arXiv subjects

Dongmin Gang

Publications and source records attributed to Dongmin Gang.

At least 19 recordsLinked to original sources

arXiv2026

Refined 3D index

We introduce a refined version of the 3D index for 3-manifolds, building on the construction of the 3D $\mathcal{N}=2$ gauge theory $T[M]$ by Dimofte-Gaiotto-Gukov and Gang-Yonekura. The refined index is a superconformal index of $T[M]$ equipped with additional gradings that capture enhanced flavor symmetries of the effective theory. Our construction is based on a Dehn surgery presentation of $M$ in terms of an ideally triangulated link complement $N$. We derive an explicit infinite-sum formula for the refined index and provide nontrivial checks in representative examples, supporting its invariance under changes of triangulation, Dehn surgery presentation, and other auxiliary data. As a strictly stronger invariant, the refined index enables finer distinctions among 3-manifolds and among distinct IR phases of the associated gauge theories. We also introduce a computational tool, \textsc{Refined Index Calculator}, for its explicit evaluation.

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arXiv2025

Torus Knots and Minimal Models Revisited : Rational VOA characters from non-hyperbolic knots

In 2003, Hikami and Kirillov uncovered an intriguing connection between torus knots $\mathcal{K}_{(P,Q)}$ and Virasoro minimal models $\mathcal{M}(P,Q)$ by relating the Kashaev invariants of the knots to the characters of the corresponding minimal models. In this work, we recover and extend this connection by combining the 3D--3D correspondence with a bulk--boundary correspondence. More concretely, we study the 3D $\mathcal{N}=2$ gauge theories associated with torus-knot complements via the Dimofte--Gaiotto--Gukov construction and show that, in the infrared, these theories either flow to a unitary TQFT (when $|P-Q| = 1$), whose boundary chiral algebra reproduces that of the associated unitary minimal model, or to a 3D $\mathcal{N}=4$ rank-0 SCFT (when $|P-Q| > 1$), which realizes the corresponding non-unitary chiral minimal model at the boundary after an appropriate topological twist. This framework yields new Nahm-sum-like expressions for the characters of Virasoro minimal models and other related rational conformal field theories, providing a systematic algorithm for constructing characters of rational VOAs directly from the combinatorial data of an ideal triangulation of a non-hyperbolic knot complement.

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arXiv2024

Three Dimensional Topological Field Theories and Nahm Sum Formulas

It is known that a large class of characters of 2d conformal field theories (CFTs) can be written in the form of a Nahm sum. In \cite{Zagier:2007knq}, D. Zagier identified a list of Nahm sum expressions that are modular functions under a congruence subgroup of $SL(2,\mathbb{Z})$ and can be thought of as candidates for characters of rational CFTs. Motivated by the observation that the same formulas appear as the half-indices of certain 3d $\mathcal{N}=2$ supersymmetric gauge theories, we perform a general search over low-rank 3d $\mathcal{N}=2$ abelian Chern-Simons matter theories which either flow to unitary TFTs or $\mathcal{N}=4$ rank-zero SCFTs in the infrared. These are exceptional classes of 3d theories, which are expected to support rational and $C_2$-cofinite chiral algebras on their boundary. We compare and contrast our results with Zagier's and comment on a possible generalization of Nahm's conjecture.

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arXiv2024

3d SUSY enhancement and non-semisimple TQFTs from four dimensions

It has been recently shown that the celebrated SCFT$_4$/VOA$_2$ correspondence can be bridged via three-dimensional field theories arising from a specific R-symmetry twisted circle reduction. We apply this twisted reduction to the $(A_1,A_{n})$ and $(A_1,D_{n})$ families of 4d $\mathcal{N}=2$ Argyres-Douglas SCFTs using their $\mathcal{N}=1$ Agarwal-Maruyoshi-Song Lagrangians. From $(A_1,A_{2n})$ we derive the Gang-Kim-Stubbs family of 3d $\mathcal{N}=2$ gauge theories with SUSY enhancement to $\mathcal{N}=4$ in the infrared, generalizing a recent derivation made in the special cases $n=1,2$. Topological twists of these theories are known to yield $semisimple$ TQFTs supporting $rational$ VOAs on holomorphic boundaries. From $(A_1,A_{2n-1})$, $(A_1,D_{2n+1})$, and $(A_1,D_{2n})$, we obtain three new infinite families of 3d $\mathcal{N}=2$ abelian gauge theories, all with monopole superpotentials, flowing to $\mathcal{N}=4$ SCFTs without Coulomb branch, but with the same non-trivial Higgs branch as the four-dimensional parent. Their topological A-twist yields $non$-$semisimple$ TQFTs related to $logarithmic$ VOAs such as $\widehat{\mathfrak{su}}(2)_{-4/3}$.

