arXiv subjects

Suvankar Dutta

Publications and source records attributed to Suvankar Dutta.

At least 19 recordsLinked to original sources

arXiv2026

Large-$N$ Torus Knots in Lens Spaces and Their Quiver Structure

We study torus knot invariants in the lens space $S^{3}/\mathbb{Z}_{p}$ within Chern--Simons theory. Using the surgery and modular description of lens spaces, we derive a general expression for the invariant of an $(α,β)$ torus knot in this background. In the large-$N$ limit these invariants simplify and acquire a universal form: the invariant of an $(α,β)$ torus knot in $S^{3}/\mathbb{Z}_{p}$ can be expressed in terms of the invariant of the $(α,α+pβ)$ torus knot in $S^{3}$. After an appropriate redefinition of knot variables, the generating functions of these invariants exhibit a structure analogous to quiver partition functions. Since the associated quiver is independent of the rank $N$ and level $k$ of Chern--Simons theory, the large-$N$ result provides a direct way to identify the underlying quiver, allowing us to determine the quiver structure associated with torus knots in $S^{3}/\mathbb{Z}_{p}$.

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arXiv2026

Black Flower Microstates

We investigate stationary, non-axisymmetric black hole solutions in AdS$_3$ gravity, known as black flower geometries, in the Chern-Simons formulation. Boundary conditions are specified by a collective field theory-inspired Hamiltonian with field-dependent chemical potentials and angularly inhomogeneous boundary data. We construct a tractable class of solutions and analyze their geometric and thermodynamic properties, obtaining an entropy with nontrivial dependence on the angular deformation. Upon quantization of the boundary theory via bosonization, the boundary degrees of freedom are mapped to relativistic free fermions. We explicitly construct and count the microstates associated with a given black flower geometry and find exact agreement with the Bekenstein-Hawking entropy.

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arXiv2025

Supersymmetric extensions of Kac-Moody boundary conditions in AdS$_3$ gravity

We extend the Kac-Moody (KM) boundary conditions of AdS$_3$ gravity by incorporating fermionic fields. For $\mathcal{N}=(1,1)$ AdS$_3$ supergravity, we show that there are two possible ways to implement the fermionic extension. In the first, the extended KM boundary conditions are related to the standard super-Virasoro (VS) boundary conditions through a large gauge transformation realized by the super-Miura map between fields and chemical potentials, establishing a supersymmetric generalization of the KM-VS correspondence. In the second, a more general boundary configuration leads to strong constraints on the fermionic chemical potentials, yet offers a much richer asymptotic structure. It provides us a novel realization of the extended Kac-Moody algebra, and a geometric interpretation in terms of folds in the relativistic free-fermion droplet. Finally, we quantize the latter theory by promoting the classical Poisson brackets to (anti-)commutators, construct the corresponding Hilbert space, and show that the resulting spectrum contains only bosonic soft excitations, with no additional fermionic soft modes.

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arXiv2025

Bosonization, BTZ Black Hole Microstates, and Logarithmic Correction to Entropy

We study three-dimensional gravity with negative cosmological constant under non-standard boundary conditions where chemical potentials are determined dynamically. Using a boundary Hamiltonian inspired by collective field theory (ColFT), the boundary dynamics reduce to those of a one-dimensional fluid on a circle, with configurations corresponding to bulk geometries such as BTZ black holes. Quantizing the system via bosonization of relativistic fermions, we obtain a microscopic description of black hole states in terms of Young diagrams, whose degeneracies match the Bekenstein-Hawking entropy. We compute the Euclidean canonical partition function and free energy for both the ColFT Hamiltonian and a relativistic free-fermion Hamiltonian. In the ColFT case, the partition function resembles that of chiral U(N) Yang-Mills theory on a torus, with N~1/(βG). This offers a novel way to compute quantum corrections to the partition function. The leading entropy term receives contributions from all genera, while the subleading logarithmic correction is one-loop exact, arising solely from the genus-one sector with coefficient -1/2 . This coefficient remains unchanged in the relativistic fermion case, suggesting the universality of the one-loop correction across different boundary Hamiltonians.

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arXiv2025

Bosonisation and BTZ Black Hole Microstates

When the boundary dynamics of $AdS_3$ gravity is governed by the collective field theory Hamiltonian proposed by Jevicki and Sakita, its asymptotic symmetry algebra becomes the centerless $U(1)$ Kac-Moody algebra. We quantize this system using the quantum bosonization of relativistic free fermions and relate these to the dynamical fields of $AdS_3$ gravity. This leads to a correspondence where different bulk configurations correspond to distinct states (particle-hole pair excitations) in the fermionic Hilbert space. This mapping allows us to construct BTZ black hole microstates, represented by Young diagrams of irreducible $U(\infty)$ representations. Notably, the logarithm of the microstate degeneracy exactly reproduces the classical entropy of the BTZ black hole.

