arXiv subjects

Sung-Soo Kim

Publications and source records attributed to Sung-Soo Kim.

At least 19 recordsLinked to original sources

arXiv2025

Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations

We investigate codimension-2 defect partition functions and quantum Seiberg-Witten curves in 5d rank-1 supersymmetric QFTs, including non-Lagrangian and Kaluza-Klein theories. Using generalized blowup equations, we compute defect partition functions in the $Ω$-background and show that, in the Nekrasov-Shatashvili limit, they satisfy certain difference equations that encode the quantization of classical Seiberg-Witten curves. Furthermore, we explore novel transitions in the defect partition functions and their relation to coordinate transformations of quantum Seiberg-Witten curves, with a focus on SL(2,$\mathbb{Z}$) transformations and Hanany-Witten transitions. These findings provide new insights into the interplay between codimension-2 defects, quantum curves, and the geometric structure of 5d supersymmetric QFTs.

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arXiv2025

Topological Vertex for Symmetric matter

We propose a novel topological vertex formalism for 5d $\mathcal{N}=1$ SU($N$) gauge theory with a hypermultiplet in the symmetric tensor representation, whose Type IIB brane construction involves an NS5-brane attached to an O7$^+$-plane. Inspired by the identification $\mathrm{O7}^+\sim \mathbb{Z}_2 + 4 \mathrm{D7}$, we introduce two new types of vertices: the $\mathbb{Z}_2$-vertex, which implements the $\mathbb{Z}_2$ orbifold action, and the FD-vertex, which encodes the monodromy cut induced by the O7$^+$-plane. This formalism generalizes the framework presented in arXiv:2412.19655 and establishes a systematic method for computing partition functions for 5-brane configurations that incorporate an O7$^+$-plane. The resulting partition functions are expressed as sums over Young diagrams, providing a powerful computational tool for studying such gauge theories.

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arXiv2025

Topological vertex formalism with O5-plane

We propose new topological vertex formalism for Type IIB $(p,q)$ 5-brane web with an O5-plane. We apply our proposal to 5d $\mathcal{N}=1$ Sp(1) gauge theory with $N_f=0,1,8$ flavors to compute the topological string partition functions and check the agreement with the known results. Especially for the $N_f=8$ case, which corresponds to E-string theory on a circle, we obtain a new, yet simple, expression of the partition function with two Young diagram sum.

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arXiv2025

O-vertex, O7$^+$-plane, and Topological Vertex

We revisit the instanton partition function for 5d $\mathcal{N}=1$ SO($N$) gauge theories compactified on S$^1$, computed from the topological vertex formalism with the O-vertex based on a 5-brane web diagram with an O5-plane. We introduce an identity that enables us to rewrite the unrefined partition function into a new expression in terms of the Nekrasov factors summed over Young diagrams, which can be interpreted as the freezing of an O7-plane. Based on this, we propose topological vertex formalism with an O7$^+$-plane.

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arXiv2024

Freezing and BPS jumping

We report a novel BPS jumping phenomenon of 5d $\mathcal{N}=1$ supersymmetric gauge theories whose brane configuration is equipped with an O$7$-plane. The study of the relation between O$7{}^+$-plane and O$7{}^-$-plane reveals that such BPS jumps take place when the Higgsing is triggered near the O7-plane upon a particular parameter tuning of the theories. We propose two types of gauge theories whose BPS spectra jump. One is the SU($2N+8$) gauge theory with a symmetric hypermultiplet converted to the SU($2N$) gauge theory with an antisymmetric hypermultiplet. The other is pure SO($2N+8$) gauge theory jumping to pure Sp($N$) gauge theory. We explicitly confirm our proposal through the (un)refined instanton partition functions. Furthermore, we discuss feasible generalizations involving an O$p$-plane for supersymmetric gauge theories of eight supercharges in four and three dimensions ($p=6, 5$ respectively).