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arXiv2024

Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs

The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 4d $\mathcal{N}=2$ superconformal field theories with fractional r-charges, there exists a special notion of high-temperature limit on higher sheets that captures data of three-dimensional topological quantum field theories arising from r-twisted circle reduction. These TQFTs are closely tied with the VOA of the 4d SCFT. We study such high-temperature limits. More specifically, we apply Di~Pietro-Komargodski type supersymmetric effective field theory techniques to r-twisted circle reductions of $(A_1,A_{2n})$ Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest $\mathcal{N}=1$ supersymmetry. The result on the second sheet is the Gang-Kim-Stubbs family of 3d $\mathcal{N}=2$ SUSY enhancing rank-$0$ theories with monopole superpotentials, whose boundary supports the Virasoro minimal model VOAs $M(2,2n+3)$. Upon topological twist, they give non-unitary TQFTs controlled by the $M(2,2n+3)$ modular tensor category (MTC). The high-temperature limit on other sheets yields their unitary or non-unitary Galois conjugates. This opens up the prospect of a broader four-supercharge perspective on the celebrated correspondence between 4d $\mathcal{N}=2$ SCFTs and 2d VOAs via interpolating 3d EFTs. Several byproducts follow, including a systematic approach to 3d SUSY enhancement from 4d SUSY enhancement, and a 3d QFT handle on Galois orbits of various MTCs associated with 4d $\mathcal{N}=2$ SCFTs.

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arXiv2024

A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs

We introduce a novel class of two-dimensional non-unitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized Haagerup-Izumi modular data. Via the bulk-boundary correspondence, they are related to the three-dimensional non-unitary Haagerup topological field theories, recently constructed by a topological twisting of three-dimensional ${\cal N}=4$ rank-zero superconformal field theories (SCFTs), called S-fold SCFTs. We propose that, up to the overall factors, the half-indices of the rank-zero SCFTs give the explicit Nahm representation of four conformal characters of the RCFTs including the vacuum character. Using the theory of Bantay-Gannon, we can successfully complete them into the full admissible conformal characters of the RCFTs.

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arXiv2024

3D bulk field theories for 2D non-unitary N=1 supersymmetric minimal models

We propose bulk 3D N=4 rank-0 superconformal field theories, which are related to 2D N=1 supersymmetric minimal models, SM(2, ...) and SM(3, ...), via recently discovered non-unitary bulk-boundary correspondence. The correspondence relates a 3D N=4 rank-0 superconformal field theory to 2D chiral rational conformal field theories. A topologically twisted theory of the rank-0 SCFT supports the rational chiral algebra at the boundary upon a proper choice of boundary condition. We test the proposal by checking several non-trivial dictionaries of the correspondence.

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arXiv2024

Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models

Using 3D-3D correspondence, we construct 3D dual bulk field theories for general Virasoro minimal models $M(P,Q)$. These theories correspond to Seifert fiber spaces $S^2 ((P,P-R),(Q,S),(3,1))$ with two integers $(R,S)$ satisfying $PS-QR =1$. In the unitary case, where $|P-Q|=1$, the bulk theory has a mass gap and flows to a unitary topological field theory (TQFT) in the IR, which is expected to support the chiral Virasoro minimal model at the boundary under an appropriate boundary condition. For the non-unitary case, where $|P-Q|>1$, the bulk theory flows to a 3D $\mathcal{N}=4$ rank-0 superconformal field theory, whose topologically twisted theory supports the chiral minimal model at the boundary. We also provide a concrete field theory description of the 3D bulk theory using $T[SU(2)]$ theories. Our proposals are supported by various consistency checks using 3D-3D relations and direct computations of various partition functions.

