From 2d droplets to 2d Yang-Mills

Chattopadhyay, Arghya; Dutta, Suvankar; Mukherjee, Debangshu; Neetu,

doi:10.1016/j.nuclphysb.2021.115648

Cited by 3 publications

(5 citation statements)

References 29 publications

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“…Expanding p ± in Fourier modes we can classify all possible deformations as quantum states in the Hilbert space. The problem was discussed in [36]. It turns out that the partition function is equal to 2D Yang-Mills partition function on torus.…”

Section: A Relation Between the Moments Of P And W ±Nmentioning

confidence: 99%

“…A generalisation of collective field theory including the interaction between the original collective fields and an infinite set of supplementary fields was proposed in [28]. One interesting feature of the collective field theory is that it admits a free fermi phase space description in terms of two dimensional droplets due to bosonisation [29][30][31][32][33][34][35][36]. A similar phase space description also exists for interacting collective field theory.…”

Section: Introductionmentioning

confidence: 99%

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Higher Spin Gravity in $AdS_3$ and Folds on Fermi Surface

Dutta¹,

Mukherjee²,

Parihar³

2023

Preprint

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In this paper, we introduce new sets of boundary conditions for higher spin gravity in AdS 3 where the boundary dynamics of spin two and other higher spin fields are governed by the interacting collective field theory Hamiltonian of Avan and Jevicki. We show that the time evolution of spin two and higher spin fields can be captured by the classical dynamics of folded fermi surfaces in the similar spirit of Lin, Lunin and Maldacena. We also construct infinite sequences of conserved charges showing the integrable structure of higher spin gravity under the boundary conditions we considered. Further, we observe that there are two possible sequences of conserved charges depending on whether the underlying boundary fermions are non-relativistic or relativistic.

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Section: A Relation Between the Moments Of P And W ±Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Higher Spin Gravity in $AdS_3$ and Folds on Fermi Surface

Dutta¹,

Mukherjee²,

Parihar³

2023

Preprint

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“…Following [1,15] we give a Hilbert space description of the q-deformed growth process. Using the connection between unitary matrix model and free Fermi droplet description, we map the Young diagrams in automodel class to different shapes of two dimensional phase space droplets.…”

Section: The Hilbert Spacementioning

confidence: 99%

“…These two sectors are isomorphic. A generic state in H + is given by Such a mapping has been discussed in [15]. Expectation value of h+ in ground state is given by 1 2 + s and has zero dispersion.…”

Section: The Hilbert Spacementioning

confidence: 99%

“…We also find the automodel class in this case and write the automodel equation satisfied by the members in this class. Following [1,15], we construct the Hilbert space by quantising the phase space droplets and set up a correspondence between q-deformed automodel diagrams and coherent states in the Hilbert space. Finally, we elaborate the connection between moments of Young diagrams and the infinite number of commuting Hamiltonians obtained from the large N droplets.…”

Section: Introductionmentioning

confidence: 99%

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A Unitary Matrix Model for $q$-deformed Plancherel Growth

Dutta,

Mukherjee,

Parihar

2021

Preprint

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In this paper we construct a unitary matrix model that captures the asymptotic growth of Young diagrams under q-deformed Plancherel measure. The matrix model is a q analog of Gross-Witten-Wadia (GWW) matrix model. In the large N limit the model exhibits a third order phase transition between no-gap and gapped phases, which is a q-deformed version of the GWW phase transition. We show that the no-gap phase of this matrix model captures the asymptotic growth of Young diagrams equipped with q-deformed Plancherel measure. The no-gap solutions also satisfies a differential equation which is the q-analogue of the automodel equation. We further provide a droplet description for these growing Young diagrams. Quantising these droplets we identify the Young diagrams with coherent states in the Hilbert space. We also elaborate the connection between moments of Young diagrams and the infinite number of commuting Hamiltonians obtained from the large N droplets and explicitly compute the moments for asymptotic Young diagrams.

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