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Jaemo Park

Publications and source records attributed to Jaemo Park.

At least 37 records · Page 2Linked to original sources
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}.

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arXiv2013

Factorization of the 3d superconformal index

We prove that 3d superconformal index for general $\mathcal N=2$ U(N) gauge group with fundamentals and anti-fundmentals with/without Chern-Simons terms is factorized into vortex and anti-vortex partition function. We show that for simple cases, 3d vortex partition function coincides with a suitable topological open string partition function. We provide much more elegant derivation at the index level for $\mathcal N=2$ Seiberg-like dualities of unitary gauge groups with fundamantal matters and $\mathcal N=4$ mirror symmetry

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arXiv2013

Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group

We work out Seiberg-like dualities for 3d $\mathcal{N}=2$ theories with SU(N) gauge group. We use the $SL(2,\mathbb{Z})$ action on 3d conformal field theories with U(1) global symmetry. One of generator S of $SL(2,\mathbb{Z})$ acts as gauging of the U(1) global symmetry. Utilizing $S=S^{-1}$ up to charge conjugation, we obtain Seiberg-like dual of SU(N) theories by gauging topological U(1) symmetry of the Seiberg-like dual of U(N) theories with the same matter content. We work out the Aharony dualities for SU(N) gauge theory with $N_f$ fundamental/anti-fundamnetal flavors, with/without one adjoint matter with the superpotential. We also work out the Giveon-Kutasov dualities for SU(N) gauge theory with Chern-Simons term and with $N_f$ fundamental/anti-fundamental flavors. For all the proposed dualities, we give various evidences such as chiral ring matching and the superconformal index computations. We find the perfect matchings.

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arXiv2013

Aharony Dualities for 3d Theories with Adjoint Matter

We study Aharony dualities for 3d N=2 gauge theories of classical gauge group with one adjoint and fundamental matters. We work out the 3d superconformal index for the dual pairs to find the perfect matchings. Along with it, we enumerate the independent monopole operators parametrizing the Coulomb branches and confirm the nonperturbative truncation of the chiral rings, consistent with the proposed dualities.

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arXiv2012

Duality between N=5 and N=6 Chern-Simons matter theory

We provide evidences for the duality between ${\cal N}=6$ $U(M)_{4} \times U(N)_{-4}$ Chern-Simons matter theory and ${\cal N}=5$ $O(\hat{M})_{2} \times USp(2\hat{N})_{-1}$ theory for a suitable $\hat{M},\hat{N}$ by working out the superconformal index, which shows perfect matching. For ${\cal N}=5$ theories, we show that supersymmetry is enhanced to ${\cal N}=6$ by explicitly constructing monopole operators filling in $SO(6)_R$ $R$-currents. Finally we work out the large $N$ index of $O(2N)_{2k} \times USp(2N)_{-k}$ and show that it exactly matches with the gravity index on $AdS_4 \times S^7/D_k$, which further provides additional evidence for the duality between the ${\cal N}=5$ and ${\cal N}=6$ theory for $k=1$

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arXiv2012

Complete type IIA superstring action on IIA plane wave background

We construct the type IIA Green-Schwarz superstring action on a ten-dimensional IIA plane wave background with 24 supersymmetries keeping the full 32 fermionic coordinates. Starting from the symmetry superalgebra for the maximally supersymmetric eleven dimensional plane wave background, we obtain the eleven dimensional superfields. The Kaluza-Klein reduction leads to the ten dimensional superfields for the IIA plane wave background, from which the type IIA superstring action is constructed. We show that the superstring action reduces correctly to the previously known light-cone gauge fixed action upon imposing the light-cone $κ$-symmetry fixing condition.

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arXiv2011

Evidence for Aharony duality for orthogonal gauge groups

We study the Aharony duality for three dimensional $\mathcal N=2$ supersymmetric gauge theories for orthogonal gauge groups with matters in vector representation. We provide the evidence for the duality by working out the partition function on $S^3$ and the superconformal index, which show perfect agreement.

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arXiv2011

Dualities for 3d Theories with Tensor Matter

We study dualities for ${\cal N}=2$ 3d Chern-Simons matter theories with gauge groups U/Sp/O, matter in the two-index tensor representations (adjoint/symmetric/antisymmetric) in addition to the fundamental representation, and a superpotential. These dualities are analogous to Kutasov-Schwimmer-Seiberg dualities in 4d. We test them by computing the superconformal index and the partition function on $S^3$ for many dual pairs and find perfect agreement. In some cases we find a simple dual description for theories with tensor matter and no superpotential, thereby generalizing the "Duality Appetizer" of Jafferis and Yin to an infinite class of theories. We also investigate nonperturbative truncation of the chiral ring proposed in the context of 4d dualities.

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arXiv2011

Annulus amplitude of FZZT branes revisited

We revisit the annulus amplitude of FZZT branes with general matter sectors (r,s) using the recent development of matrix model and minimal Liouville gravity. Following the boundary description of the 1-matrix model and bulk resonance transformation between primary operators we find the consistency of the brane decomposition into (1,1)-branes. We also investigate the corresponding results obtained directly from the minimal Liouville gravity and demonstrate the perfect agreement with the matrix results.

