Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications

Abstract

Using heterotic/type II string duality, we obtain exact nonperturbative results for the point particle limit (α ′ → 0) of some particular four dimensional, N = 2 supersymmetric compactifications of heterotic strings. This allows us to recover recent exact nonperturbative results on N = 2 gauge theory directly from tree-level type II string theory, which provides a highly non-trivial, quantitative check on the proposed string duality. We also investigate to what extent the relevant singular limits of Calabi-Yau manifolds are related to the Riemann surfaces that underlie rigid N = 2 gauge theory.

Nonsupersymmetric flux vacua and perturbed 𝒩 = 2 systems

“…Type IIB string theory compactified on the Calabi-Yau (3.13) without flux geometrically engineers [46,25] an N = 2 Seiberg-Witten theory [35,47]. In particular, the SU(N) Seiberg-Witten curve of gauge theory [48,49] is geometrically identified with the curve (3.14) underlying the Calabi-Yau.…”

Non-critical strings, del Pezzo singularities and Seiberg-Witten curves

“…The above implies a rather interesting property of this kind of sub-monodromy problems: in contrast to the embeddings of SYM theories considered previously [18,19], these theories inherit the instanton expansion -that is, the Gromov-Witten invariants -from the Calabi-Yau manifold. In the special sub-monodromy problem that we will consider below, this is related to the fact that the underlying geometry is that of a non-compact…”

Geometric engineering of N = 1 quantum field theories

“…Gauge groups arise through ADE singularities of geometry (and their fibrations [8] [9]), whereas matter arises as loci of enhanced singularities [10]. This not only leads to a unified description of gravitational and gauge theory dynamics, but it also leads directly to a deeper understanding of gauge dynamics, even in the limit of turning off gravitational effects [11][12] [13]. The basic idea is to geometrically engineer the gauge symmetry and matter content one is interested in, and then study the corresponding theory using string techniques.…”