arXiv subjects

Dongmin Gang

Publications and source records attributed to Dongmin Gang.

At least 37 records · Page 2Linked to original sources

arXiv2019

Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere

We study a perturbative expansion of the squashed 3-sphere ($S^3_b$) partition function of 3d $\mathcal{N}=2$ gauge theories around the squashing parameter $b= 1$. Our proposal gives the coefficients of the perturbative expansion as a finite sum over the saddle points of the supersymmetric-localization integral in the limit $b \rightarrow 0$ (the so-called Bethe vacua), and the contribution from each Bethe vacua can be systematically computed using saddle-point methods. Our expansion provides an efficient and practical method for computing basic CFT data ($F,C_T,C_{JJ}$ and higher-point correlation functions of the stress-energy tensor) of the IR superconformal field theory without performing the localization integrals.

hep-th↗

arXiv2019

Adjoint Reidemeister torsions from wrapped M5-branes

We introduce a vanishing property of adjoint Reidemeister torsions of a cusped hyperbolic 3-manifold derived from the physics of wrapped M5-branes on the manifold. To support our physical observation, we present a rigorous proof for the figure-eight knot complement with respect to all slopes. We also present numerical verification for several knots.

math.GT↗

arXiv2019

Precision Microstate Counting for the Entropy of Wrapped M5-branes

We study the large $N$ expansion of twisted partition functions of 3d $\mathcal{N}=2$ superconformal field theories arising from $N$ M5-branes wrapped on a hyperbolic 3-manifold, $M_3$. Via the 3d-3d correspondence, the partition functions of these 3d ${\cal N}=2$ 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 $PSL(N,\mathbb{C})$ Chern-Simons theory around irreducible flat connections on $M_3$. Using mathematical results on the asymptotics of the invariants, we compute the twisted partition functions in the large $N$ limit including perturbative corrections to all orders in $1/N$. Surprisingly, the perturbative expansion terminates at finite order. The leading part of the partition function is of order $N^3$ and agrees with the Bekenstein-Hawking entropy of the dual black holes. The subleading part, in particular the $\log N$-terms in the field theory partition function is found to precisely match the one-loop quantum corrections in the dual eleven dimensional supergravity. The field theory results of other terms in $1/N$ provide a stringent prediction for higher order corrections in the holographic dual, which is M-theory.

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arXiv2019

Three-dimensional gauge theories with supersymmetry enhancement

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 $U(1)$ gauge group has the Chern-Simons level $-\frac{3}2$ 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 evidences for the conjecture: 1) exact match between the central charges of the $U(1)$ R-symmetry current and the $U(1)$ topological symmetry current, 2) semi-classical construction of the $\mathcal{N}=4$ stress-tensor multiplet, and 3) an IR duality between a direct product of the two copies of the 3d theory on the one hand, and an $\mathcal{N}=4$ theory obtained by gauging the diagonal $SU(2)$ flavor symmetry of the $T[SU(2)]$ theory, on the other. The duality in 3) follows from geometrical aspects of the 3d-3d correspondence.

hep-th↗

arXiv2018

All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory

We propose an extension of the recently-proposed volume conjecture for closed hyperbolic 3-manifolds, to all orders in perturbative expansion. We first derive formulas for the perturbative expansion of the partition function of complex Chern-Simons theory around a hyperbolic flat connection, which produces infinitely-many perturbative invariants of the closed oriented 3-manifold. The conjecture is that this expansion coincides with the perturbative expansion of the Witten-Reshetikhin-Turaev invariants at roots of unity $q=e^{2 πi/r}$ with $r$ odd, in the limit $r \to \infty$. We provide numerical evidence for our conjecture.

hep-th↗

arXiv2018

Large $N$ twisted partition functions in 3d-3d correspondence and Holography

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 perturbtaive Chern-Simons invariants around the flat connections, we find universal expressions for the large $N$ twisted partition functions contributed from the two Bethe vacua in term of the hyperbolic volume of $M$. The two large $N$ partition functions perfectly match the on-shell actions for two Bolt-type solutions in the holographic dual $AdS_4$ gravity respectively.

hep-th↗

arXiv2018

Quantum Approach to Dehn Surgery Problem

We propose a new algorithm for Dehn surgery problem, finding exceptional Dehn filling slopes for a given hyperbolic 3-manifold with a torus boundary, using a quantum invariant called "3D index". The invariant is defined using an ideal triangulation of the cusped 3-manifold. We test the algorithm for many examples.

math.GT↗

arXiv2018

Symmetry enhancement and closing of knots in 3d/3d correspondence

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 $\mathcal{N}=(2,0)$ theory of $A_1$-type on a 3-manifold, we propose a topological criterion for $SU(2)/SO(3)$ flavor symmetry enhancement for the $u(1)$ symmetry in the theory associated to a torus boundary, which is expected from the 6d viewpoint. Base on the understanding of symmetry enhancement, we generalize the construction to closed 3-manifolds by identifying the gauge theory counterpart of Dehn filling operation. The generalized construction predicts infinitely many 3d dualities from surgery calculus in knot theory. Moreover, by using the symmetry enhancement criterion, we show that theories associated to all hyperboilc twist knots have surprising $SU(3)$ symmetry enhancement which is unexpected from the 6d viewpoint.

