Related papers: Multi-cut Solutions in Chern-Simons Matrix Models
These notes provide a brief introduction to the ABJM theory, the level k U(N) x U(N) superconformal Chern-Simons matter theory which has been conjectured to describe N coincident M2-branes. We discuss its dual formulation in terms of…
Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more…
It has been proved by S.L.Ziglin, for a large class of 2-degree-of-freedom (d.o.f) Hamiltonian systems, that transverse intersections of the invariant manifolds of saddle fixed points imply infinite branching of solutions in the complex…
We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become…
We study 3d $\mathcal{N}=2$ Chern-Simons (CS) quiver theories on $S^3$ and ${\Sigma}_{\mathfrak{g}}\times S^1$. Using localization results, we examine their partition functions in the large rank limit and requiring the resulting matrix…
In hypercube approach to correlation functions in Chern-Simons theory (knot polynomials) the central role is played by the numbers of cycles, in which the link diagram is decomposed under different resolutions. Certain functions of these…
We construct large $N$ saddle points of the matrix model for the $\mathcal{N}=4$ Yang-Mills index dual to the BPS black holes in $AdS_5\times S^5$, in two different setups. When the two complex chemical potentials for the angular momenta…
We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4,…
Three-dimensional supersymmetric Chern-Simons Matter (CSM) theories typically preserve $ \mathcal{N}=3$ supersymmetry but can exhibit enhanced $\mathcal{N}=4$ supersymmetry under special conditions. A detailed understanding of the moduli…
Extending previous work that involved D3-branes ending on a fivebrane with $\theta_{\mathrm{YM}}\not=0$, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional…
We revisit the Holographic duality between $SU(N)_\kappa$ Chern-Simons theory and the A-model Topological String Theory. We develop a strategy to systematically compute the large $N$ saddles for correlation functions of Wilson lines in…
The off-shell vector-tensor multiplet is considered in an arbitrary background of N=2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the…
We study a system of equations arising in the Chern-Simons model on finite graphs. Using the iteration scheme and the upper and lower solutions method, we get existence of solutions in the non-critical case. The critical case is dealt with…
We study conical defect geometries in the SL(N) Chern-Simons formulation of higher spin gauge theories in AdS_3. We argue that (for N\geq 4) there are special values of the deficit angle for which these geometries are actually smooth…
We study CFT data of 3-dimensional superconformal field theories (SCFTs) arising from wrapped two M5-branes on closed hyperbolic 3-manifolds. Via so-called 3d/3d correspondence, central charges of these SCFTs are related to a $SL(2)$…
We study the phase transitions of three-dimensional $\mathcal{N}=2$ $U(N)$ Chern-Simons theory on $\mathbb{S}^3$ with a varied number of massive fundamental hypermultiplets and with a Fayet-Iliopoulos parameter. We characterize the various…
The partition function of complex Chern-Simons theory on a 3-manifold with torus boundary reduces to a finite dimensional state-integral which is a holomorphic function of a complexified Planck's constant $\tau$ in the complex cut plane and…
It was known that the U$(N)^4$ super Chern-Simons matrix model describing the worldvolume theory of D3-branes with two NS5-branes and two $(1,k)$5-branes in IIB brane configuration (dual to M2-branes after taking the T-duality and the…
We study abelian and non-abelian orbifolds of the ABJM model. We compute the precise moduli space of these models by analyzing the classical BPS equations for the theory on the cylinder, which include classical solutions of magnetic…
The Stokes multipliers in the matrix models are invariants in the string-theory moduli space and related to the D-instanton chemical potentials. They not only represent non-perturbative information but also play an important role in…