BPS states, conserved charges and centres of symmetric group algebras

Kemp, Garreth; Ramgoolam, Sanjaye

doi:10.1007/jhep01(2020)146

Cited by 14 publications

(20 citation statements)

References 28 publications

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“…We will give a description of this for the case where G is symmetric group S n , where known facts about the centre of Z(C(S n )) allow a concrete discussion. We will make use of T k ∈ Z(C(S n )) given by summing all permutations with a single non-trivial cycle of length k. This alternative description follows by exploiting the fact that conjugacy classes labeled by partitions of n provide a basis for the centre of the group algebra C(S n ), denoted as Z(C(S n )) [47]. It turns out that a subset of these basis elements, those given by T k with k ≤ k * (n), will generate Z(C(S n )) [47].…”

Section: S-duality For G-ctstmentioning

confidence: 99%

“…We will make use of T k ∈ Z(C(S n )) given by summing all permutations with a single non-trivial cycle of length k. This alternative description follows by exploiting the fact that conjugacy classes labeled by partitions of n provide a basis for the centre of the group algebra C(S n ), denoted as Z(C(S n )) [47]. It turns out that a subset of these basis elements, those given by T k with k ≤ k * (n), will generate Z(C(S n )) [47]. k * (n) is a (not explicitly known) function of n whose form is determined by the degeneracies in the characters of S n .…”

Section: S-duality For G-ctstmentioning

confidence: 99%

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Integrality, duality and finiteness in combinatoric topological strings

Koch

Kemp

et al. 2022

J. High Energ. Phys.

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A remarkable result at the intersection of number theory and group theory states that the order of a finite group G (denoted |G|) is divisible by the dimension dR of any irreducible complex representation of G. We show that the integer ratios $$ {\left|G\right|}^2/{d}_R^2 $$ G 2 / d R 2 are combinatorially constructible using finite algorithms which take as input the amplitudes of combinatoric topological strings (G-CTST) of finite groups based on 2D Dijkgraaf-Witten topological field theories (G-TQFT2). The ratios are also shown to be eigenvalues of handle creation operators in G-TQFT2/G-CTST. These strings have recently been discussed as toy models of wormholes and baby universes by Marolf and Maxfield, and Gardiner and Megas. Boundary amplitudes of the G-TQFT2/G-CTST provide algorithms for combinatoric constructions of normalized characters. Stringy S-duality for closed G-CTST gives a dual expansion generated by disconnected entangled surfaces. There are universal relations between G-TQFT2 amplitudes due to the finiteness of the number K of conjugacy classes. These relations can be labelled by Young diagrams and are captured by null states in an inner product constructed by coupling the G-TQFT2 to a universal TQFT2 based on symmetric group algebras. We discuss the scenario of a 3D holographic dual for this coupled theory and the implications of the scenario for the factorization puzzle of 2D/3D holography raised by wormholes in 3D.

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Section: S-duality For G-ctstmentioning

confidence: 99%

Section: S-duality For G-ctstmentioning

confidence: 99%

Integrality, duality and finiteness in combinatoric topological strings

Koch

Kemp

et al. 2022

J. High Energ. Phys.

Self Cite

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“…Some recent studies relating to the large R-charge JHEP08(2021)006 limit or Penrose limit, as well as applications in more general theories can be found in e.g. [14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Non-negativity of BMN two-point functions with three string modes

Huang

2021

J. High Energ. Phys.

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Recently, we proposed a novel entry of the pp-wave holographic dictionary, which equated the Berenstein-Maldacena-Nastase (BMN) two-point functions in free $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory with the norm squares of the quantum unitary transition amplitudes between the corresponding tensionless strings in the infinite curvature limit, for the cases with no more than three string modes in different transverse directions. A seemingly highly non-trivial conjectural consequence, particularly in the case of three string modes, is the non-negativity of the BMN two-point functions at any higher genus for any mode numbers. In this paper, we further perform the detailed calculations of the BMN two-point functions with three string modes at genus two, and explicitly verify that they are always non-negative through mostly extensive numerical tests.

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“…Matrix models interconnect, in a nonexhaustive fashion, integrable models, 2D gravity, gauge theory, string theory and Riemannian geometry. The symmetric groups and their representation were established master tools to tame correlators and observables of matrix models, and thereby to understand the half-BPS sector of N = 4 SYM [19,20,21,22]. This success emanates from importing Schur-Weyl duality as an instrument for grasping Gauge-String duality [23].…”

Section: Introductionmentioning

confidence: 99%

On the counting tensor model observables as U(N) and O(N) classical invariants

Geloun¹

2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle to study their combinatorial, topological and algebraic properties. We give here an overview of the symmetric group-theoretic formulation of the enumeration of unitary and orthogonal invariant observables which turns out to bear a rich structure. From their counting formulae, one finds a correspondence with topological field theory on 2-cellular complexes that brings other interpretations of the same countings. Furthermore, tensor model observables span an algebra that turns out to be semi-simple. Dealing with complex tensors, we discuss the representation theoretic base of the algebra making explicit its Wedderburn-Artin decomposition. The real case is more subtle as a base of its Wedderburn-Artin decomposition is yet unknown.

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BPS states, conserved charges and centres of symmetric group algebras

Cited by 14 publications

References 28 publications

Integrality, duality and finiteness in combinatoric topological strings

Integrality, duality and finiteness in combinatoric topological strings

Non-negativity of BMN two-point functions with three string modes

On the counting tensor model observables as U(N) and O(N) classical invariants

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