Target Space Duality in String Theory

TL;DR

The article establishes target-space duality as a fundamental, symmetry-based organizing principle in string theory, linking circle and torus compactifications through R ↔ α'/R and O(d,d,Z) transformations. It develops a multi-layered framework: (i) worldsheet CFTs and their marginal deformations generate moduli spaces; (ii) a discrete duality group acts as a solution-generating set and as a gauge symmetry with Weyl-reflection interpretations; (iii) low-energy effective actions for toroidal, orbifold, and Calabi–Yau backgrounds exhibit duality-invariant structure, including completely duality-invariant EFTs via the DISG algebra for N=4 heterotic strings; (iv) duality extends to curved backgrounds with Abelian isometries, enabling Buscher-type transformations, black-hole/Cosmology applications, and gauge-symmetry interpretations of axial-vector dualities. The results illuminate the deep interconnections between worldsheet and target-space symmetries, constrain effective actions, and highlight dualities as robust, nonperturbative features of string theory with broad phenomenological implications. Mathematically, dualities act via fractional linear transformations on background data E, G,B, and dilatons, and relate spectra through Narain lattices and generalized gauge algebras, enabling a unified treatment across flat, orbifold, CY, and curved backgrounds. The interplay between O(d,d,Z) and gauge symmetries, plus the role of fixed points with enhanced symmetry, provides a powerful toolkit for predicting duality-invariant couplings, superpotentials, and threshold effects in diverse string vacua.

Abstract

A review article submitted to Physics Report: Target space duality and discrete symmetries in string theory are reviewed in different settings.