From Gauss graphs to giants

Koch, Robert de Mello; Nkumane, Lwazi

doi:10.1007/jhep02(2018)005

Cited by 6 publications

(3 citation statements)

References 39 publications

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“…The eventual goal of such a program would be to simplify the types of analysis found in the works [68,69]. It is likely that this basis is close to the so called Gauss graph basis described in [70,71].…”

Section: More Open Stringsmentioning

confidence: 99%

BPS coherent states and localization

Berenstein,

Wang

2022

Preprint

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We introduce coherent states averaged over a gauge group action to study correlators of half BPS states in N = 4 SYM theory. The overlaps of these averaged coherent states are a generating function of correlators and can be written in terms of the Harish-Chandra-Itzykzon-Zuber (HCIZ) integral. We show that this formula immediately leads to a computation of the normalization of two point functions in terms of characters obtained originally in the work of Corley, Jevicki and Ramgoolam. We also find various generalizations for A n−1 quivers that follow directly from other solvable integrals over unitary groups. All of these can be computed using localization methods. When we promote the parameters of the generating function to collective coordinates, there is a dominant saddle that controls the effective action of these coherent states in the regime where they describe single AdS giant gravitons. We also discuss how to add open strings to this formulation. These will produce calculations that rely on correlators of matrix components of unitaries in the ensemble that is determined by the HCIZ integral to determine anomalous dimensions. We also discuss how sphere giants arise from Grassman integrals, how one gets a dominant saddle and how open strings are added in that case. The fact that there is a dominant saddle helps to understand how a 1/N expansion arises for open strings. We generalize the coherent state idea to study 1/4 and 1/8 BPS states as more general integrals over unitary groups.

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Section: More Open Stringsmentioning

confidence: 99%

BPS coherent states and localization

Berenstein,

Wang

2022

Preprint

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“…Quantizing the space of Mikhailov's solutions leads to N non-interacting bosons in a harmonic oscillator [39,40,41]. It is tempting to speculate that it is precisely these oscillators that we are uncovering in our study; for evidence in harmony with this suggestion see [42]. It would be interesting to make this speculation precise.…”

Section: Discussionmentioning

confidence: 57%

Anomalous dimensions from boson lattice models

2018

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Operators dual to strings attached to giant graviton branes in AdS 5 × S 5 can be described rather explicitly in the dual N ¼ 4 super-Yang-Mills theory. They have a bare dimension of order N so that for these operators the large N limit and the planar limit are distinct; summing only the planar diagrams will not capture the large N dynamics. Focusing on the one-loop SUð3Þ sector of the theory, we consider operators that are a small deformation of a 1 2 -Bogomol'nyi-Prasad-Sommerfield (BPS) multigiant graviton state. The diagonalization of the dilatation operator at one loop has been carried out in previous studies, but explicit formulas for the operators of a good scaling dimension are only known when certain terms which were argued to be small are neglected. In this article, we include the terms which were neglected. The diagonalization is achieved by a novel mapping which replaces the problem of diagonalizing the dilatation operator with a system of bosons hopping on a lattice. The giant gravitons define the sites of this lattice, and the open strings stretching between distinct giant gravitons define the hopping terms of the Hamiltonian. Using the lattice boson model, we argue that the lowest energy giant graviton states are obtained by distributing the momenta carried by the X and Y fields evenly between the giants with the condition that any particular giant carries only X or Y momenta, but not both.

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“…Near half-BPS states have been studied in the context of the BMN limit of AdS/CFT [61]. In the context of giant gravitons, the physics of perturbations, in some sense small, of well-separated multi-giants has been understood [62,63,64].…”

Section: Partitions With One Dominant Row or Columnmentioning

confidence: 99%

Quarter-BPS states, multi-symmetric functions and set partitions

Lewis-Brown,

Ramgoolam

2020

Preprint

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We give a construction of general holomorphic quarter BPS operators in N = 4 SYM at weak coupling with U (N ) gauge group at finite N . The construction employs the Möbius inversion formula for set partitions, applied to multi-symmetric functions, alongside computations in the group algebras of symmetric groups. We present a computational algorithm which produces an orthogonal basis for the physical inner product on the space of holomorphic operators. The basis is labelled by a U (2) Young diagram, a U (N ) Young diagram and an additional plethystic multiplicity label. We describe precision counting results of quarter BPS states which are expected to be reproducible from dual computations with giant gravitons in the bulk, including a symmetry relating sphere and AdS giants within the quarter BPS sector. In the case n ≤ N (n being the dimension of the composite operator) the construction is analytic, using multi-symmetric functions and U (2) Clebsch-Gordan coefficients. Counting and correlators of the BPS operators can be encoded in a two-dimensional topological field theory based on permutation algebras and equipped with appropriate defects.

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From Gauss graphs to giants

Cited by 6 publications

References 39 publications

BPS coherent states and localization

BPS coherent states and localization

Anomalous dimensions from boson lattice models

Quarter-BPS states, multi-symmetric functions and set partitions

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