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arXiv2011

Ab Initio Wall-Crossing

We derive supersymmetric quantum mechanics of n BPS objects with 3n position degrees of freedom and 4n fermionic partners with SO(4) R-symmetry. The potential terms, essential and sufficient for the index problem for non-threshold BPS states, are universal, and 2(n-1) dimensional classical moduli spaces M_n emerge from zero locus of the potential energy. We emphasize that there is no natural reduction of the quantum mechanics to M_n, contrary to the conventional wisdom. Nevertheless, via an index-preserving deformation that breaks supersymmetry partially, we derive a Dirac index on M_n as the fundamental state counting quantity. This rigorously fills a missing link in the "Coulomb phase" wall-crossing formula in literature. We then impose Bose/Fermi statistics of identical centers, and derive the general wall-crossing formula, applicable to both BPS black holes and BPS dyons. Also explained dynamically is how the rational invariant ~Ω(β)/p^2, appearing repeatedly in wall-crossing formulae, can be understood as the universal multiplicative factor due to p identical, coincident, yet unbound, BPS particles of charge β. Along the way, we also clarify relationships between field theory state countings and quantum mechanical indices.

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arXiv2011

ABCD of 3d ${\cal N}=8$ and 4 Superconformal Field Theories

We argue the equivalence between the infrared conformal field theory of the 3d $\mathcal{N}=8$ supersymmetric Yang-Mills theories of ABCD ($U(N), SO(2N+1), Sp(2N), O(2N)$) gauge groups and the ABJ(M) theories of $U(N)_k\times U(\tilde N)_{-k}$ for $k=1,2$. We support this duality by comparing the superconformal index of the IR limit of these super Yang-Mills theories and that of those ABJ(M) models. Especially we find the match between two indices of (mirror dual of) the $\mathcal{N}=8$ U(N) SYM and of $U(N)_1\times U(N)_{-1}$ ABJM model. Also we take large $N$ limit of ABCD super Yang-Mills theories with additional fundamental hyper-multiplets and infer the large N limit of $\mathcal{N}=8$ ABCD theories themselves, finding the expected gravitational duals. With the additional input on finite N, we argue the equivalence of Yang-Mills and ABJ(M) theories for all N. We further explore similar dualities to Chern-Simons matter theories for $\mathcal{N}=4$ Yang-Mills theories related by mirror symmetry.

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arXiv2011

Emergent Schrodinger geometries from mass-deformed CFT

We study an M-theory solution for the holographic flow of AdS4 times Sasaki-Einstein 7-manifolds with skew-whiffing, perturbed by a mass operator. The infrared solution contains the 5 dimensional Schrodinger geometry after considering the gravity dual of the standard non-relativistic limit of relativistic field theories. The mass deformation of the field theory is discussed in detail for the case with 7 manifold being a round sphere.

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arXiv2011

Refined test of AdS4/CFT3 correspondence for N=2,3 theories

We investigate the superconformal indices for the Chern-Simons-matter theories proposed for M2-branes probing the cones over N^{010}/Z_k, Q^{111}, M^{32} with N=2,3 supersymmetries and compare them with the corresponding dual gravity indices. For N^{010}, we find perfect agreements. In addition, for N^{010}/Z_k, we also find an agreement with the gravity index including the contributions from two types of D6-branes wrapping RP^3. For Q^{111}, we find that the model obtained by adding fundamental flavors to the N=6 theory has the right structure to be the correct model. For M^{32}, we find the matching with the gravity index modulo contributions from peculiar saddle points.

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arXiv2010

AGT on the S-duality Wall

Three-dimensional gauge theory T[G] arises on a domain wall between four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L. We argue that the N=2^* mass deformation of the bulk theory induces a mass-deformation of the theory T[G] on the wall. The partition functions of the theory T[SU(2)] and its mass-deformation on the three-sphere are shown to coincide with the transformation coefficient of Liouville one-point conformal block on torus under the S-duality.

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arXiv2010

Probing AdS4/CFT3 proposals beyond chiral rings

We calculate the superconformal Witten index for the Chern-Simons-matter theory which was proposed to describe multiple M2-branes on $C^2 X C^2/Z_k$. We consider a variant of this model, which exhibits explicit N=3 supersymmetry and has the advantage of not having an exotic branch of the moduli space. At $k=1$, we compare the index with that from the proposed gravity dual and find a disagreement.

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arXiv2010

The BPS spectrum of monopole operators in ABJM: towards a field theory description of the giant torus

We study the BPS spectrum of monopole operators in ABJM theory. First we work out the complete spectrum of the chiral ring by using a semiclassical analysis of the field theory compactified on a two sphere. By properly taking into account the full quantization condition of monopole charges, we show that the moduli space of ABJM theory with Chern-Simons level k, -k is a particular Z_k cover of the symmetric product of C^4/Z_k. We also work out in detail the spectrum of fluctuations around half-BPS monopole configurations and we find candidate states for a dual BPS configuration to the giant torus solution found by Nishioka and Takayanagi in the supergravity limit. We also discuss more general BPS states.

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