hep-th↗

arXiv2017

S duality and Framed BPS States via BPS Graphs

We study a realization of S dualities of four-dimensional $\mathcal{N}=2$ class $\mathcal{S}$ theories based on BPS graphs. S duality transformations of the UV curve are explicitly expressed as a sequence of topological transitions of the graph, and translated into cluster transformations of the algebra associated to the dual BPS quiver. Our construction applies to generic class $\mathcal{S}$ theories, including those with non-maximal flavor symmetry, generalizing previous results based on higher triangulations. We study the the action of S duality on UV line operators, and show that it matches precisely with the mapping class group, by a careful analysis of framed wall-crossing. We comment on the implications of our results for the computation of three-manifold invariants via cluster partition functions.

hep-th↗

arXiv2017

S-duality resurgence in SL(2) Chern-Simons theory

We find that an S-duality in SL(2) Chern-Simons theory for hyperbolic 3-manifolds emerges by the Borel resummation of a semiclassical expansion around a particular flat connection associated to the hyperbolic structure. We demonstrate it numerically with two representative examples of hyperbolic 3-manifolds.

hep-th↗

arXiv2017

Smallest 3d hyperbolic manifolds via simple 3d theories

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

hep-th↗

arXiv2016

3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes

We study CFT data of 3-dimensional superconformal field theories (SCFTs) arising from wrapped two M5-branes on closed hyperbolic 3-manifolds. Via so-called 3d/3d correspondence, central charges of these SCFTs are related to a $SL(2)$ Chern-Simons (CS) invariant on the 3-manifolds. We give a rigorous definition of the invariant in terms of resurgence theory and a state-integral model for the complex CS theory. We numerically evaluate the central charges for several closed 3-manifolds with small hyperbolic volume. The computation suggests that the wrapped M5-brane systems give infinitely many discrete SCFTs with small central charges. We also analyze these `minimal' SCFTs in the eye of 3d $\mathcal{N}=2$ superconformal bootstrap.

hep-th↗

arXiv2015

Aspects of Defects in 3d-3d Correspondence

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 $SL(N, \mathbb{C})$) on $M$ and a 3d $\mathcal{N}=2$ theory $T_{N}[M]$. We establish a dictionary for 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 for complex Chern-Simons theory, cluster algebra techniques, domain wall theory $T[SU(N)]$, 5d $\mathcal{N}=2$ SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, in particular for non-maximal punctures and $N>2$. We also highlight the non-Abelian description of the 3d $\mathcal{N}=2$ $T_N[M]$ theory with defect included, as well as its Higgsing prescription and the resulting `refinement' in complex CS theory. This paper is a companion to our shorter paper arXiv:1510.03884, which summarizes our main results.

hep-th↗

arXiv2015

Taming Supersymmetric Defects in 3d-3d Correspondence

We study knots in 3d Chern-Simons theory with complex gauge group $SL(N,\mathbb{C})$, in the context of its relation with 3d $\mathcal{N}=2$ theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d $(2,0)$ theory, which is compactified on a 3-manifold $\hat{M}$. We identify such defects in various corners of the 3d-3d correspondence, namely in 3d $SL(N,\mathbb{C})$ Chern-Simons theory, in 3d $\mathcal{N}=2$ theory, in 5d $\mathcal{N}=2$ super Yang-Mills theory, and in the M-theory holographic dual. We can make quantitative checks of the 3d-3d correspondence by computing partition functions at each of these theories. This Letter is a companion to a longer paper, which contains more details and more results.

hep-th↗

arXiv2015

Holography of Wrapped M5-branes and Chern-Simons theory

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 N^3 scaling with precise coefficients.

hep-th↗

arXiv2014

Holography of 3d-3d correspondence at Large N

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 AdS$_4$ 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 perturbative free energy of a Chern-Simons theory on hyperbolic 3-manifold. The conjecture claims that the tree, one-loop and two-loop terms all share the same $N^3$ scaling behavior and are proportional to the volume of the 3-manifold, while the three-loop and higher terms are suppressed at large $N$. Under mild assumptions, we prove the tree and one-loop parts of the conjecture. For the two-loop part, we test the conjecture numerically in a number of examples and find precise agreement. We also confirm the suppression of higher loop terms in a few examples.

hep-th↗

arXiv2013

Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus

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 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 the corresponding 3d theory associated with ideal triangulation. The equality between the indices from the two descriptions for the mapping torus theory is reduced to a basis change of the Hilbert space for the SL(2,C) Chern-Simons theory on RxΣ_{1,1}.

hep-th↗

arXiv2012

Superconformal Index with Duality Domain Wall

We study a superconformal index for ${\cal N}=4$ super Yang-Mills on $S^1 \times S^3$ with a half BPS duality domain wall inserted at the great two-sphere in $S^3$. The index is obtained by coupling the 3d generalized superconformal index on the duality domain wall with 4d half-indices. We further consider insertions of line operators to the configuration and propose integral equations which express that the 3d index on duality domain wall is a duality kernel relating half indices of two line operators related by the duality map. We explicitly check the proposed integral equations for various duality domain walls and line operators in the ${\cal N}=4$ SU(2) theory. We also briefly comment on a generalization to $\mathcal{N}=2$ $A_1$ Gaiotto theories with a simple example, ${\cal N}=2$ SU(2) SYM with four flavors.

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