arXiv subjects

Raju Mandal

Publications and source records attributed to Raju Mandal.

6 recordsLinked to original sources

arXiv2026

Note on higher spins and holographic symmetry algebra

In this paper we discuss a higher spin extension of the holographic symmetry algebra for graviton and gluon. Our primary observation is that in the presence of higher spin particles the soft symmetry algebra has a subalgebra isomorphic to $w_{\infty}$ which is generated by the \textit{conformally soft higher spin particles}. This $w_{\infty}$ subalgebra does not commute with the $w_{1+\infty}$ subalegbra generated by the conformally soft gravitons. The same thing holds for the colored higher spin particles. One gets a subalgebra isomorphic to the $S$-algebra which is generated by the conformally soft colored higher spin particles. We further verify the soft algebra for colored higher spin particles using the (tree-level) $4$-point MHV amplitude of the higher spin Yang-Mills theory constructed in arXiv:2210.07130. At the end we also discuss the higher spin extension of the deformed holographic symmetry algebra for non-zero cosmological constant as constructed in arXiv:2312.00876.

hep-th↗

arXiv2026

All loop soft photon theorems and higher spin currents on the celestial sphere

Soft factorization theorems can be reinterpreted as Ward identities for (asymptotic) symmetries of scattering amplitudes in asymptotically flat space-time. In this paper we study the symmetries implied by the all loop soft photon theorems when all the charged particles are highly energetic and the relation $ω<< m << E$ holds where $E$ is the typical energy of a charged particle, $m$ is the typical mass and $ω$ is the soft photon energy. Loop level soft theorems are qualitatively different from the tree level soft theorems because loop level soft factors contain multi-particle sums. If we want to interpret them as Ward identities or define celestial OPE between between soft and hard operators then we need to introduce additional fields which live on the celestial sphere but do not appear as asymptotic states in any scattering experiment. For example, if we want to interpret the one-loop exact $\mathcal{O}(\lnω)$ soft theorem for a positive helicity soft photon (with energy $ω$) as a Ward identity then we need to introduce a pair of antiholomorphic currents on the celestial sphere which transform as a doublet under the $SL(2,\mathbb{R})_{R}$. We call them dipole currents because the corresponding charges measure the monopole and the dipole moment of an electrically charged particle on the celestial sphere. More generally, the soft photon theorem at $\mathcal{O}(ω^{2j-1}(\lnω)^{2j})$ for every $j\in \frac{1}{2}\mathbb{Z}_+$ gives rise to $(2j+1)$ antiholomorphic currents which transform in the spin-$j$ representation of the $SL(2,\mathbb{R})_{R}$. These currents exist in the quantum theory because they follow from loop level soft theorems. We argue that under certain circumstances the (classical) algebra of the higher spin currents is the wedge subalgebra of the $w_{1+\infty}$.

hep-th↗

arXiv2025

Holographic symmetry algebra for the MHV sector revisited

We revisit the holographic symmetry algebra in the MHV sector. We find an infinite dimensional Abelian symmetry algebra whose generators are the conformally soft negative helicity gravitons and gluons. So the complete symmetry algebra in the MHV graviton sector is a semideirect product of the $w_{1+\infty}$ algebra and the infinite dimensional Abelian algebra. Similarly in the MHV gluon sector the symmetry algebra is a semidirect product of the $S$ algebra and the infinite dimensional Abelian algebra. The extended symmetry algebra has some use. For example, it is known for sometime that an $n$ point MHV amplitude satisfies $(n-2)$ Knizhnik-Zamolodchikov (KZ) type equations. So two equations are missing. We show that the extended symmetry algebra has additional null states whose decoupling give rise to the two missing equations.

hep-th↗

arXiv2024

Singularity Structure of the Four Point Celestial Leaf Amplitudes

In this paper, we study the four-point celestial leaf amplitudes of massless scalar and MHV gluon scattering. These leaf amplitudes are non-distributional decompositions of the celestial amplitudes associated with a hyperbolic foliation of the Klein spacetime. Bulk scale invariance imposes constraints on the total conformal weights of the massless scalars or gluons. Using this constraint we show that the four-point leaf amplitudes have a \textit {simple pole singularity at $ z = \bar z $}, where, $ z,\bar z $ are two real independent conformal cross ratios. The distributional nature of the four-point celestial amplitudes is recovered by adding the leaf amplitudes in the timelike and spacelike wedges of the spacetime. We also verify that the MHV gluon leaf amplitudes satisfy a set of differential equations previously obtained for celestial MHV gluon amplitudes by considering the soft gluon theorems and the subleading terms in the OPE expansion between two positive helicity gluons.

hep-th↗

arXiv2023

All $S$ invariant gluon OPEs on the celestial sphere

$S$ algebra is an infinite dimensional Lie algebra which is known to be the symmetry algebra of some gauge theories. It is a "coloured version" of the $w_{1+\infty}$. In this paper we write down all possible $S$ invariant (celestial) OPEs between two positive helicity outgoing gluons and also find the Knizhnik-Zamolodchikov type null states for these theories. Our analysis hints at the existence of an infinite number of $S$ invariant gauge theories which include the (tree-level) MHV-sector and the self-dual Yang-Mills theory.

hep-th↗

arXiv2023

MHV Gluon Scattering in the Massive Scalar Background and Celestial OPE

In this paper we study the OPE between two positive helicity outgoing gluons in the celestial CFT for the Yang-Mills theory chirally coupled to a massive scalar background. This theory breaks the translation as well as scale invariance. We compute the subleading terms in the OPE expansion and show that they are same as the subleading terms of the OPE expansions in the MHV sector. As a result the amplitudes of this theory also satisfy the set of differential equations obtained previously for MHV amplitudes in pure YM theory. This is not surprising because the symmetries coming from the leading and subleading soft gluon theorems do not change in the presence of a massive scalar background.

hep-th↗