Dongmin Gang - Academia.edu (original) (raw)
Papers by Dongmin Gang
Using localization technique, we calculate the partition function and the expectation value of Wi... more Using localization technique, we calculate the partition function and the expectation value of Wilson loop operator in Chern-Simons theory on general lens spaces L(p,q)(including S2XS1). Our results are consistent with known results.
We argue the equivalence between the infrared conformal field theory of the 3d N = 8 supersymmetr... more We argue the equivalence between the infrared conformal field theory of the 3d 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 × U (Ñ ) −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 N = 8 U (N ) SYM and of U (N ) 1 × 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 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 N = 4 Yang-Mills theories related by mirror symmetry.
We derive a general formula of an index for N = 2 superconformal field theories on S 1 × S 3 with... more We derive a general formula of an index for N = 2 superconformal field theories on S 1 × S 3 with insertions of BPS Wilson line or 't Hooft line operator at the north pole and their anti-counterpart at the south pole of S 3 . One-loop and monopole bubbling effects are taken into account in the computation. As examples, we calculate the indices for N = 4 theories and N = 2 SU (2) theory with N f = 4, and find good agreements between indices of line operators related by S-duality. The relation between Verlinde loop operators and the indices is explored. The holographic correspondence between the fundamental (anti-symmetric) Wilson line operator and the fundamental string (D5 brane) in AdS 5 ×S 5 is confirmed by the index comparison.
We investigate the superconformal indices for the Chern-Simons-matter theories proposed for M2-br... more 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.
Journal of High Energy Physics, 2015
We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one ha... more 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 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.
Physics Letters B, 2014
We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge... more 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.
Journal of High Energy Physics, 2012
ABSTRACT
Journal of High Energy Physics, 2012
We study a superconformal index for N = 4 super Yang-Mills on S 1 × S 3 with a half BPS duality d... more We study a superconformal index for N = 4 super Yang-Mills on S 1 × S 3 with a half BPS duality domain wall inserted at the great twosphere 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 N = 4 SU (2) theory. We also briefly comment on a generalization to N = 2 A 1 Gaiotto theories with a simple example, N = 2 SU (2) SYM with four flavors.
Journal of High Energy Physics, 2008
We study superconformal defect lines in the tricritical Ising model in 2 dimensions. By the foldi... more We study superconformal defect lines in the tricritical Ising model in 2 dimensions. By the folding trick, a superconformal defect is mapped to a superconformal boundary of the N = 1 superconformal unitary minimal model of c = 7/5 with D 6 − E 6 modular invariant. It turns out that the complete set of the boundary states of c = 7/5 D 6 − E 6 model cannot be interpreted as the consistent set of superconformal defects in the tricritical Ising model since it does not contain the "no defect" boundary state. Instead, we find a set of 18 consistent superconformal defects including "no defect" and satisfying the Cardy condition. This set also includes some defects which are not purely transmissive or purely reflective.
Journal of High Energy Physics, 2011
We propose a recursion relation for tree-level scattering amplitudes in threedimensional Chern-Si... more We propose a recursion relation for tree-level scattering amplitudes in threedimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher dimensions. Using background field methods, we show that all tree-level superamplitudes of the ABJM theory vanish for large deformations, establishing the validity of the recursion formula. Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. Using generalized unitarity methods, we extend this symmetry to the cut-constructible parts of the loop amplitudes. *
Journal of High Energy Physics, 2011
ABSTRACT We investigate the superconformal indices for the Chern-Simons-matter theories proposed ... more ABSTRACT 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 {R}{{P}^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.
Journal of High Energy Physics, 2009
We consider the conformal dimension of an operator with large spin, using a spinning D3-brane wit... more We consider the conformal dimension of an operator with large spin, using a spinning D3-brane with electric flux in AdS 5 × S 5 instead of spinning fundamental string. This spinning D3-brane solution seems to correspond to an operator made by taking trace in a large symmetric representation. The conformal dimension, the spin and the R-charge show a scaling relation in a certain region of parameters. In the small string charge limit, the result is consistent with the fundamental string picture. There is a phase transition when the fundamental string charge become larger than a certain critical value; there is no stable D3-brane solution above the critical value.
Journal of High Energy Physics, 2014
We probe the 3d-3d correspondence for mapping cylinder/torus using the superconformal index. We f... more 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 simple basis change of the Hilbert space for the SL(2, C) Chern-Simons theory on R × Σ 1,1 .
