arXiv subjects

Adarsh Sudhakar

Publications and source records attributed to Adarsh Sudhakar.

6 recordsLinked to original sources

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2024

Gravitational Poisson brackets at null infinity compatible with smooth superrotations

Superrotations are local extensions of the Lorentz group at null infinity that have been argued to be symmetries of gravitational scattering. In their smooth version, they can be identified with the group of diffeomorphisms on the celestial sphere. Their canonical realization requires treating the celestial metric as a variable in the gravitational phase space, along with the news and shear tensors. In this paper, we derive the resulting Poisson brackets (PB). The standard PB algebra of the news and shear tensors is augmented by distributional terms at the boundaries of null infinity, including novel PB relations between the celestial metric and the radiative variables.

gr-qc↗

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.

hep-th↗

arXiv2023

The Radiative Phase Space for the Dynamical Celestial Metric

Generalized BMS (gBMS) is the Lie group of the asymptotic symmetries at null infinity, and is proposed to be a symmetry of the quantum S-matrix. Despite much progress in understanding the symplectic structure at null infinity consistent with the gBMS symmetries, the construction of a radiative phase space where all the physical soft modes and their conjugate partners are identified remains elusive. We construct just such a radiative phase space for linearized gravity by a systematic constraint analysis. In addition, we highlight the difficulties that arise in extending this analysis to the non-linear case. In order to analyze the difficulties we face in extending these ideas to the non-linear setting, we consider a toy model in which we gauge the action of the Weyl scaling in the Weyl BMS group. We find that supertranslations are no longer well-defined symmetries on the reduced phase space of the gauged Weyl, as Weyl scalings do not commute with supertranslations. In this restricted case we obtain the symplectic form and derive the reduced phase space.

hep-th↗