Surface terms in effective action of O-plane at order $$\alpha '^2$$

The effective action of string theory has both bulk and boundary terms if the spacetime is an open manifold. Recently, the known classical effective action of string theory at the leading order of $$\alpha '$$ α ′ and its corresponding boundary action have been reproduced by constraining the effective actions to be invariant under gauge transformations and under string duality transformations. In this paper, we use this idea to find the classical effective action of the O-plane and its corresponding boundary terms in type II superstring theories at order $$\alpha '^2$$ α ′ 2 and for NS–NS couplings. We find that these constraints fix the bulk action and its corresponding boundary terms up to one overall factor. They also produce three multiplets in the boundary action that their coefficients are independent of the bulk couplings under the string dualities.

Aspects of gauge/string dualities

In this thesis we investigate on the role that dualities play nowadays in our under-standing of string and Quantum Field Theories.The first part is devoted to holographic dualities, where the case of the string dual of certain one-, two- and four dimensional field theories is explored in detail. We begin in Chapter 1 by discussing the holographic dual of a broad class of four-dimensional field theories. We specialise to the case of quiver field theories where a number of formulas computing charges, number of branes and Linking Numbers are given. We then introduce marginal deformations in the supergravity backgrounds to uncover infinite new families of solutions to type II supergravity and M-theory. In Chapter 2, we discuss spin 2 fluctuations around a class of warped AdS3 backgrounds. We identify explicitly the dual operators of a given protected sector. Also, a formula for the central charge of the dual two-dimensional field theories is derived. In Chapter 3, we introduce two new classes of geometries with an AdS2 factor. We outline the importance to black hole physics and in one case give a prescription for the dual field theories.The second part is devoted to QFT/QFT dualities in Chern-Simons theories, and how dualities between Chern-Simons theories in three dimensions can be motivated in string theory. It is found that a known duality between three-dimensional Chern-Simons theories with unitary gauge symmetry can be motivated by a brane setup in Type 0B string theory with an orientifold. In particular, the phase diagram of unitary QCD3 is inferred from a dual theory.

String theory

This article discusses the link between matrix models and string theory, giving emphasis on topological string theory and the Dijkgraaf–Vafa correspondence, along with applications of this correspondence and its generalizations to supersymmetric gauge theory, enumerative geometry, and mirror symmetry. The article first provides an overview of strings and matrices, noting that the correspondence between matrix models and string theory makes it possible to solve both non-critical strings and topological strings. It then describes some basic aspects of topological strings on Calabi-Yau manifolds and states the Dijkgraaf–Vafa correspondence, focusing on how it is connected to string dualities and how it can be used to compute superpotentials in certain supersymmetric gauge theories. In addition, it shows how the correspondence extends to toric manifolds and leads to a matrix model approach to enumerative geometry. Finally, it reviews matrix quantum mechanics and its applications in superstring theory.