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arXiv2023

Three-Dimensional Topological Field Theories and Non-Unitary Minimal Models

We find an intriguing relation between a class of 3-dimensional non-unitary topological field theories (TFTs) and Virasoro minimal models $M(2,2r+3)$ with $r \geq 1$. The TFTs are constructed by topologically twisting $3d$ ${\mathcal N}=4$ superconformal field theories (SCFTs) of rank-0, i.e. having zero-dimensional Coulomb and Higgs branches. We present ultraviolet (UV) field theory descriptions of the SCFTs with manifest ${\mathcal N}=2$ supersymmetry, which we argue is enhanced to ${\mathcal N}=4$ in the infrared. From the UV description, we compute various partition functions of the TFTs and reproduce some basic properties of the minimal models, such as their characters and modular matrices. We expect more general correspondence between topologically twisted $3d$ ${\mathcal N}=4$ rank-0 SCFTs and $2d$ non-unitary rational conformal field theories.

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arXiv2023

Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs

By applying the recently proposed (3D rank-0 $\mathcal{N}$=4 SCFT)/(non-unitary TQFTs) correspondence to S-fold SCFTs, we construct an exotic class of non-unitary TQFTs labelled by an integer $k\geq 3$. The SCFTs are obtained by gauging diagonal $SU(2)$ subgroup of $T[SU(2)]$ theory with Chern-Simons level $k$. We give the explicit expression for modular data, $S$ and $T$ matrices, of the TQFTs. When $k=4m^2+4m+3$ with an integer $m\geq 1$, the modular data (modulo a decoupled semion) is identical to a non-unitary Haagerup-Izumi modular data. Thus, we give a physical realization of the exotic non-unitary modular data as well as its generalization using an exotic class of SCFTs.

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arXiv2022

Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs

We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT$_\pm [\mathcal{T}_{\rm rank \;0}]$, to a (2+1)D interacting $\mathcal{N}=4$ superconformal field theory (SCFT) $\mathcal{T}_{\rm rank \;0}$ of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that $F = \max_α\left(- \log |S^{(+)}_{0α}| \right) = \max_α\left(- \log |S^{(-)}_{0α}|\right)$, where $F$ is the round three-sphere free energy of $\mathcal{T}_{\rm rank \;0 }$ and $S^{(\pm)}_{0α}$ is the first column in the modular S-matrix of TFT$_\pm$. From the dictionary, we derive the lower bound on $F$, $F \geq -\log \left(\sqrt{\frac{5-\sqrt{5}}{10}} \right) \simeq 0.642965$, which holds for any rank 0 SCFT. The bound is saturated by the minimal $\mathcal{N}=4$ SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

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arXiv2022

Infrared phases of 3D Class R theories

We study the IR phases of 3D class R theories associated with closed non-hyperbolic 3-manifolds. Non-hyperbolic 3-manifolds can be obtained by performing Dehn fillings on 1-cusped hyperbolic 3-manifolds along exceptional slopes. In 3D-3D correspondence, the `exceptional' Dehn filling corresponds to the gauging of an $SU(2)$ flavor symmetry in a superconformal field theory associated with a 1-cusped 3-manifold with `small' Chern-Simons levels. With several explicit examples, we analyze various interesting non-perturbative IR phenomena (such as spontaneous SUSY breaking, generation of mass gap and supersymmetry enhancement) from the `exceptional' gaugings. Interestingly, distinguished features of the IR phases can be captured by simple topological properties of non-hyperbolic 3-manifolds. We also find that 3D class R theories associated with certain classes of atoroidal non-hyperbolic 3-manifolds always exhibit supersymmetry enhancement at low energy and actually flow to 3D rank-0 $\mathcal{N}=4$ SCFTs with trivial vacuum moduli space.

