arXiv subjects

Abhishek Mehta

Publications and source records attributed to Abhishek Mehta.

10 recordsLinked to original sources

arXiv2026

Data Facts: A Metadata Schema for Structured Data Exchange in the NANDini Multi-Agent Ecosystem

NANDini (Networked Agents Natural Distillation of Interconnected Nodal Intelligence) envisions an automated ecosystem where intelligent agents independently create, process, and exchange data to drive decisions at scale. Realizing this vision requires infrastructure beyond agent discovery and communication: agents must be able to advertise, evaluate, and verify the datasets they hold. Current protocols, including NANDA for federated registry and A2A and MCP for inter-agent messaging, address identity and communication but provide no mechanism for structured data exchange. Existing enterprise data-sharing frameworks, such as IDS-RAM, Gaia-X, and Ocean Protocol, assume human-in-the-loop governance that is incompatible with autonomous, real-time agent interactions. We introduce Data Facts, a core NANDini concept: a lightweight JSON metadata schema that bridges agent discovery and data access through a single pointer, `data_facts_url`, added to an existing Agent Facts registry record. The linked document encodes dataset identity, access tier, whether public, semi-private, or private, endpoint, a time-to-live for freshness validation, and a SHA-256 integrity checksum. For private and semi-private data, we implement a three-layer security pipeline: JWT authentication, capability-scoped gateway authorization, and an A2A credential delegation protocol. Across 840 decision-making evaluations, data-informed agents achieve 100% accuracy versus 35.2% without data access (p < 0.001); TTL enforcement reduces stale-data errors from 37.6% to 8.8%; checksum verification achieves 100% corruption detection at all injection rates; and the security pipeline blocks all 46 forgery attempts with zero data leakage.

cs.CR↗

arXiv2022

A CFT interpretation of cosmological correlation functions in $α-$vacua in de-Sitter space

de-Sitter(dS) space allows for a generalized class of vacua, known as $α-$vacua, described by some parameters. The Bunch-Davies (BD) vacua is a point in this parameter space. The cosmological correlation function is mostly discussed in BD vacuum in four dimensions and can be interpreted as $CFT_3$ correlation function of certain operators. However, the correlation function in $α-$vacua takes a much more complicated form. In this paper, we give a simple prescription to compute correlation function in $α-$vacua in terms of correlation function of BD vacuum. We also show that the correlation function in the $α-$vacua can be related to three-dimensional CFT correlation functions if we relax the requirement of consistency with OPE limit. Relaxation of consistency with OPE limit can be naturally achieved in momentum space.

hep-th↗

arXiv2022

4D Flat-space scattering amplitude /$CFT_3$ correlator correspondence revisited

In this paper, we make connection between CFT$_3$ three point correlation function of conserved currents and 4D three point amplitude of general spin massless gauge field explicit. We do so by taking flat space limit of momentum space CFT correlation function and show how they reproduce flat space amplitudes. We then point out a mismatch between number of independent structures in 3D CFT correlator of conserved currents and 4D flat space covariant vertex of massless higher spin fields. This is in contrast with general expectation that counting of 3d CFT correlator and 4d flat space amplitude should match. This mismatch is even more pronounced in spinor helicity variables. We also point out an interesting relation between parity even and parity odd flat space amplitude in momentum space. This observation helps us to construct a new momentum space CFT strtucture which accounts for the mismatch. However we should mention that this extra CFT structure can't be constructed out of conserved currents and hence counting mismatch between CFT correlation of conserved currents and flat space amplitude of massless gauge field persists. Story in spinor helicity variable is more complicated and is discussed in detail. We further comment on the connection of CFT correlation function in spinor helicity variables to AdS amplitudes in spinor helicity variables and light cone variables.