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arXiv2023

$U(N)$ Torus Link Invariants in the Large $N$ limit from Matrix Model Approach

In this paper we study $U(N)$ colored HOMFLY-PT polynomials of torus links in the double scaling limit (polynomial variable $q\rightarrow 1$, $N\rightarrow \infty$ keeping $q^N$ fixed). We show that, in this limit, the colored HOMFLY-PT polynomial of any $(Lα,Lβ)$ torus link can be expressed in terms of the colored HOMFLY-PT polynomial of $(L,L)$ torus link. Using the connection between matrix models and the Chern-Simons field theoretic invariants, we show that the colored torus link invariants are uniquely expressed in terms of connected correlation functions of operators in $U(N)$ matrix model. We determine the leading and subleading contribution to some of the correlators at large $N$ from the matrix model approach and find that they match exactly with those obtained from the corresponding colored HOMFLY-PT polynomials.

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arXiv2023

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

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 (for spin 3) 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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arXiv2022

TsT vs. LCR and Gravity Dual of Non-relativistic Fluid

We discuss two different approaches to synthesise holographic non-relativistic fluid from its relativistic counterpart. In the first approach we obtain the non-relativistic fluid by light-cone reduction of a relativistic conformal fluid. In the second approach we consider the bulk dual of the relativistic fluid, uplift the solution to 10 dimensions and perform TsT transformations on the bulk solution to change the asymptotic structure. Reducing the TsT transformed geometry over $S^5$ we find an effective 5 dimensional locally boosted solution. We then use the bulk-boundary dictionary to compute the non-relativistic constitutive relations. We show that the non-relativistic fluids obtained by these two methods are equivalent up to second order in derivative expansion. Our results also provide explicit expressions for different constitutive relations and transports of holographic $U(1)$ charged non-relativistic fluids (both parity odd and even) up to second order in derivative expansion.

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arXiv2022

String Theory Corrections to Holographic Black Hole Chemistry

The connection between the bulk and the boundary first law of thermodynamics in adS space has been discussed in generic higher derivative gravity. String theory corrections to the supergravity render higher derivative terms in the bulk action, proportional to different powers of string theory parameter $α'$. A variation in the cosmological constant induces a variation in the 't Hooft coupling in the boundary theory. We show that in order to match the bulk first law and Smarr relation with the boundary side one needs to include the variation of $α'$ in the bulk thermodynamics as a book keeping device. Accordingly, the boundary first law and Euler relation are modified with the inclusion of two central charges ($a$, $c$) and/or other chemical potentials as thermodynamic variables. We consider four and six derivative terms as well as the $\text{Weyl}^4$ terms (in type IIB) in bulk in support of our generic result.

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arXiv2022

Large $N$ Invariants of Torus Links in Lens Spaces

We compute the invariants for a class of knots and links in arbitrary representations in $S^3/\mathbb{Z}_p$ in the large $k$ (level), large $N$ (rank) limit, keeping $N/(k+N)=λ$ fixed, in $U(N)$ and $Sp(N)$ Chern-Simons theories. Using the relation between the saddle point description and collective field theory, we first find that the invariants for the Hopf link and unknot are given by the on shell collective field theory action. We next show that the results of these two invariants can be used to compute the invariants of other torus knots and links. We also discuss the large $N$ phase structure of the Hopf link invariant and observe that the same may admit a Douglas-Kazakov type phase transition depending on the choice of representations and $λ$.

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arXiv2021

Interaction Between AdS Black Hole Molecules

We take a bottom-up approach to find the interaction potential between the $AdS$ black hole molecules under mean-field approximation. We start with the equation of state of dyonic $AdS$ black holes in fixed charge ensemble and use the method of classical cluster expansion to find the mean-field potential. We show that the Lennard-Jones (LJ) potential is a feasible choice to describe the equation of state. The LJ potential describes a two-body interaction. There exists a critical distance $r_0$ such that two interacting particles repel (attract) each other for $r < r_0$ ($r > r_0$). We compute the value of $r_0$ for dyonic $AdS$ black holes and compare the result obtained from the Ruppeiner scalar curvature. Our analysis shows how the electric (and magnetic) charge effects the interaction between black hole molecules.

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arXiv2021

New phase in Chern-Simons theory on lens space

We consider $U(N)_k$ Chern-Simons theory on $S^3$ in Seifert framing and write down the partition function as a unitary matrix model. In the large $k$ and large $N$ limit the eigenvalue density satisfies an upper bound $\frac{1}{2πλ}$ where $λ=N/(k+N)$. We study the partition function under saddle point approximation and find that the saddle point equation admits a gapped solution for the eigenvalue density. The on-shell partition function on this solution matches with the partition function in the canonical framing up to a phase. However the eigenvalue density saturates the upper cap at a critical value of $λ$ and ceases to exist beyond that. We find a new phase (called cap-gap phase) in this theory for $λ$ beyond the critical value and see that the on-shell free energy for the cap-gap phase is less than that of the gapped phase. We also check the level-rank duality in the theory and observe that the level-rank dual of the gapped phase is a \emph{capped} phase whereas the cap-gap phase is level-rank dual to itself.

