Related papers: Matrix Models, Integrable Structures, and T-dualit…
It is generally accepted that the double-scaled 1D matrix model is equivalent to the $c=1$ string theory with tachyon condensation. There remain however puzzles that are to be clarified in order to utilize this connection for our quest…
We discuss the moduli space of nine dimensional N=1 supersymmetric compactifications of M theory / string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein…
We study limits of infinite distance in the moduli space of 4d $\mathcal{N} = 2$ string compactifications, in which instanton effects dominate. We first consider trajectories in the hypermultiplet moduli space of type IIB Calabi-Yau…
We examine the T-duality relation between 1+1 NCOS and the DLCQ limit of type IIA string theory. We show that, as long as there is a compact dimension, one can meaningfully define an `NCOS' limit of IIB/A string theory even in the absence…
We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the…
It is conjectured that the two closed bosonic string theories, Type 0A and Type 0B, correspond to certain supersymmetry breaking orbifold compactifications of M-theory. Various implications of this conjecture are discussed, in particular…
The recent developments in string theory suggest that the space-time coordinates should be generalized to non-commuting matrices. Postulating this suggestion as the fundamental geometrical principle, we formulate a candidate for covariant…
We will report on recent advances in the understanding of non-perturbative interconnections between different string dualities. Weak-strong coupling duality (S-duality) and T-duality (symmetry under compactification on dual tori) allows one…
We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi…
Certain limits of the duality between M-theory on ${T^5/Z_2}$ and IIB on K3 are analyzed in Matrix theory. The correspondence between M-theory five-branes and ALE backgrounds is realized as three dimensional mirror symmetry. Non-critical…
We show that the most general two--matrix model with bilinear coupling underlies $c=1$ string theory. More precisely we prove that $W_{1+\infty}$ constraints, a subset of the correlation functions and the integrable hierarchy characterizing…
We investigate quantum corrections to the hypermultiplet moduli space M in Calabi-Yau compactifications of type II string theories, with particular emphasis on instanton effects from Euclidean NS5-branes. Based on the consistency of D- and…
Scattering of fundamental states of type IIB supergravity and superstring theory is discussed at low orders in perturbation theory in the background of a D-instanton. The integration over fermionic zero modes in both the low energy…
We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering. The moduli space on the Coulomb branch is hyperkaehler…
The arcane ADHM construction of Yang-Mills instantons can be very naturally understood in the framework of D-brane dynamics in string theory. In this point-of-view, the mysterious auxiliary symmetry of the ADHM construction arises as a…
Extending a recent result of S.B. Giddings, F. Hacquebord and H. Verlinde, we show that in the U(N) SYM Matrix theory there exist classical BPS instantons which interpolate between different closed string configurations via…
We review aspects of entanglement entropy in the quantum mechanics of $N\times N$ matrices, i.e. matrix quantum mechanics (MQM), at large $N$. In doing so we review standard models of MQM and their relation to string theory, D-brane…
In these notes we review the method to construct integrable deformations of the compactified c=1 bosonic string theory by primary fields (momentum or winding modes), developed recently in collaboration with S. Alexandrov and V. Kazakov. The…
We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter…
A review of M-(atrix) theory (the BFFS matrix quantum mechanics), type IIB matrix model (the IKKT matrix model) and Matrix String Theory (the DVV matrix gauge theory) is presented.