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arXiv2023

Seiberg-Witten curves with O7$^\pm$-planes

We construct Seiberg-Witten curves for 5d $\mathcal{N}=1$ gauge theories whose Type IIB 5-brane configuration involves an O7-plane and discuss an intriguing relation between theories with an O7$^+$-plane and those with an O7$^-$-plane and 8 D7-branes. We claim that 5-brane configurations with an O7$^+$-plane can be effectively understood as 5-brane configurations with a set of an O7$^-$-plane and eight D7-branes with some special tuning of their masses such that the D7-branes are frozen at the O7$^-$-plane. We check this equivalence between SU($N$) gauge theory with a symmetric hypermultiplet and SU($N$) gauge theory with an antisymmetric with 8 fundamentals, and also between SO($2N$) gauge theory and Sp($N$) gauge theory with eight fundamentals. We also compute the Seiberg-Witten curves for non-Lagrangian theories with a symmetric hypermultiplet, which includes the local $\mathbb{P}^2$ theory with an adjoint.

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arXiv2023

Superconformal indices for non-Lagrangian theories in five dimensions

We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O$7^+$-plane and O$7^-$-plane with eight D7-branes, which applies to particular non-Lagrangian theories realized by brane configurations involving an O$7^+$-plane. As a concrete application of our method, we compute the superconformal indices for all known rank-1 non-Lagrangian theories, which we also use to identify flavor symmetries and their global forms at the conformal field theory (CFT) fixed points.

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arXiv2023

$DE$-type little strings from glued brane webs

We propose brane web configurations for $D$-type and $E$-type $\mathcal{N}=(1,0)$ little string theories based on a trivalent or quadrivalent gluing of 5-brane web diagrams. Tri-/quadri-valent gluing is a powerful way of computing 5d/6d partition functions for supersymmetric gauge theories based on the topological vertex. We generalize the gluing techniques to little string theories by introducing a new compact direction and compute their supersymmetric partition functions on Omega-deformed $\mathbb{R}^4\times T^2$. As concrete examples, we consider little string theories arising from Type IIB NS5-branes probing $D_4$ or $D_5$ singularity. Their effective gauge theory descriptions as the affine $D_4$ or $D_5$ quiver gauge theory can be realized with quadrivalent or trivalent gluing, respectively. Based on these gluings of 5-brane webs, we compute their refined partition functions and compare them with the known results. We extend the computation of the partition function to little string theory engineered from IIB NS5-branes probing $E_6$ singularity based on a trivalent gluing. We also discuss the generalization to higher rank cases and the symmetries of the partition functions.

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arXiv2023

Topological vertex for 6d SCFTs with $\mathbb{Z}_2$-twist

We compute the partition function for 6d $\mathcal{N}=1$ $SO(2N)$ gauge theories compactified on a circle with $\mathbb{Z}_2$ outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5-planes. As representative examples, we consider 6d $SO(8)$ and $SU(3)$ gauge theories with $\mathbb{Z}_2$ twist. We confirm that these partition functions obtained from the topological vertex with O5-planes indeed agree with the elliptic genus computations.

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arXiv2022

Refined topological vertex with ON-planes

We propose refined topological vertex formalism for 5-brane systems with ON-planes by introducing a new vertex associated with reflection over an ON-plane, which gives rise to new vertex and edge factors. We test our proposal against various 5d $\mathcal{N}=1$ gauge theories which can be realized as 5-brane webs with ON-planes, which include $D$-type quiver theories. In particular, we compute the refined partition functions for 6d E-string theory on a circle as well as 5d SU(3) theory at the Chern-Simons level 9, which can be realized as 5-brane webs with two ON-planes. Our results completely agree with the known results.

