Related papers: An $\mathcal{N}=1$ 3d-3d Correspondence
We provide a physical definition of new homological invariants $\mathcal{H}_a (M_3)$ of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on $M_3$ times a…
We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well…
We extend the localization calculation of the 3D Chern-Simons partition function over Seifert manifolds to an analogous calculation in five dimensions. We construct a twisted version of N=1 supersymmetric Yang-Mills theory defined on a…
We calculate the Witten index for 3d supersymmetric Yang-Mills-Chern-Simons theories with matter. For N=2 theories, our results coincide with the results of recent [1]. We compare the situation in 3d to that in 4d N = 1 theories with…
We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a…
We discuss fractional D3-branes on the orbifold C^3/Z_2*Z_2. We study the open and the closed string spectrum on this orbifold. The corresponding N=1 theory on the brane has, generically, a U(N_1)*U(N_2)*U(N_3)*U(N_4) gauge group with…
We study the topologically twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories with unitary gauge groups. We implement a Gr\"obner basis algorithm for computing the $\Sigma_g\times S^1$ index explicitly and exactly in terms of…
This is an introductory review of the AdS/CFT correspondence and of the ideas that led to its formulation. We show how comparison of stacks of D3-branes with corresponding supergravity solutions leads to dualities between conformal large…
We consider unitary SQCD, a three-dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-matter theory consisting of one $U(N_c)_{k, k+l N_c}$ vector multiplet coupled to $n_f$ fundamental and $n_a$ antifundamental chiral multiplets, where…
By identifying a bosonic consistent truncation from the 1/4-BPS wrapped M5-brane geometry of Maldacena, Strominger and Witten in D = 11 supergravity and finding a supersymmetric extension, we recover an N = 2 D = 3 supergravity theory.…
We study surface defects in 4d $\mathcal{N}=1$ $SU(N)$ superconformal gauge theories of class $\mathcal{S}_k$ obtained from the 6d (1,0) theories of type $A_{N-1}$, which are worldvolume theories on $N$ M5-branes at…
We study 3d $\mathcal{N}=2$ Chern--Simons matter theories describing the R-twisted $S^1$-reduction of Argyres--Douglas theories of $(A_{M-1},A_{N-1})$ type with $\text{gcd}(M,N)=1$, via a recently-proposed 4d/3d correspondence. In…
We propose a new partially topological theory in three dimensions which couples Chern-Simons theory to matter. The 3-manifolds needed for this construction admit transverse holomorphic foliation (THF). The theory depends only on the choice…
Chern-Simons gauge theory is formulated on three dimensional $Z_2$ orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum…
We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This theory can be obtained from 5d MSYM theory by performing the maximal topological twist. We put the theory on a five-manifold and compute the partition function.…
We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI…
We work out the superconformal index for N=2 supersymmetric Chern-Simons matter theories exhibiting Seiberg-like dualities proposed by Giveon and Kutasov. We consider $U(N)/Sp(2N)/O(N)$ gauge theories of QCD type and find the perfect…
We study three dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-Matter theories on the direct product of a circle and a two dimensional hemisphere ($S^1 \times D^2$) with specified boundary conditions by the method of localization.…
We present a trace formula for a Witten type Index for superconformal field theories in d=3,5 and 6 dimensions, generalizing a similar recent construction in d=4. We perform a detailed study of the decomposition of long representations into…
The D1-D5 system is believed to have an `orbifold point' in its moduli space where its low energy theory is a N=4 supersymmetric sigma model with target space M^N/S^N, where M is T^4 or K3. We study correlation functions of chiral operators…