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arXiv2021

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

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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arXiv2021

Quantum Mechanics of Plancherel Growth

Growth of Young diagrams, equipped with Plancherel measure, follows the automodel equation of Kerov. Using the technology of unitary matrix model we show that such growth process is exactly same as the growth of gap-less phase in Gross-Witten and Wadia (GWW) model. The limit shape of asymptotic Young diagrams corresponds to GWW transition point. Our analysis also offers an alternate proof of limit shape theorem of Vershik-Kerov and Logan-Shepp. 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. Quantising these droplets we further set up a correspondence between automodel diagrams and coherent states in the Hilbert space. Thus growth of Young diagrams are mapped to evolution of coherent states in the Hilbert space. Gaussian fluctuations of large $N$ Young diagrams are also mapped to quantum (large $N$) fluctuations of the coherent states.

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arXiv2020

From 2d Droplets to 2d Yang-Mills

We establish a connection between time evolution of free Fermi droplets and partition function of \emph{generalised} \emph{q}-deformed Yang-Mills theories on Riemann surfaces. Classical phases of $(0+1)$ dimensional unitary matrix models can be characterised by free Fermi droplets in two dimensions. We quantise these droplets and find that the modes satisfy an abelian Kac-Moody algebra. The Hilbert spaces $\mathcal{H}_+$ and $\mathcal{H}_-$ associated with the upper and lower free Fermi surfaces of a droplet admit a Young diagram basis in which the phase space Hamiltonian is diagonal with eigenvalue, in the large $N$ limit, equal to the quadratic Casimir of $u(N)$. We establish an exact mapping between states in $\mathcal{H}_\pm$ and geometries of droplets. In particular, coherent states in $\mathcal{H}_\pm$ correspond to classical deformation of upper and lower Fermi surfaces. We prove that correlation between two coherent states in $\mathcal{H}_\pm$ is equal to the chiral and anti-chiral partition function of $2d$ Yang-Mills theory on a cylinder. Using the fact that the full Hilbert space $\mathcal{H}_+ \otimes \mathcal{H}_-$ admits a \emph{composite} basis, we show that correlation between two classical droplet geometries is equal to the full $U(N)$ Yang-Mills partition function on cylinder. We further establish a connection between higher point correlators in $\mathcal{H}_\pm$ and higher point correlators in $2d$ Yang-Mills on Riemann surface. There are special states in $\mathcal{H}_\pm$ whose transition amplitudes are equal to the partition function of $2d$ \emph{q}-deformed Yang-Mills and in general character expansion of Villain action. We emphasise that the \emph{q}-deformation in the Yang-Mills side is related to special deformation of droplet geometries without deforming the gauge group associated with the matrix model.

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arXiv2020

Holographic Constraints on Generalised Rivlin-Ericksen Fluid

The Rivlin-Ericksen model is one of the oldest models in fluid dynamics to describe non-Newtonian properties. The model comes with two independent transports at second order. In this paper, we study the relativistic origin of the Rivlin-Ericksen fluid. Starting from a relativistic Weyl invariant uncharged fluid in $3+1$ dimensions, we reduce it over light-cone directions and obtain a generic non-relativistic uncharged fluid in one lower dimension with all possible second order terms in the constitutive relations. We observe that the Rivlin-Ericksen fluid is a subclass of our generalised non-relativistic system. We also compute the holographic values of all the non-relativistic second order transports and find that three of them satisfy a universal constraint relation.

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arXiv2020

Bhargava's Cube and Black Hole Charges

Black holes in a class of string compactifications, known as STU models, carry four electric and four magnetic charges. Furthermore a duality group, given by the product of three congruence subgroups of $SL(2,\mathbb{Z})$, acts on these integer valued charges. By placing these eight charges at the eight corners of a Bhargava cube, we provide a classification of the duality orbits in these theories.

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arXiv2020

Matrix Model for Riemann Zeta via its Local Factors

We propose the construction of an ensemble of unitary random matrices (UMM) for the Riemann zeta function. Our approach to this problem is `$p$-iecemeal', in the sense that we consider each factor in the Euler product representation of the zeta function to first construct a UMM for each prime $p$. We are able to use its phase space description to write the partition function as the trace of an operator that acts on a subspace of square-integrable functions on the $p$-adic field. This suggests a Berry-Keating type Hamiltonian. We combine the data from all primes to propose a Hamiltonian and a matrix model for the Riemann zeta function.

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