강동민 교수

We conjecture infrared emergent $\mathcal{N}=4$ supersymmetry for a class of three-dimensional $\mathcal{N}=2$ U(1) gauge theories coupled with a single chiral multiplet. One example is the case where the U(1) gauge group has the Chern-Simons level $\ensuremath{-}\frac{3}{2}$ and the chiral multiplet has gauge charge $+1$. Other examples are related to this example either by known dualities or rescaling the Abelian gauge field. We give three independent pieces of evidence for the conjecture: (i)

A bstract We revisit Dimofte-Gaiotto-Gukov’s construction of 3d gauge theories associated to 3-manifolds with a torus boundary. After clarifying their construction from a viewpoint of compactification of a 6d $$ \mathcal{N}=\left(2,0\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mfenced><mml:mn>2</mml:mn><mml:mn>0</mml:mn></mml:mfenced></mml:math> theory of A 1 -type on a 3-manifold, we propose a topological criterion for SU(2) / SO(3

We study the large N expansion of twisted partition functions of 3d N = 2 superconformal field theories arising from N M5-branes wrapped on a hyperbolic 3- manifold, M₃. Via the 3d-3d correspondence, the partition functions of these 3d N = 2 superconformal field theories are related to simple topological invariants on the 3-manifold. The partition functions can be expressed using only classical and one-loop perturbative invariants of PSL(N, C) Chern-Simons theory around irreducible fl

Using localization technique, we calculate the partition function and expectation values of Wilson loop operators in Chen-Simons theory on general lens spaces L(p,q) (including S2 × S1). Our results are consistent with known results.

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d (2, 0) theory of type A_N-1 on a 3-manifold M . The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group SL(N,C) ) on M and a 3d N=2 theory T N [M ]. We study this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models

We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one hand, it leads to the 3d-3d correspondence which maps an $$ \mathcal{N}=2 $$ superconformal field theory to a pure Chern-Simons theory on the 3-manifold. On the other hand, it leads to a warped AdS4 geometry in M-theory holographically dual to the superconformal field theory. Combining the holographic duality and the 3d-3d correspondence, we propose a conjecture for the large N limit of the perturbativ

A bstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT ± [ $$ \mathcal{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> rank 0 ], to a (2+1)D interacting $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</

A bstract We probe the 3d-3d correspondence for mapping cylinder/torus using the superconformal index. We focus on the case when the fiber is a once-punctured torus (Σ 1,1 ). The corresponding 3d field theories can be realized using duality domain wall theories in 4d $ \mathcal{N} $ = 2 ∗ theory. We show that the superconformal indices of the 3d theories are the SL(2, C) Chern-Simons partition function on the mapping cylinder/torus. For the mapping torus, we also consider another realization of

We study the large $N$ limit of twisted partition functions on ${\mathcal{M}}_{g,p}$, the ${S}^{1}$ bundle of degree $p$ over a Riemann surface of genus $g$, for 3D $\mathcal{N}=2$ superconformal field theories arising as low-energy limit of wrapped $N$ M5-branes on hyperbolic 3-manifold $M$. We study contributions from two Bethe vacua which correspond to two canonical irreducible $SL(N,\mathbb{C})$ flat connections on $M$ via 3D-3D correspondence. Using mathematical results on perturbative Cher

We provide strong pieces of evidence that mathematics of three-dimensional hyperbolic manifolds of the first, second and third smallest volume are captured by the physics of three-dimensional theories composed of a complex boson and a Dirac fermion, both of a unit charge, coupled to a U(1) gauge field with the Chern-Simons levels $\ensuremath{-}5/2$, $\ensuremath{-}7/2$ and $\ensuremath{-}3/2$, respectively.

We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d–3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern–Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N limit. We check the correspondence numerically in a number of examples, and confirm the N3 scaling with precise coefficients.