arXiv subjects

Ravisankar Rajagopal

Publications and source records attributed to Ravisankar Rajagopal.

5 recordsLinked to original sources

arXiv2026

Mutual Information of Measurement in Conformal Field Theories

The mutual information of measurement of a local operator between two spatial regions characterizes the reduction in the uncertainty of measurement outcomes in one region given the outcome in the other. We study the Rényi-Shannon mutual information of measurement in conformal field theories (CFTs). Explicit calculations for scalar primaries and descendants in large $N$ CFTs are performed in the two extreme limits of the intervals being adjacent or largely separated. The results depend on only the cross ratio and the scaling dimension $Δ$ of the operator being measured, with striking similarities to the mutual information of entanglement. We find a surprising quadratic dependence as $(Δ-1/2)^2$ for adjacent intervals. This dependence superficially seems to violate the information processing inequality, which we discuss and resolve. We also offer a holographic interpretation of the mutual information of measurement.

hep-th↗

arXiv2026

An elementary approach to the Szegő theorems

The strong Szegő theorem and the Fisher-Hartwig formula describe the asymptotic behavior of determinants obtained by restricting translationally invariant operators to large finite regions. In particular, Szegő's theorem states that, beyond the leading extensive contribution to such a determinant, there is a universal finite correction, $\sum_{r>0} rV_rV_{-r}$ where $V_r$ are the Fourier coefficients of the logarithm of the symbol. Although this formula appears throughout analysis and mathematical physics, the origin of its quadratic form and of the weight $r$ is often obscured in its standard analytic derivations. We develop an elementary picture in which the strong Szegő term arises from boundary leakage: paths contributing to the matrix exponential leave the finite interval and subsequently return. Counting the shortest such excursions immediately produces the factor $r$. We then show that an isolated boundary contributes exactly one half of the strong Szegő correction, while the two boundaries of a long interval decouple. For finite-range matrices this gives a rigorous and intuitive elementary derivation of the asymptotics, with extensions to sufficiently rapidly decaying interactions. A complementary free-fermion argument provides a physical interpretation of the same cancellation mechanism. Numerical examples illustrate the asymtotics in the well controlled regime, the Fisher Hartwig logarithmic correction. The boundary formulation does not itself require translation invariance and therefore suggests natural extensions to disordered systems, higher dimensions, and symbols with internal matrix structure. To illustrate this we numerically go beyond the formal applicability region of the Szegő formula, considering slow decay and disordered cases, and showing in some cases a robustness of the approach even for slowly decaying but disordered potentials.

math-ph↗

arXiv2026

Higher-Derivative Corrections to Reissner--Nordström Black Holes from Worldline QFT

In this paper we derived the corrections to the Reissner-Nordström black hole when higher-derivative $RF^2$ terms (contractions of the Riemann tensor with the Maxwell field strength squared) are added to the Einstein-Maxwell action. Such terms arise naturally in the context of effective field theories. We used wordline QFT methods to obtain the leading order post-Minkowskian corrections. We verified these results by solving the modified Einstein-Maxwell field equations in closed form, to all orders in Newton's constant $G$. We discussed the first law and computed the entropy of the perturbed black holes. When fixing the mass to that of the extremal Reissner-Nordström black hole, the entropy shift is positive if the weak gravity conjecture holds. In fact, this condition is nothing but the requirement that the spacetime with the extremal Reissner-Nordström mass possesses an outer horizon in higher-derivative gravity. This condition also rules out Drummond-Hathrell theory.

hep-th↗

arXiv2025

Worldline Proof of Eikonal Exponentiation

In this paper, working in the eikonal approximation, we present a proof for the exponentiation of the 2-body eikonal phase to {\it all orders in the eikonal expansion}, for scalar particles interacting electromagnetically or gravitationally. The proof is based on the worldline formalism, which is an alternative, first quantized method to the standard QFT calculation of the scattering amplitude. We show that in the worldline formalism the 2-body scattering amplitude written in impact parameter space naturally factorizes at each loop order. This factorization is responsible for the exponentiation of the eikonal phase, a result which was anticipated in the work of Mogull, Plefka, and Steinhoff [2010.02865 [hep-th]].

hep-th↗

arXiv2025

Worldline Formalism, Eikonal Expansion and the Classical Limit of Scattering Amplitudes

We revisit the fundamentals of two different methods for calculating classical observables: the eikonal method, which is a scattering amplitude-based method, and the worldline quantum field theory (WQFT) method. The latter has been considered an extension of the worldline effective field theory. We show that the eikonal and WQFT methods are equivalent and that calculations can be translated freely between them. Concretely, we focus on 2-into-2 scattering processes mediated by massless force carriers. On the one hand, taking the classical limit of the QFT scattering amplitude leads to the eikonal method. On the other hand, since in the classical limit the scattering particles are almost on-shell throughout the scattering process, the worldline, a first quantized formalism, is the most efficient framework to study the scattering amplitude. This is an alternate but equivalent formalism to the quantum field theoretic (QFT) framework. By taking the classical limit of the scattering amplitude computed in the worldline, we can derive the WQFT rules of Mogull, Plefka and Steinhoff. In WQFT, the Feynman diagrams are reorganized into a new set of diagrams that facilitate the $\hbar$ expansion. Unlike the QFT eikonal method, which works recursively in identifying the eikonal phase, the worldline-based computation allows to target and systematically extract the classical contributions directly through a specific set of WQFT diagrams. In worldline formalism the perturbative expansion of the scattering amplitude is naturally organized in diagrams which factorize (reducible) and diagrams which are new to that order (irreducible), in a one-to-one map with the structure of the amplitude in the eikonal method. This opened up the possibility to investigate and prove the conjectured exponentiation of the eikonal phase in arXiv: 2409.12895.

hep-th↗