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arXiv2022

Quantum trace map for 3-manifolds and a 'length conjecture'

We introduce a quantum trace map for an ideally triangulated hyperbolic knot complement $S^3\backslash \mathcal{K}$. The map assigns a quantum operator to each element of Kauffmann Skein module of the 3-manifold. The quantum operator lives in a module generated by products of quantized edge parameters of the ideal triangulation modulo some equivalence relations determined by gluing equations. Combining the quantum map with a state-integral model of $SL(2,\mathbb{C})$ Chern-Simons theory, one can define perturbative invariants of knot $K$ in the knot complement whose leading part is determined by its complex hyperbolic length. We then conjecture that the perturbative invariants determine an asymptotic expansion of the Jones polynomial for a link composed of $\mathcal{K}$ and $K$. We propose the explicit quantum trace map for figure-eight knot complement and confirm the length conjecture up to the second order in the asymptotic expansion both numerically and analytically.

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arXiv2020

Black holes and Large $N$ complex saddles in 3D-3D correspondence

We study the large $ N$ sign oscillation of the twisted indices for 3D theories of class $\mathcal{R}$ obtained from M5-branes wrapped on a hyperbolic 3-manifold. Holographically, the oscillatory behavior can be understood from the imaginary part of on-shell actions for the two Euclidean supergravity solutions, Bolt$_{\pm}$ with $p=0$, which are Wick rotation of magnetically charged AdS$_4$ black holes. The two solutions have the same imaginary part with opposite sign. The imaginary part comes from the $F\wedge F$-term in the supergravity and the coefficient is proportional to the Chern-Simons invariant of 3-manifold. Combining the holographic computation with 3D-3D relation for twisted indices, we propose a non-trivial mathematical conjecture regarding the phase factor of a twisted Reidemeister-Ray-Singer torsion on hyperbolic 3-manifold.

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arXiv2020

Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$

We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $\mathcal{R}$. Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large-$N$ expansion of supersymmetric partition functions for an infinite class of three-dimensional $\mathcal{N}=2$ SCFTs of class $\mathcal{R}$. We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS$_4$ black holes arising from wrapped M5-branes. In addition, we propose and test some conjectures about the perturbative partition function of Chern-Simons theory with complexified ADE gauge groups on closed hyperbolic three-manifolds.

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arXiv2020

M-theoretic Genesis of Topological Phases

We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction, the topological phases emerge as macroscopic world-volume theories of M5-branes wrapped around certain types of non-hyperbolic 3-manifolds. We devise a systematic algorithm for identifying the emergent topological phases from topological data of the internal wrapped 3-manifolds. As a benchmark of our approach, we reproduce all the known unitary bosonic topological orders up to rank 4. Remarkably, our construction is not restricted to an unitary bosonic theory but it can also generate fermionic and/or non-unitary topological phases in an equivalent fashion. Hence, we pave a new route toward the classification of topological phases of matter.

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arXiv2020

Rotating Black Hole Entropy from M5-branes

We compute the superconformal index of 3d $\mathcal{N}=2$ superconformal theories obtained from $N$ M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence, we use perturbative invariants of $SL(N,\mathbb{C})$ Chern-Simons theory to determine the superconformal index in the large $N$ limit, including corrections logarithmic in $N$. The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS$_4$ black holes. We also verify that the supergravity one-loop contribution to the $\log N$ term coincides with the field theoretic result. We propose a 3d-3d formulation for the refined topologically twisted index, and provide strong evidence in support of its vanishing --- which agrees with the fact that the expected dual rotating magnetically-charged black hole does not exist. This provides an interesting link between gravity and a tantalizing mathematical result.

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arXiv2019

Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds

We study the twisted index of 4d $\mathcal{N}$ = 2 class S theories on a closed hyperbolic 3-manifold $M_3$. Via 6d picture, the index can be written in terms of topological invariants called analytic torsions twisted by irreducible flat connections on the 3-manifold. Using the topological expression, we determine the full perturbative 1/N expansion of the twisted index. The leading part nicely matches the Bekestein-Hawking entropy of a magnetically charged black hole in the holographic dual $AdS_5$ with $AdS_2\times M_3$ near-horizon.

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