Aspects of type I-type II-heterotic triality in four dimensions

Abstract

We discuss the equivalence between Type I, Type II and Heterotic N = 2 superstring theories in four dimensions. We study the effective field theory of Type I models obtained by orientifold reductions of Type IIB compactifications on K 3 × T 2 . We show that the perturbative prepotential is determined by the one-loop corrections to the Planck mass and is associated to an index. As is the case for threshold corrections to gauge couplings, this renormalization is entirely due to N = 2 BPS states that originate from D = 6 massless string modes. We apply our result to the so-called S-T -U model which admits simultaneous Type II and Heterotic descriptions, and show that all three prepotentials agree in the appropriate limits as expected from the superstring triality conjecture.

Induced gravity in orientifold models

“…We will proof that the normalization of the partition function is given by (23) in the case that N is prime. The proof in the general case N ∈ N relies on the fact that every natural number can uniquely be written as a product of prime numbers and is quite lengthy as there are sectors with hv i ∈ Z and one has more cases to consider.…”

Update of D3/D7-brane inflation on

“…In refs. [47,48], however, a simple, "lowest order", description in terms of another, extended, cubic prepotential was proposed: 10) where y r 3 (r = 1, . .…”

“…More precisely, if one follows [27,28,29] and describes the "lowest order" theory at the N = 2 level in terms of a cubic holomorphic prepotential F (t) = c ijk t i t j t k , where t i denote the moduli living in vector multiplets, the resulting Kähler potential, K, only depends on the imaginary parts of the moduli: K = K(t i −t i ). 5 Moreover, for the particular cubic prepotential suggested in [47,48], it was observed in [16] that the relevant D7-gauge couplings (still at the N = 2 level) likewise do not depend on the real part of y 3 . This inflaton shift symmetry is not expected to survive all quantum corrections (e.g.…”

“…The purely cubic prepotential of ref. [47,48] by itself certainly gives rise to a consistent N = 2 supergravity theory in 4D. It was stressed in [19], however, that the cubic prepotential already contains part of the open string threshold corrections.…”

“…Note, moreover, that the definition of u refers to the orientifold point at which the D7-brane charge is canceled locally. In general, its definition includes the D7-brane scalars, in analogy to the T-dual situation with D9/D5-branes discussed in [48]; see also [28]. Finally, we would like to mention that, throughout the paper, we use the notation of Ferrara and collaborators for the vector multiplets [27,28,29].…”