-theory compactification to three dimensions on a Calabi-Yau four-fold X. For certain X, the superpotential is identically zero, while for other X, a non-perturbative superpotential is generated. Using F-theory, these results carry over to certain Type IIB and heterotic string compactifications to four dimensions with N = 1 supersymmetry. In the heterotic string case, the non-perturbative superpotential can be interpreted as coming from space-time and world-sheet instantons; in many simple cases contributions come only from finitely many values of the instanton numbers.

Exact results for N=2 compactifications of heterotic strings

We search for N = 2, d = 4 theories which can be realized both as heterotic string compactifications on K 3 × T 2 and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on N=2 Yang-Mills theory, corrected by gravitational/stringy effects. We also discuss some examples which shed light on how the moduli spaces of different N=2 heterotic vacua are connected (This contribution to the conference proceeding has already been published in Nucl. Phys. B 450 (1995) 69).

Exact results for N = 2 compactifications of heterotic strings

We search for N = 2, d = 4 theories which can be realized both as heterotic string compactifications on K3 × T 2 and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on N = 2 Yang-Mills theory, corrected by gravitational/ stringy effects. We also discuss some examples which shed light on how the moduli spaces of different N = 2 heterotic vacua are connected.

Stringy domain walls and target-space modular invariance.

Based on the target-space modular invariance of the nonperturbative superpotential of the four-dimensional {ital N}=1 supersymmetric string vacua, we find topologically stable, stringy domain walls of nontrivial compactification modulus field configurations. They are supersymmetric solutions, thus saturating the Bogomolnyi bound. Their physical implications are discussed.

Decoupling gravity in F-theory

We study seven-brane SU(5) GUT models of string phenomenology which can be consistently analyzed in a purely local framework. The requirement that gravity can decouple constrains the form of four-dimensional physics as well as the geometry of spacetime. We rule out a large family of candidate UV completions of such models and derive a priori constraints on the local singularities of compact elliptic Calabi-Yau fourfolds. These constraints are strong enough to obstruct a wide class of brane constructions from UV completion in string theory. It is demonstrated that consistent local models always have exotic Yukawa coupling structures, and hidden sectors or interesting non-perturbative superpotentials which merit further investigation.