Superpotentials from stringy instantons without orientifolds

Abstract

In this paper we show that it is possible to derive non-perturbative superpotential terms from a stringy instanton without introducing orientifold planes. The instanton is realized by a Euclidean D brane wrapping a non-trivial cycle upon which we also wrap a single space-filling D brane. The standard problem of unwanted neutral fermionic zero modes is evaded by the appearance of couplings to charged bosonic zero modes in the instanton moduli action. Since the Euclidean D brane wraps a cycle which is not associated to any low energy gauge dynamics, it can not be interpreted as an ordinary gauge instanton, but rather as a stringy one. By considering such a brane configuration at an orbifold singularity, we can explicitly evaluate the instanton moduli space integral and find a holomorphic superpotential term with the structure of a baryonic mass term.

Stringy instantons as strong dynamics

“…In this appendix we show that there is no disagreement between the stringy instanton contributions of [8,7] and our results.…”

“…In this appendix we show, via dimensional arguments similar to [8], that the integration over the bosonic zero modes of the stringy instantons change the results of the fermionic integration only by a constant factor. We analyze the general bosonic integration for the U(1) and the SP (2) instanton.…”

“…A stringy instanton on a SU(1) node gives rise to a superpotential term [5,8,10]. The cycle wrapped by the euclidean D-brane is occupied also by one D-brane and the non trivial interaction lifts the fermionic zero modes.…”

“…the integral on λα can be performed as in [8] using the S 1 part of the instanton action and it gives the ADHM fermionic constraints. It also saturates the fermionic integration on µ AA and µ AA .…”

“…The theory studied in [8] is the C 3 /(Z 2 × Z 2 ) orbifold. This is a quiver gauge theory with four gauge groups, described by the superpotential The ranks of the groups are (N 1 , N 2 , N 3 , N 4 ) = (N 1 , N 2 , 1, 0).…”