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arXiv2022

S-foldings of 5d SCFTs

We explore the $\mathbb{Z}_{2,3,4,6}$ S-foldings of some 5d superconformal field theories from the $(p,q)$ 5-brane web perspective. The S-folding involves both a spatial quotient and an $\mathrm{SL}(2,\mathbb{Z})$ transformation on 5-branes simultaneously. The $\mathbb{Z}_{2,3,4,6}$ S-foldings are achieved by the insertion of the $D_4, E_6, E_7, E_8$ 7-branes, respectively. The deficit angles and monodromies of these 7-branes are exactly those necessary for the S-foldings. We explore the details of the S-folding process, especially the enhancement of global flavor symmetry in various simple cases. The characteristic of the S-folding depends sharply on whether the fixed point of the discrete symmetry is at the center of a compact face (or surface), at a 5-brane, or at a crossing point of 5 branes. The analysis of the prepotential greatly supports this view of the discrete gauging.

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arXiv2022

Exploring the orthosymplectic zoo

We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to propose (naively) inequivalent magnetic quivers, which will turn out to have the same moduli spaces of vacua, at least locally around their most singular loci. We encounter several interesting new phenomena occurring in the magnetic quivers, such as hypermultiplets between neighbouring symplectic gauge nodes and matter in two-index representations of unitary nodes. We also give a prescription for computing the local Coulomb branch Hilbert series for quivers involving bad USp(2) gauge nodes.

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arXiv2021

Refined topological vertex for a 5D $Sp(N)$ gauge theory with antisymmetric matter

We consider Type IIB 5-brane web diagrams for a 5D $Sp(N)$ gauge theory with an antisymmetric hypermultiplet and $N_f$ fundamental hypermultiplets. The corresponding 5-branes can be obtained by Higgsing a 5-brane web for quiver gauge theory. We use the refined topological vertex formalism to compute Nekrasov partition functions of 5D $Sp(2)$ theories with one antisymmetric hypermultiplet and flavors. Our results agree with the known results obtained from the ADHM method. We also discuss a particular tuning of Kähler parameters associated with this Higgsing.

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arXiv2021

5d/6d Wilson loops from blowups

We generalize Nakajima-Yoshioka's blowup formula to calculate the partition functions counting the spectrum of bound states to half-BPS Wilson loop operators in 5d (and 6d) supersymmetric field theories. The partition function in the presence of a Wilson loop operator on the $Ω$-background is factorized when put on the blowup $\hat{\mathbb{C}}^2$ into two Wilson loop partition functions under the localization. This structure provides a set of blowup equations for Wilson loop operators. We explain how to formulate the blowup equations and solve them to compute the partition functions of Wilson loop operators. We test this idea by explicitly calculating the Wilson loop partition functions in various 5d/6d field theories and comparing them against known results and expected dualities.

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arXiv2021

Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers

We study the moduli space of 3d $\mathcal{N}=4$ quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $\mathcal{N}=1$ superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.

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arXiv2021

Bootstrapping BPS spectra of 5d/6d field theories

We propose a systematic approach to computing the BPS spectra of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka's blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup $\hat{\mathbb{C}}^2$ and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d $\mathcal{N}=(1,0)$ superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d $SU(3)_8$ gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.

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arXiv2020

Surface defects on E-string from 5-brane webs

We study 6d E-string theory with defects on a circle. Our basic strategy is to apply the geometric transition to the supersymmetric gauge theories. First, we calculate the partition functions of the 5d SU(3)$_0$ gauge theory with 10 flavors, which is UV-dual to the 5d Sp(2) gauge theory with 10 flavors, based on two different 5-brane web diagrams, and check that two partition functions agree with each other. Then, by utilizing the geometric transition, we find the surface defect partition function for E-string on $\mathbb{R}^4\times T^2$. We also discuss that our result is consistent with the elliptic genus. Based on the result, we show how the global symmetry is broken by the defects, and discuss that the breaking pattern depends on where/how we insert the defects.

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arXiv2020

Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers

We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in arXiv:2004.04082, by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and $\mathbb{Z}_2$ gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.

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