Journal of High Energy Physics, 2008
Using localization technique, we calculate the partition function and the expectation value of Wi... more Using localization technique, we calculate the partition function and the expectation value of Wilson loop operator in Chern-Simons theory on general lens spaces L(p,q)(including S2XS1). Our results are consistent with known results.
We argue the equivalence between the infrared conformal field theory of the 3d N = 8 supersymmetr... more We argue the equivalence between the infrared conformal field theory of the 3d 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 × U (Ñ ) −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 N = 8 U (N ) SYM and of U (N ) 1 × 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 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 N = 4 Yang-Mills theories related by mirror symmetry.
We derive a general formula of an index for N = 2 superconformal field theories on S 1 × S 3 with... more We derive a general formula of an index for N = 2 superconformal field theories on S 1 × S 3 with insertions of BPS Wilson line or 't Hooft line operator at the north pole and their anti-counterpart at the south pole of S 3 . One-loop and monopole bubbling effects are taken into account in the computation. As examples, we calculate the indices for N = 4 theories and N = 2 SU (2) theory with N f = 4, and find good agreements between indices of line operators related by S-duality. The relation between Verlinde loop operators and the indices is explored. The holographic correspondence between the fundamental (anti-symmetric) Wilson line operator and the fundamental string (D5 brane) in AdS 5 ×S 5 is confirmed by the index comparison.
We investigate the superconformal indices for the Chern-Simons-matter theories proposed for M2-br... more 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.
Journal of High Energy Physics, 2015
We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one ha... more 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 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.
Physics Letters B, 2014
We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge... more 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.
Journal of High Energy Physics, 2012
ABSTRACT
Journal of High Energy Physics, 2012
We study a superconformal index for N = 4 super Yang-Mills on S 1 × S 3 with a half BPS duality d... more We study a superconformal index for N = 4 super Yang-Mills on S 1 × S 3 with a half BPS duality domain wall inserted at the great twosphere 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 N = 4 SU (2) theory. We also briefly comment on a generalization to N = 2 A 1 Gaiotto theories with a simple example, N = 2 SU (2) SYM with four flavors.
Journal of High Energy Physics, 2008
We study superconformal defect lines in the tricritical Ising model in 2 dimensions. By the foldi... more We study superconformal defect lines in the tricritical Ising model in 2 dimensions. By the folding trick, a superconformal defect is mapped to a superconformal boundary of the N = 1 superconformal unitary minimal model of c = 7/5 with D 6 − E 6 modular invariant. It turns out that the complete set of the boundary states of c = 7/5 D 6 − E 6 model cannot be interpreted as the consistent set of superconformal defects in the tricritical Ising model since it does not contain the "no defect" boundary state. Instead, we find a set of 18 consistent superconformal defects including "no defect" and satisfying the Cardy condition. This set also includes some defects which are not purely transmissive or purely reflective.
Journal of High Energy Physics, 2011
We propose a recursion relation for tree-level scattering amplitudes in threedimensional Chern-Si... more We propose a recursion relation for tree-level scattering amplitudes in threedimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher dimensions. Using background field methods, we show that all tree-level superamplitudes of the ABJM theory vanish for large deformations, establishing the validity of the recursion formula. Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. Using generalized unitarity methods, we extend this symmetry to the cut-constructible parts of the loop amplitudes. *
Journal of High Energy Physics, 2011
ABSTRACT We investigate the superconformal indices for the Chern-Simons-matter theories proposed ... more ABSTRACT 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 {R}{{P}^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.
Journal of High Energy Physics, 2009
We consider the conformal dimension of an operator with large spin, using a spinning D3-brane wit... more We consider the conformal dimension of an operator with large spin, using a spinning D3-brane with electric flux in AdS 5 × S 5 instead of spinning fundamental string. This spinning D3-brane solution seems to correspond to an operator made by taking trace in a large symmetric representation. The conformal dimension, the spin and the R-charge show a scaling relation in a certain region of parameters. In the small string charge limit, the result is consistent with the fundamental string picture. There is a phase transition when the fundamental string charge become larger than a certain critical value; there is no stable D3-brane solution above the critical value.
Journal of High Energy Physics, 2014
We probe the 3d-3d correspondence for mapping cylinder/torus using the superconformal index. We f... more 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 simple basis change of the Hilbert space for the SL(2, C) Chern-Simons theory on R × Σ 1,1 .
Journal of High Energy Physics, 2008