arXiv subjects

Tanmoy Sengupta

Publications and source records attributed to Tanmoy Sengupta.

6 recordsLinked to original sources

arXiv2026

Modular properties of correlators in generalised Gibbs ensembles

We study the modular properties of torus correlators in a generalised Gibbs ensemble (GGE) of a two-dimensional conformal field theory. For the free fermion with KdV charges, we compute the exact two-point function and derive its modular $S$-transformation as a formal power series in the chemical potential. The transformed correlator admits a factorised description: an effective charge deforms the ensemble, while a local dressing operator acts on the external fields. Both are determined by nested operator product expansions involving the deforming current. Motivated by this result, we conjecture an analogous transformation law for $n$-point functions in rational chiral conformal field theories. Using Zhu's recursion, we establish the conjecture at the lowest explicit power of the modular parameter to all orders in the chemical potential, thereby determining the dressing operator. We also verify the full conjectured transformation through cubic order in the chemical potential, retaining all explicit powers of the modular parameter. These results extend the nested-OPE description of modular transformations of GGE partition functions to local correlation functions.

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arXiv2026

Universal Modular Properties of Generalized Gibbs Ensembles and Chiral Deformations

We study modular properties of conformal field theories perturbed by holomorphic fields. We prove an asymptotic formula for the modular S-transform of a generalized partition function that includes zero modes of higher spin holomorphic currents. The derivation makes use of general properties of torus correlation functions, in particular the Zhu recursion relation. The asymptotic expansion of the modular transformed partition function takes a universal form that is determined iteratively by the second order pole coefficients in the operator product expansion of the holomorphic currents. We have also found an explicit expression for the multiplicities of terms generated by the iteration. This proves and generalizes a conjecture regarding the modular transformation properties of generalized Gibbs ensembles.

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arXiv2025

Modular Properties of $\mathcal{W}_3$ Generalised Gibbs Ensembles

In this paper we make a proposal for the solution to a long-standing problem - the asymptotic expansions of the modular $S$-transform of a generalised Gibbs ensemble (GGE) in a theory with $\mathcal{W}_3$ symmetry where the GGE includes the first non-trivial charge. Equivalently, we give a proposal for the modular $S$-transform of traces of arbitrary powers of the zero mode $W_0$. We provide evidence in the form of exact results using Zhu's recursion, results obtained using conjectured results for Verma modules, and exact results for the particular value $c=-2$. We expect these have generalisations to other symmetry algebras/hierarchies such as the Virasoro algebra/KdV charges, and to GGEs with arbitrary finite sets of charges.

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arXiv2024

Integrable Structure of Higher Spin CFT and the ODE/IM Correspondence

We study two dimensional systems with extended conformal symmetry generated by the ${\mathcal W}_3$ algebra. These are expected to have an infinite number of commuting conserved charges, which we refer to as the quantum Boussinesq charges. We compute the eigenvalues of the quantum Boussinesq charges in both the vacuum and first excited states of the higher spin module through the ODE/IM correspondence. By studying the higher spin conformal field theory on the torus, we also calculate thermal correlators involving the energy-momentum tensor and the spin-3 current by making use of the Zhu recursion relations. By combining these results, we show that it is possible to derive the current densities, whose integrals are the quantum Boussinesq charges. We also evaluate the thermal expectation values of the conserved charges, and show that these are quasi-modular differential operators acting on the character of the higher spin module.

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arXiv2024

Thermal Correlators and Currents of the $\mathcal{W}_3$ Algebra

Two dimensional conformal field theories with the extended $\mathcal{W}_3$ symmetry algebra have an infinite number of mutually commuting conserved charges, which are referred to as the quantum Boussinesq charges. In this work we construct local operators whose zero modes are precisely these conserved charges. For this purpose we study the higher spin conformal field theory on the torus and compute thermal correlators involving the stress tensor and the spin-3 current in a higher spin module of the W3 algebra. In addition we independently obtain the excited state eigenvalues of the quantum Boussinesq charges within the higher spin module via the ODE/IM correspondence. A judicious combination of these data allows us to derive the local operators, whose integrals are the conserved charges of the integrable hierarchy.

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arXiv2022

Modular linear differential equations for four-point sphere conformal blocks

We construct modular linear differential equations (MLDEs) w.r.t. subgroups of the modular group whose solutions are Virasoro conformal blocks appearing in the expansion of a crossing symmetric 4-point correlator on the sphere. This uses a connection between crossing transformations and modular transformations. We focus specifically on second order MLDEs with the cases of all identical and pairwise identical operators in the correlator. The central charge, the dimensions of the above operators and those of the intermediate ones are expressed in terms of parameters that occur in such MLDEs. In doing so, the $q$-expansions of the solutions to the MLDEs are compared with those of Virasoro blocks; hence, Zamolodchikov's elliptic recursion formula provides an important input. Using the actions of respective subgroups, bootstrap equations involving the associated 3-point coefficients have been set up and solved as well in terms of the MLDE parameters. We present explicit examples of MLDEs corresponding to BPZ and novel non-BPZ equations, as well as unitary and non-unitary CFTs.

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