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. ⋆ Research supported in part by: the NSF, under grant PHY–90–09850 (V.K.); the Robert A. Welch Foundation (V.K.); the Heisenberg Fellowship of the DFG (J.L.); the NATO, under grant CRG 931380 (V.K.&J.L.); the German-Israeli Foundation for Scientific Research (J.L.&S.T.). † Email: [email protected] ‡ Email: [email protected] § Email: [email protected] 1. The recent advances in understanding non-perturbative aspects of N = 2 supersymmetric Yang-Mills theories [1] 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 conjectured that such a duality exists between heterotic vacua compactified on the six-dimensional manifoldK3×T 2 and type II vacua compactified on a CalabiYau threefold [2–5]. The coupling constant in string theory is a dynamical variable determined by the vacuum expectation value of the dilaton S. In N = 2 heterotic vacua S resides in an abelian vector multiplet while in type II vacua it is a member of a hypermultiplet [6]. Combining the facts that there are no gauge neutral couplings between vector and hypermultiplets [7] and that S organizes the string perturbation theory implies a non-renormalization theorem for both, heterotic and type II vacua. For the heterotic vacua the tree level couplings of the hypermultiplets are exact whereas the tree level couplings of the vector multiplets are corrected at one-loop and non-perturbatively. In type II vacua the situation is reversed and the tree level couplings of the vector multiplets are exact while the hypermultiplets suffer perturbative and non-perturbative corrections. Thus, if a string vacuum has a dual representation as both heterotic and type II the exact effective Lagrangian can be obtained by computing the couplings of the vector multiplets in the type II theory and the couplings of the hypermultiplets in the heterotic theory. Concrete examples of ‘dual pairs’ of N = 2 string vacua have been suggested