hep-th↗

arXiv2021

Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound

Consistency with position space OPE limit requires momentum space CFT correlators to have only total energy singularity. We show that this requirement gives a simple proof of the known result that the parity-odd structure cannot exist for three-point correlators of exactly conserved currents with spins $s_i,s_j,s_k$, when triangle inequality $s_i\le s_j+s_k$ is violated. We also show that even for parity even correlation functions the properties are different inside and outside the triangle inequality. It was previously shown that if we allow for weakly broken higher spin symmetry, parity-odd correlators can exist even when triangle inequality is violated. In this paper we establish a relation between non-conservation Ward-Takahashi (WT) identities for weakly broken currents using known WT identities for exactly conserved currents. This allows us to calculate the parity violating results outside the triangle inequality using parity-even free bosonic and free fermionic results. In general, there is one parity-odd structure and two parity-even structures for three-point functions. It can be shown that the coefficient of one of the parity-even and odd parts can be combined into a complex parameter $c$ when correlators are expressed in spinor-helicity variables. When this complex parameter takes real value $c=\pm 1$ it corresponds to either the free boson or free fermion theory. When $c$ is a pure phase, it corresponds to Chern-Simons matter theories. Furthermore, re-expressing known results for conformal collider bounds we see that $\lvert c\rvert\le 1$ for generic 3d CFTs and $\lvert c\rvert\le f(Δ_{gap})$ for holographic CFTs.

hep-th↗

arXiv2021

Higher spin 3-point functions in 3d CFT using spinor-helicity variables

In this paper we use the spinor-helicity formalism to calculate 3-point functions involving scalar operators and spin-$s$ conserved currents in general 3d CFTs. In spinor-helicity variables we notice that the parity-even and the parity-odd parts of a correlator are related. Upon converting spinor-helicity answers to momentum space, we show that correlators involving spin-$s$ currents can be expressed in terms of some simple conformally invariant conserved structures. This in particular allows us to understand and separate out contact terms systematically, especially for the parity-odd case. We also reproduce some of the correlators using weight-shifting operators.

hep-th↗

arXiv2021

An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models

We present a conjecture for the leading $1/N$ anomalous dimension of the scalar primary operator in $U(N)_k$ Chern-Simons theories coupled to a single fundamental field, to all orders in the t'Hooft coupling $λ=\frac{N}{k}$. Following this we compute the anomalous dimension of the scalar in a Regular Bosonic theory perturbatively at two-loop order and demonstrate that matches exactly with the result predicted by our conjecture. We also show that our proposed expression for the anomalous dimension is consistent with all other existing two-loop perturbative results, which constrain its form at both weak and strong coupling thanks to the bosonization duality. Furthermore, our conjecture passes a novel non-trivial all loop test which provides a strong evidence for its consistency.

hep-th↗

arXiv2021

Double copy structure of parity-violating CFT correlators

We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts - called homogeneous and non-homogeneous - we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in $dS_4$. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-$s$ current correlator can be thought of as $s$ copies of the spin one current correlator.

hep-th↗

arXiv2021

Momentum space parity-odd CFT 3-point functions

We study the parity-odd sector of 3-point functions comprising of scalar operators and conserved currents in conformal field theories in momentum space. We use momentum space conformal Ward identities as well as spin-raising and weight-shifting operators to fix the form of these correlators. We discuss in detail the regularisation of divergences and their renormalisation using specific counter-terms.

hep-th↗

arXiv2020

Wheeler-DeWitt equation in Null-foliated spacetimes

In this paper, the Wheeler-DeWitt (WDW) equation is derived in null-foliated 4D spacetimes. WDW equation written in null-foliated spacetime presents an enormous simplification compared to the spacelike-foliated spacetime as the null-foliations are 2D. These can be solved exactly and uniquely to give the vertex operators of non-critical strings as a solution. A correspondence is established between null surfaces in 4D to string worldsheet geometry. Attempts are made to derive the physical consequences of this correspondence.

gr-qc↗

arXiv2019

Correlation functions in ${\cal N}=2$ Supersymmetric vector matter Chern-Simons theory

We compute the two, three point function of the opearators in the spin zero multiplet of ${\cal N}=2$ Supersymmetric vector matter Chern-Simons theory at large $N$ and at all orders of 't Hooft coupling by solving the Schwinger-Dyson equation. Schwinger-Dyson method to compute four point function becomes extremely complicated and hence we use bootstrap method to solve for four point function of scaler operator $J_0^{f}=\barψψ$ and $J_0^{b}=\barϕϕ$. Interestingly, due to the fact that $\langle J_0^{f}J_0^{f}J_0^{b} \rangle$ is a contact term, the four point function of $ J_0^{f}$ operator looks like that of free theory up to overall coupling constant dependent factors and up to some bulk AdS contact terms. On the other hand the $J_0^{b}$ four-point function receives an additional contribution compared to the free theory expression due to the $J_0^{f}$ exchange. Interestingly, double discontinuity of this single trace operator $J_0^{f}$ vanishes and hence it only contributes to AdS-contact term.

hep-th↗