Localization at large<i>N</i>in Chern–Simons-matter theories

Mariño, Marcos

doi:10.1088/1751-8121/aa5f69

Cited by 35 publications

(50 citation statements)

References 237 publications

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“…Most of the contents in this section are reviews, though in section 2.1.3 and section 2.2.3 we will also raise some questions and clarify some points which we believe are not so trivial even to the experts but important for our later analysis. The main references of the review part are [17,18,23] (see also [40,41]). …”

Section: Abjm Theory and (2 2) Modelmentioning

confidence: 99%

Instanton effects in rank deformed superconformal Chern-Simons theories from topological strings

Moriyama¹,

Nakayama²,

Nosaka³

2017

J. High Energ. Phys.

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In the so-called (2, 2) theory, which is the U(N ) 4 circular quiver superconformal Chern-Simons theory with levels (k, 0, −k, 0), it was known that the instanton effects are described by the free energy of topological strings whose Gopakumar-Vafa invariants coincide with those of the local D 5 del Pezzo geometry. By considering two types of one-parameter rank deformations U(N )×U(N + M )×U(N + 2M )×U(N + M ) and U(N + M )×U(N )×U(N + M )×U(N ), we classify the known diagonal BPS indices by degrees. Together with other two types of one-parameter deformations, we further propose the topological string expression when both of the above two deformations are turned on.

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Section: Abjm Theory and (2 2) Modelmentioning

confidence: 99%

Instanton effects in rank deformed superconformal Chern-Simons theories from topological strings

Moriyama¹,

Nakayama²,

Nosaka³

2017

J. High Energ. Phys.

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“…For example, in the context of the ABJM model [46], which is the U(N) k × U(N) −k Chern-Simons gauge theory in d = 3 coupled to massless matter, it is possible to take the large N limit while keeping k fixed (this is is different from the 't Hooft limit where N/k is held fixed). In this so-called "M-theory limit", there is strong evidence that the ABJM theory is dual to M-theory on the AdS 4 × S 7 /Z k background, and one finds N dof ∼ k 1/2 N 3/2 [47][48][49][50] (for reviews see [51,52]). An even more exotic situation is when the Chern-Simons theory is U(N) k 1 × U(N) k 2 with k 1 + k 2 = 0; then N dof ∼ |k 1 + k 2 | 1/3 N 5/3 [53].…”

Section: Introductionmentioning

confidence: 99%

TASI Lectures on Large $N$ Tensor Models

Klebanov

Popov²,

Tarnopolsky

2018

Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017)

130

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The first part of these lecture notes is mostly devoted to a comparative discussion of the three basic large N limits, which apply to fields which are vectors, matrices, or tensors of rank three and higher. After a brief review of some physical applications of large N limits, we present a few solvable examples in zero space-time dimension. Using models with fields in the fundamental representation of O(N), O(N) 2 , or O(N) 3 symmetry, we compare their combinatorial properties and highlight a competition between the snail and melon diagrams. We exhibit the different methods used for solving the vector, matrix, and tensor large N limits. In the latter example we review how the dominance of melonic diagrams follows when a special "tetrahedral" interaction is introduced. The second part of the lectures is mostly about the fermionic quantum mechanical tensor models, whose large N limits are similar to that in the Sachdev-Ye-Kitaev (SYK) model. The minimal Majorana model with O(N) 3 symmetry and the tetrahedral Hamiltonian is reviewed in some detail; it is the closest tensor counterpart of the SYK model. Also reviewed are generalizations to complex fermionic tensors, including a model with SU(N) 2 × O(N) × U(1) symmetry, which is a tensor counterpart of the complex SYK model. The bosonic large N tensor models, which are formally tractable in continuous spacetime dimension, are reviewed briefly at the end.

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“…It would be interesting to explore also localizable SUSY QFT, for which asymptotic and resurgence properties have recently been studied [45][46][47][48][49][50][51]. As a simple analogy, consider the canonical example of localization in finite dimensional integrals, the exponential of the height function on S 2 ; this example is in one-to-one correspondence with SUSY QM.…”

Section: Discussionmentioning

confidence: 99%

Deconstructing zero: resurgence, supersymmetry and complex saddles

Dunne

Ünsal

2016

J. High Energ. Phys.

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We explain how a vanishing, or truncated, perturbative expansion, such as often arises in semi-classically tractable supersymmetric theories, can nevertheless be related to fluctuations about non-perturbative sectors via resurgence. We also demonstrate that, in the same class of theories, the vanishing of the ground state energy (unbroken supersymmetry) can be attributed to the cancellation between a real saddle and a complex saddle (with hidden topological angle π), and positivity of the ground state energy (broken supersymmetry) can be interpreted as the dominance of complex saddles. In either case, despite the fact that the ground state energy is zero to all orders in perturbation theory, all orders of fluctuations around non-perturbative saddles are encoded in the perturbative E(N, g). We illustrate these ideas with examples from supersymmetric quantum mechanics and quantum field theory.

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Localization at largeNin Chern–Simons-matter theories

Cited by 35 publications

References 237 publications

Instanton effects in rank deformed superconformal Chern-Simons theories from topological strings

Instanton effects in rank deformed superconformal Chern-Simons theories from topological strings

TASI Lectures on Large $N$ Tensor Models

Deconstructing zero: resurgence, supersymmetry and complex saddles

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