Young diagrams, Brauer algebras, and bubbling geometries

Kimura, Yusuke; Lin, Hai

doi:10.1007/jhep01(2012)121

Cited by 11 publications

(13 citation statements)

References 56 publications

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“…A basis for the local operators which organizes the theory using the quantum numbers of the global symmetries was given in [13,14]. Another basis, employing projectors related to the Brauer algebra was put forward in [15] and developed in a number of interesting works [16][17][18][19][20][21][22]. For the systems we are interested in, the most convenient basis to use is provided by the restricted Schur polynomials.…”

Section: Jhep03(2016)156mentioning

confidence: 99%

Anomalous dimensions of heavy operators from magnon energies

Koch

Tahiridimbisoa

Mathwin

2016

J. High Energ. Phys.

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Abstract:We study spin chains with boundaries that are dual to open strings suspended between systems of giant gravitons and dual giant gravitons. Motivated by a geometrical interpretation of the central charges of su(2|2), we propose a simple and minimal all loop expression that interpolates between the anomalous dimensions computed in the gauge theory and energies computed in the dual string theory. The discussion makes use of a description in terms of magnons, generalizing results for a single maximal giant graviton. The symmetries of the problem determine the structure of the magnon boundary reflection/scattering matrix up to a phase. We compute a reflection/scattering matrix element at weak coupling and verify that it is consistent with the answer determined by symmetry. We find the reflection/scattering matrix does not satisfy the boundary Yang-Baxter equation so that the boundary condition on the open spin chain spoils integrability. We also explain the interpretation of the double coset ansatz in the magnon language.

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Section: Jhep03(2016)156mentioning

confidence: 99%

Anomalous dimensions of heavy operators from magnon energies

Koch

Tahiridimbisoa

Mathwin

2016

J. High Energ. Phys.

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“…The result of these studies is a basis of local operators that also diagonalizes the free field two point function. These bases have been useful for exploring giant gravitons [13,14,15,16,17,18,54,20,21,22,23] and new background geometries [24,25,26,27,28,29,30,31,32,33,34,35] in AdS/CFT [36], as well as for the computations of anomalous dimensions in large N but non-planar limits [37,38,39,40,41,42,43]. Elements in the basis are labeled by Young diagrams.…”

Section: Discussionmentioning

confidence: 99%

FiniteNquiver gauge theory

2014

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At finite N the number of restricted Schur polynomials is greater than or equal to the number of generalized restricted Schur polynomials. In this note we study this discrepancy and explain its origin. We conclude that, for quiver gauge theories, in general, the generalized restricted Shur polynomials correctly account for the complete set of finite N constraints and they provide a basis, while the restricted Schur polynomials only account for a subset of the finite N constraints and are thus overcomplete. We identify several situations in which the restricted Schur polynomials do in fact account for the complete set of finite N constraints. In these situations the restricted Schur polynomials and the generalized restricted Schur polynomials both provide good bases for the quiver gauge theory. Finally, we demonstrate situations in which the generalized restricted Schur polynomials reduce to the restricted Schur polynomials.

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“…Because such conserved charges correspond to parameters of the dual physics, it would be helpful to conduct an analysis in the string/gravity side. In [39] we have studied a correspondence between 1/4 BPS operators and 1/4 BPS geometries, where it was shown that the geometries are characterised by an integer that has the same upper bound as the integer k (: recall k ≤ min(m, n)). This fact might be a clue to solve the operator mixing dual to geometries.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…This leads to considering the restriction 2), which determines the mixing structure. Denoting an irreducible representation of B N (1, 2) by γ 3 , the necessary condition for the non-zero mixing is that the M γ γ 2 ,γ 3 , which is given by the same form as (39), is non-zero. Denoting the number of boxes in a partition α by n(α), we find that n(δ) and n(ζ) take 0, 1, 2, and n(ǫ) and n(κ) take 0, 1.…”

Section: More General Differential Operatorsmentioning

confidence: 99%

Non-planar operator mixing by Brauer representations

Kimura

2013

Nuclear Physics B

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We study the action of the dilatation operator on the basis of local operators constructed from the elements of the walled Brauer algebra, with non-planar corrections fully taken into account. We will see that the operator mixing can be neatly expressed in terms of the irreducible representations of the algebra. In particular we focus on a role of the integer that determines the number of boxes in the representations.Comment: 19 page

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Young diagrams, Brauer algebras, and bubbling geometries

Cited by 11 publications

References 56 publications

Anomalous dimensions of heavy operators from magnon energies

Anomalous dimensions of heavy operators from magnon energies

FiniteNquiver gauge theory

Non-planar operator mixing by Brauer representations

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