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We construct supersymmetric $AdS_5\times \Sigma$ solutions of $D=7$ gauged supergravity, where $\Sigma$ is a two-dimensional orbifold known as a spindle. These uplift on $S^4$ to solutions of $D=11$ supergravity which have orbifold…
We show that boundary conditions in topological open string theory on Calabi-Yau manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry proposal of Kontsevich. Together with…
We give an overview of various composite BPS configurations of string theory and M-theory p-branes represented as classical supergravity solutions. Type II string backgrounds can be obtained by S- and T- dualities from NS-NS string -…
Classical configurations of a M2-brane, a D2-brane and D0-branes are investigated in the background of an infinite array of M5-branes or NS5-branes. On the M2-brane, we discuss three kinds of configurations, such as a sphere, a cylinder and…
We show that refined Chern-Simons theory and large N duality can be used to study the refined topological string with and without branes. We derive the refined topological vertex of hep-th/0701156 and hep-th/0502061 from a link invariant of…
M-theory is known to possess supersymmetric solutions where the geometry is $\mathrm{AdS}_3\times S^3\times S^3$ warped over a Riemann surface $\Sigma_{2}$. The simplest examples in this class can be engineered by placing M2 and M5 branes…
We determine (p,q)-string and (p,q)-five brane solutions of type IIB supergravity using SL(2,Z)-symmetry of the full type IIB superstring theory. We also determine SL(2,Z)-transformed solution corresponding to the bound state of NS5-branes…
We present two classes of regular supergravity backgrounds dual to supersymmetric and non-supersymmetric gauge theories living on the world-volume of wrapped branes. In particular we consider the Maldacena Nunez and the Klebanov Strassler…
The supergravity solutions to various $p$-branes are presented and typically it breaks one quarter of supersymmetry except for the D1 brane case, where it breaks one half of supersymmetry and are manifestly non-relativistic in nature. The…
We study IIA/B string theory compactified on twisted circles. These models possess closed string tachyons and reduce to type 0B/A theory in a special limit. Using methods of gauged linear sigma models and mirror symmetry we construct a…
We consider N=1 supersymmetric SU(N_c) gauge theories, using the type IIB brane construction recently proposed by Hanany and Zaffaroni. At non-zero string coupling, we find that the bending of branes imposes consistency conditions that…
In this thesis we give a pedagogical introduction to the construction of NS5-D6(-O6)-D8(-O8) brane setups in massive type IIA string theory and the six-dimensional $(1,0)$ SCFT's they engineer. After describing how to introduce the various…
We explore the supergravity solution of D5-branes intersecting as an I1-brane. In a suitable near-horizon limit the geometry is in qualitative agreement with that found in the microscopic open-string analysis as well as the NS5-brane…
The compactness of the closed string in the classical Type II string theory reveals the duality, whereas the compactness of the open string reveals that the end of the string is on the hypersurface which satisfies the Dirichlet boundary…
We describe the intersecting brane configurations, consisting of NS-branes, D4-branes(and anti-D4-branes), in type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of N=1 SU(N_c) x SU(N_c') x SU(N_c'') gauge theory…
In type II string theories, we examine intersecting brane constructions containing brane-antibrane pairs suspended between 5-branes, and more general non-BPS constructions. The tree-level spectra are obtained in each case. We identify…
We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories which include hyper-multiplets in all cases. We show that the solutions preserve 1,2,3,4 and 8 supersymmetries. We find models with self-dual string…
We comment on the D-brane solutions for the boundary H3+ model that have been proposed so far and point out that many more types of D-branes should be considered possible. We start a systematic derivation of the 1/2- and b^{-2}/2-shift…
We study the two-matrix model which represents the sum over closed and open random surfaces coupled to an Ising Model. The boundary conditions are characterized by the fact that the Ising spins sitting at the vertices of the boundaries are…
We present the twisted covariant form hierarchies (TCFHs) of warped (massive) IIA AdS backgrounds. As a consequence we demonstrate that all Killing spinor form bilinears satisfy a generalisation of the conformal Killing-Yano equation with…