In string theory, non-perturbative effects play a crucial role in understanding the theory beyond its perturbative approximation. Perturbation theory in string theory involves expanding physical quantities in powers of the string coupling constant (usually denoted as g_s). However, at strong coupling (large values of g_s), perturbation theory breaks down, and non-perturbative effects become important.
Here are some key roles of non-perturbative effects in string theory:
Dualities: Non-perturbative effects are intimately connected to the phenomenon of duality in string theory. String dualities relate different string theories to each other, providing different descriptions of the same underlying physics. These dualities often involve non-perturbative effects. For example, the celebrated AdS/CFT correspondence, or gauge/gravity duality, relates a string theory in an Anti-de Sitter (AdS) space to a quantum field theory (CFT) living on its boundary. This duality is based on the non-perturbative effects of the string theory and the strong coupling regime of the field theory.
Solitons and D-branes: Non-perturbative effects in string theory give rise to various types of extended objects known as solitons. Solitons are stable and localized solutions that exist due to non-perturbative effects. In string theory, solitonic objects include D-branes (extended objects on which strings can end) and higher-dimensional branes. These solitons are crucial for the realization of dualities, the understanding of black holes, and the exploration of the theory at strong coupling.
Compactification and Moduli Stabilization: Compactification is the process of reducing the number of dimensions in string theory. Non-perturbative effects play a significant role in the stabilization of the extra dimensions and the moduli fields associated with them. In the absence of non-perturbative effects, these dimensions and moduli would remain unfixed, leading to inconsistencies. Various mechanisms, such as flux compactification and gaugino condensation, utilize non-perturbative effects to stabilize the moduli fields and obtain realistic four-dimensional effective theories.
Supersymmetry Breaking: Supersymmetry is a fundamental symmetry in string theory that relates bosons and fermions. However, in our observed universe, supersymmetry is not manifest, and it must be broken. Non-perturbative effects play a crucial role in supersymmetry breaking mechanisms in string theory. For instance, gaugino condensation in certain string compactifications can lead to the spontaneous breaking of supersymmetry.
Overall, non-perturbative effects in string theory provide essential insights into the strong coupling regime, duality symmetries, stabilization of extra dimensions, solitonic objects, and supersymmetry breaking. Understanding these non-perturbative aspects is crucial for obtaining a more complete and realistic description of the physical phenomena within the framework of string theory.