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We study D3-branes in an NS5-branes background defined by an arbitrary 4d harmonic function. Using a gauge-invariant formulation of Born-Infeld dynamics as well as the supersymmetry condition, we find the general solution for the…
We construct explicitly time-dependent exact solutions to the field equations of 6D gauged chiral supergravity, compactified to 4D in the presence of up to two 3-branes situated within the extra dimensions. The solutions we find are scaling…
In this paper we investigate the finite $N$ exact values of the $S^3$ partition function of the ${\cal N}=4$ super Yang-Mills theory with one adjoint hypermultiplet and $N_\text{f}$ fundamental hypermultiplets, which describes $N$ M2-branes…
We discuss the relation between supersymmetric gauge theory of branes and supergravity; as it was discovered in D-brane physics, and as it appears in Matrix theory, with emphasis on motion in curved backgrounds. We argue that gauged sigma…
We present solutions in six-dimensional gravity coupled to a sigma model, in the presence of three-brane sources. The space transverse to the branes is a compact non-singular manifold. The example of O(3) sigma model in the presence of two…
The background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are…
Motivated by Sen's spacetime prescription for the construction of theories with self-dual field strengths, we present a rigid superspace Lagrangian describing noninteracting tensor multiplets living on a stack of M5-branes and containing…
We review in a pedagogical manner some of the efforts aiming to extend the gauge/gravity correspondence to non-conformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific…
In this paper, we begin the study of zero-dimensional field theories with fields taking values in a semistrict Lie 2-algebra. These theories contain the IKKT matrix model and various M-brane related models as special cases. They feature…
We study two dimensional $N=(4,4)$ supersymmetric gauge theories with various gauge groups and various hypermultiplets in the fundamental as well as bi-fundamental and adjoint representations. They have " mirror theories " which become…
We consider the equations of motion of the non-abelian 5-branes theory recently constructed in http://arxiv.org/abs/arXiv:1203.4224 and find exact string solutions both for uncompactified and compactified spacetime. Although one does not…
We study non-relativistic limits of the N=6 Chern-Simons-Matter theory that arises as a low-energy limit of the M2-brane gauge theory with background flux. The model admits several different non-relativistic limits and we find that the…
Well-defined non-perturbative formulations of the physics of string theories, sometimes with D-branes present, were identified over a decade ago, from a careful study of double scaled matrix models. Following recent work which recasts some…
We apply the technique of twisted extensions of infinite-dimensional Lie algebras to find new 3D integrable {\sc pde}s related to the deformations of Lie algebra $\mathbb{R}_N[s]\otimes \mathfrak{w}$ with $N=1, 2$ as well as to the Lie…
Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N=8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as…
We study classical twists of Lie bialgebra structures on the polynomial current algebra $\mathfrak{g}[u]$, where $\mathfrak{g}$ is a simple complex finite-dimensional Lie algebra. We focus on the structures induced by the so-called…
In this review, we introduce the electrified Dp-branes intersections in the low energy effective theory. We focus on D1-D3, D1-D5 and D0-D2 branes. We give the solutions configurations in the low energy effective theory in the absence and…
We propose the study and description of the structure of complex Lie algebras with nilradical a nilpotent Lie algebra of type 2 by using sl2(C)-representation theory. Our results will be applied to review the classification given in [1] (J.…
In this Thesis, we focus on the study of the low energy approximation to non-critical string theories. We present an exhaustive study of their solutions, which are divided in three cases: vacuum, NSNS charged, and RR charged solutions. In…
We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…