송재원 교수

We study certain $$ \mathcal{N}=1 $$ preserving deformations of four-dimensional $$ \mathcal{N}=2 $$ superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an $$ \mathcal{N}=1 $$ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow t

A bstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3 c − 2 a . We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 &lt; a / c &lt; 3/2

We study superconformal indices of 4d $$ \mathcal{N}=2 $$ class S theories with certain irregular punctures called type I k,N . This class of theories include generalized Argyres-Douglas theories of type (A k−1 , A N −1) and more. We conjecture the superconformal indices in certain simplified limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture I k,N . We write the Schur limit of the wave function when k and N are

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d $$ \mathcal{N}=\left(2,\ 0\right) $$ theory of type J on a punctured sphere. We denote the AD theories as (J b [k], Y), where J b [k] and Y represent an irregular and a regular singularity respectively. We restrict to the ‘minimal’ case where J b [k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to

We study a class of four-dimensional $$ \mathcal{N}=1 $$ superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify fourdimensional UV descriptions of the SCFTs corresponding to curves with a class of punctures. The quiver tails appearing in these UV descriptions differ significantly from their $$ \mathcal{N}=2 $$ counterpart. We find a new type of object that we call the ‘Fan’. We show how to construct new $$ \mathcal{N}=1 $$ superconformal the

For any 4d $$ \mathcal{N} $$ = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector sp

We generalize recent construction of four-dimensional $ \mathcal{N} $ = 1 SCFT from wrapping six-dimensional $ \mathcal{N} $ = (2, 0) theory on a Riemann surface to the case of D-type with outer-automorphism twists. This construction allows us to build various dual theories for a class of $ \mathcal{N} $ = 1 quiver theories of SO-USp type. In particular, we find there are five dual frames to SO(2N)/USp(2N−2)/G 2 gauge theories with (4N−4)/(4N)/8 fundamental flavors, where three of them being non

We discuss two infinite classes of 4d supersymmetric theories, T () and $$ {\mathcal{U}}_N^{(m)} $$ , labelled by an arbitrary non-negative integer, m. The T () theory arises from the 6d, A N − 1 type $$ \mathcal{N}=\left(2,0\right) $$ theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree (m + 1, −m); the m = 0 case is the $$ \mathcal{N}=2 $$ supersymmetric T N theory. The novelty is the negative-degree line bundle. The $$ {\mathcal{U}}_N^{(m)} $$ theories li

A bstract We find large N gauge theories containing a large number of operators within a band of low conformal dimensions. One of such examples is the four-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 supersymmetric SU( N ) gauge theory with one adjoint and a pair of fundamental/anti-fundamental chiral multiplets. This theory flows to a superconformal theory in the infrared upon a superpotential coupling with gauge sin

A bstract We study the large N limit of the matrix models associated with the superconformal indices of four-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 superconformal field theories. We find that for a large class of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 superconformal gauge theories, the superconformal indices in the large N limit of such theor

In this thesis, we study the 4d/2d correspondence of Alday-Gaiotto-Tachikawa, which relates the class of 4-dimensional N=2 gauge theories (theories of class S) to a 2-dimensional conformal field theory. The 4d gauge theories are obtained by compactifying 6-dimensional N=(2, 0) theory of type A, D, E on a Riemann surface C. On the 2-dimensional side, we have Toda theory on the surface C with W-algebra symmetry, which is an extension of the Virasoro symmetry. In particular, the instanton partition

A hybrid bistable optical device is realized by using a simple liquid crystal light modulator based on the dynamic scattering. Its low driving voltage and high transmission for the ON state make the amplification of feedback signal unnecessary and may facilitate a 2-D spatial array of devices. Regenerative oscillation and monostable pulse generation have also been demonstrated to study its transient behavior.

A bstract We propose a new dual description of four-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 SU( N ) gauge theory with one adjoint ( X ) and N f fundamental matters with a superpotential W = Tr X p +1 . The dual theory consists of the $$ \mathcal{D} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> </mml:math> p [SU( N )] Argyres-Douglas theory coupled to SU( N ) gauge theory and N f f

A bstract The Weak Gravity Conjecture (WGC) in anti-de Sitter spacetime (AdS) asserts the existence of an operator in the boundary conformal field theory (CFT) whose scaling dimension-to-charge ratio satisfies a certain upper bound. This bound is specified by the ratio of the conformal central charge c and the flavor central charge k F . We propose a modified bound in AdS 5 /CFT 4 , determined by a combination of two central charges 3 c − 2 a instead of c . This combination arises in the Cardy-l